SPHINCS+~[CCS '19] is one of the selected post-quantum digital signature schemes of NIST's post-quantum standardization process. The scheme is a hash-based signature and is considered one of the most secure and robust proposals. The proposal includes a fast (but large) variant and a small (but costly) variant for each security level. The main problem that might hinder its adoption is its large signature size. Although SPHINCS+ supports a trade-off between signature size and the computational cost of signing, further reducing the signature size (below the small variants) results in a prohibitively high computational cost for the signer. This paper presents several novel methods for further compressing the signature size while requiring negligible added computational costs for the signer and further reducing verification time. Moreover, our approach enables a much more efficient trade-off curve between signature size and the computational costs of the signer. In many parameter settings, we achieve small signatures and faster running times simultaneously. For example, for $128$-bit security, the small signature variant of SPHINCS+ is $7856$ bytes long, while our variant is only $6304$ bytes long: a compression of approximately $20$% while still reducing the signer's running time. However, other trade-offs that focus, e.g., on verification speed, are possible. The main insight behind our scheme is that there are predefined specific subsets of messages for which the WOTS+ and FORS signatures (that SPHINCS+ uses) can be compressed, and generation can be made faster while maintaining the same security guarantees. Although most messages will not come from these subsets, we can search for suitable hashed values to sign. We sign a hash of the message concatenated with a counter that was chosen such that the hashed value is in the subset. The resulting signature is both smaller and faster to sign and verify. Our schemes are simple to describe and implement. We provide an implementation, a theoretical analysis of speed and security, as well as benchmark results.

Functional Encryption (FE) has been extensively studied in the recent years, mainly focusing on the feasibility of constructing FE for general functionalities, as well as some realizations for restricted functionalities of practical interest, such as inner-product. However, little consideration has been given to the issue of key leakage on FE. The property of FE that allows multiple users to obtain the same functional keys from the holder of the master secret key raises an important problem: if some users leak their keys or collude to create a pirated decoder, how can we identify at least one of those users, given some information about the compromised keys or the pirated decoder? Moreover, how do we disable the decryption capabilities of those users (i.e. traitors)? Two recent works have offered potential solutions to the above traitor scenario. However, the two solutions satisfy weaker notions of security and traceability, can only tolerate bounded collusions (i.e., there is an a priori bound on the number of keys the pirated decoder obtains), or can only handle a polynomially large universe of possible identities. In this paper, we study trace-and-revoke mechanism on FE and provide the first construction of trace-and-revoke FE that supports arbitrary identities, is both fully collusion resistant and fully anonymous. Our construction relies on a generic transformation from revocable predicate functional encryption with broadcast (RPFE with broadcast, which is an extension of revocable predicate encryption with broadcast proposed by Kim and J. Wu at ASIACRYPT'2020) to trace-and-revoke FE. Since this construction admits a generic construction of trace-and-revoke inner-product FE (IPFE), we instantiate the trace-and-revoke IPFE from the well-studied Learning with Errors (LWE). This is achieved by proposing a new LWE-based attribute-based IPFE (ABIPFE) scheme to instantiate RPFE with broadcast.

Every public-key encryption/decryption algorithm where the set of possible plain-texts is identical to the set of possible cipher-texts may be converted into a digital signature algorithm. That is quite different in the lattice (code)-based public-key cryptography. The decryption algorithm on a random input produces a valid plain-text, that is a signature, with a negligible probability. That explains why it is so difficult to construct a new secure and efficient lattice-based digital signature system. Though several solutions are known and taking part in the NIST Post Quantum Standardisation Process there is still a need to construct digital signature algorithms based on new principles. In this work, a new and efficient digital signature algorithm is suggested. Its design is simple and transparent. Its security is based on the hardness of an approximate closest vector problem in the maximum norm for some $q$-ary lattices. The signature is shorter than that provided by the NIST Selected Digital Signature Algorithms with a comparable security level, while the public key size is larger.

In this article, we prove a generic lower bound on the number of $\mathfrak{O}$-orientable supersingular curves over $\mathbb{F}_{p^2}$, i.e curves that admit an embedding of the quadratic order $\mathfrak{O}$ inside their endomorphism ring. Prior to this work, the only known effective lower-bound is restricted to small discriminants. Our main result targets the case of fundamental discriminants and we derive a generic bound using the expansion properties of the supersingular isogeny graphs. Our work is motivated by isogeny-based cryptography and the increasing number of protocols based on $\mathfrak{O}$-oriented curves. In particular, our lower bound provides a complexity estimate for the brute-force attack against the new $\mathfrak{O}$-uber isogeny problem introduced by De Feo, Delpech de Saint Guilhem, Fouotsa, Kutas, Leroux, Petit, Silva and Wesolowski in their recent article on the SETA encryption scheme.

Attribute-based encryption (ABE) extends public-key encryption to enable fine-grained control to encrypted data. However, this comes at the cost of needing a central trusted authority to issue decryption keys. A multi-authority ABE (MA-ABE) scheme decentralizes ABE and allows anyone to serve as an authority. Existing constructions of MA-ABE only achieve security in the random oracle model. In this work, we develop new techniques for constructing MA-ABE for the class of subset policies (which captures policies such as conjunctions and DNF formulas) whose security can be based in the plain model without random oracles. We achieve this by relying on the recently-proposed "evasive" learning with errors (LWE) assumption by Wee (EUROCRYPT 2022) and Tsabury (CRYPTO 2022). Along the way, we also provide a modular view of the MA-ABE scheme for DNF formulas by Datta et al. (EUROCRYPT 2021) in the random oracle model. We formalize this via a general version of a related-trapdoor LWE assumption by Brakerski and Vaikuntanathan (ITCS 2022), which can in turn be reduced to the plain LWE assumption. As a corollary, we also obtain an MA-ABE scheme for subset policies from plain LWE with a polynomial modulus-to-noise ratio in the random oracle model. This improves upon the Datta et al. construction which relied on LWE with a sub-exponential modulus-to-noise ratio. Moreover, we are optimistic that the generalized related-trapdoor LWE assumption will also be useful for analyzing the security of other lattice-based constructions.

Several broadcast encryption (BE) constructions have been proposed since Fiat and Naor introduced the concept, some achieving short parameters size while others achieve better security. Since 1994, a lot of alternatives to BE have moreover been additionally proposed, such as the broadcast and trace (BT) primitive which is a combination of broadcast encryption and traitor tracing. Among the other variants of BE, the notion of augmented BE (AugBE), introduced by Boneh and Waters in 2006, corresponds to a BE scheme with the particularity that the encryption algorithm takes an index as an additional parameter. If an AugBE scheme is both message and index hiding, it has been proved that it can generically be used to construct a secure BT scheme. Hence, any new result related to the former gives an improvement to the latter. In this paper, we first show that both BE and AugBE can be obtained by using an identity-based encryption scheme with wildcard (WIBE). We also introduce the new notion of anonymous AugBE, where the used users set is hidden, and prove that it implies index hiding. We then provide two different WIBE constructions. The first one has constant size ciphertext and used to construct a new constant size ciphertext BE scheme with adaptive CPA security, in the standard model (under the $\SXDH{}$ assumption). The second WIBE provides pattern-hiding, a new definition we introduced, and serves as a basis for the first anonymous AugBE scheme (and subsequently a BT scheme since our scheme is also index hiding by nature) in the literature, with adaptive security in the standard model (under the $\XDLin{}$ assumption).

Anonymity of public key encryption (PKE) requires that, in a multi-user scenario, the PKE ciphertexts do not leak information about which public keys are used to generate them. Corruptions are common threats in the multi-user scenario but anonymity of PKE under corruptions is less studied in the literature. In TCC 2020, Benhamouda et al. first provide a formal characterization for anonymity of PKE under a specific type of corruption. However, no known PKE scheme is proved to meet their characterization. To the best of our knowledge, all the PKE application scenarios which require anonymity also require confidentiality. However, in the work by Benhamouda et al., different types of corruptions for anonymity and confidentiality are considered, which can cause security pitfalls. What's worse, we are not aware of any PKE scheme which can provide both anonymity and confidentiality under the same types of corruptions. In this work, we introduce a new security notion for PKE called ANON-RSO$_k\&$C security, capturing anonymity under corruptions. We also introduce SIM-RSO$_k\&$C security which captures confidentiality under the same types of corruptions. We provide a generic framework of constructing PKE scheme which can achieve the above two security goals simultaneously based on a new primitive called key and message non-committing encryption (KM-NCE). Then we give a general construction of KM-NCE utilizing a variant of hash proof system (HPS) called Key-Openable HPS. We also provide Key-Openable HPS instantiations based on the matrix decisional Diffie-Hellman assumption. Therefore, we can obtain various concrete PKE instantiations achieving the two security goals in the standard model with compact ciphertexts. Furthermore, for some PKE instantiation, its security reduction is tight.

Anonymity and authenticity are apparently conflicting goals. Anonymity means hiding a party's identity whereas authenticity means proving a party's identity. So how can a set of senders authenticate their messages without revealing their identity? Despite the paradoxical nature of this problem, there exist many cryptographic schemes designed to achieve both goals simultaneously, in some form. This paper provides a composable treatment of communication channels that achieve different forms of anonymity and authenticity. More specifically, three channel functionalities for many senders and one receiver are introduced which provide some trade-off between authenticity and anonymity (of the senders). For each of them, composably realizing it is proved to corresponds to the use of a certain type of cryptographic scheme, namely (1) a new type of scheme which we call bilateral signatures (syntactically related to designated verifier signatures), (2) partial signatures, and (3) ring signatures. This treatment hence provides composable semantics for (game-based) security definitions for these types of schemes. The results of this paper can be interpreted as the dual of the work by Kohlweiss et al. (PETS 2013), where composable notions for anonymous confidential communication were introduced and related to the security definitions of certain types of public-key encryption schemes, and where the treatment of anonymous authenticated communication was stated as an open problem.

Non-repudiation of messages generated by users is a desirable feature in a number of applications ranging from online banking to IoT scenarios. However, it requires certified public keys and usually results in poor usability as a user must carry around his certificate (e.g., in a smart-card) or must install it in all of his devices. A user-friendly alternative, adopted by several companies and national administrations, is to have a ``cloud-based'' PKI. In a nutshell, each user has a PKI certificate stored at a server in the cloud; users authenticate to the server---via passwords or one-time codes---and ask it to sign messages on their behalf. As such, there is no way for the server to prove to a third party that a signature on a given message was authorized by a user. As the server holds the user's certified key, it might as well have signed arbitrary messages in an attempt to impersonate that user. In other words, a user could deny having signed a message, by claiming that the signature was produced by the server without his consent. The same holds in case the secret key is derived deterministically from the user's password, for the server, by knowing the password, may still frame the user. In this paper we provide a "password-only" solution to non-repudiation of user messages by introducing Auditable Asymmetric Password Authenticated Public Key Establishment (A2PAKE). This is a PAKE-like protocol that generates an asymmetric key-pair where the public key is output to every participant, but the secret key is private output to just one of the parties (e.g., the user). Further, the protocol can be audited, i.e., given the public key output by a protocol run with a user, the server can prove to a third party that the corresponding secret key is held by that specific user. Thus, if the user signs messages with that secret key, then signatures are non-repudiable. We provide a universally composable definition of A2PAKE and an instantiation based on a distributed oblivious pseudo-random function. We also develop a prototype implementation of our instantiation and use it to evaluate its performance in realistic settings.

Multi-input functional encryption, MIFE, is a powerful generalization of functional encryption that allows computation on encrypted data coming from multiple different data sources. In a recent work, Agrawal, Goyal, and Tomida (CRYPTO 2021) constructed MIFE for the class of quadratic functions. This was the first MIFE construction from bilinear maps that went beyond inner product computation. We advance the state-of-the-art in MIFE, and propose new constructions with stronger security and broader functionality. Stronger Security: In the typical formulation of MIFE security, an attacker is allowed to either corrupt all or none of the users who can encrypt the data. In this work, we study MIFE security in a stronger and more natural model where we allow an attacker to corrupt any subset of the users, instead of only permitting all-or-nothing corruption. We formalize the model by providing each user a unique encryption key, and letting the attacker corrupt all non-trivial subsets of the encryption keys, while still maintaining the MIFE security for ciphertexts generated using honest keys. We construct a secure MIFE system for quadratic functions in this fine-grained corruption model from bilinear maps. Our construction departs significantly from the existing MIFE schemes as we need to tackle a more general class of attackers. Broader Functionality: The notion of multi-client functional encryption, MCFE, is a useful extension of MIFE. In MCFE, each encryptor can additionally tag each ciphertext with appropriate metadata such that ciphertexts with only matching metadata can be decrypted together. In more detail, each ciphertext is now annotated with a unique label such that ciphertexts encrypted for different slots can now only be combined together during decryption as long as the associated labels are an exact match for all individual ciphertexts. In this work, we upgrade our MIFE scheme to also support ciphertext labelling. While the functionality of our scheme matches that of MCFE for quadratic functions, our security guarantee falls short of the general corruption model studied for MCFE. In our model, all encryptors share a secret key, therefore this yields a secret-key version of quadratic MCFE, which we denote by SK-MCFE. We leave the problem of proving security in the general corruption model as an important open problem.

Bootstrapping, which enables the full homomorphic encryption scheme that can perform an infinite number of operations by restoring the modulus of the ciphertext with a small modulus, is an essential step in homomorphic encryption. However, bootstrapping is the most time and memory consuming of all homomorphic operations. As we increase the precision of bootstrapping, a large amount of computational resources is required. Specifically, for any of the previous bootstrap designs, the precision of bootstrapping is limited by rescaling precision. In this paper, we propose a new bootstrapping algorithm of the Cheon-Kim-Kim-Song (CKKS) scheme to use a known bootstrapping algorithm repeatedly, so called { Meta-BTS}. By repeating the original bootstrapping operation twice, one can obtain another bootstrapping with its precision essentially doubled; it can be generalized to be $k$-fold bootstrapping operations for some $k>1$ while the ciphertext size is large enough. Our algorithm overcomes the precision limitation given by the rescale operation.

This paper presents a new McEliece-type encryption scheme based on Gabidulin codes, which uses linearized transformations to disguise the private key. When endowing this scheme with the partial cyclic structure, we obtain a public key of the form $GM^{-1}$, where $G$ is a partial circulant generator matrix of Gabidulin code and $M$ as well as $M^{-1}$ is a circulant matrix of large rank weight, even as large as the code length. Another difference from Loidreau's proposal at PQCrypto 2017 is that both $G$ and $M$ are publicly known. Recovering the private key can be reduced to deriving from $M$ a linearized transformation and two circulant matrices of small rank weight. This new scheme is shown to resist all the known distinguisher-based attacks, such as the Overbeck attack and Coggia-Couvreur attack, and also has a very small public key size. For instance, 2592 bytes are enough for our proposal to achieve the security of 256 bits, which is 400 times smaller than Classic McEliece that has been selected into the fourth round of the NIST Post-Quantum Cryptography (PQC) standardization process.

In this short note, we describe a process for halving a point on a twisted Edwards curve. This can be used to test whether a given point is in the subgroup of prime order $\ell$, which is used by some cryptographic protocols. On Curve25519, this new test is about twice faster than the classic method consisting of multiplying the source point by $\ell$.

Inspired by Maurer's universal zero knowledge (UZK) abstract perspective and building on legally fair contract signing protocols without keystones, we propose and analyze the security of the first UZK class of co-signing protocols. We construct our main idea considering the stringent issue of scheme compatibility which characterizes communication systems. Typical examples are the cases of certificates in a public key infrastructure and the general issue of upgrading the version of a system. Thus, working in a general framework may reduce implementation errors and save application development and maintenance time.

Timed-release encryption can encrypt a message to a future time such that it can only be decrypted after that time. Potential applications include sealed bid auctions, scheduled confidential transactions, and digital time capsules. To enable such applications as decentralized smart contracts, we explore how to use timed-release encryption on blockchains. Practical constructions in literature rely on a trusted server (or servers in a threshold setting), which periodically publishes an epoch-specific decryption key based on a long-term secret. Their main idea is to model time periods or epochs as identities in an identity-based encryption scheme. However, these schemes suffer from a fatal flaw: an epoch’s key does not let us decrypt ciphertexts locked to prior epochs. Paterson and Quaglia [SCN'10] address this concern by having encryption specify a range of epochs when decryption is allowed. However, we are left with an efficiency concern: in each epoch, the server(s) must publish (via a smart contract transaction) a decryption key of size logarithmic in the lifetime (total number of epochs). For instance, on Ethereum, for a modest lifetime spanning 2 years of 1-minute long epochs, a server must spend over \$6 in gas fees, every minute; this cost multiplies with the number of servers in a threshold setting. We propose a novel timed-release encryption scheme, where a decryption key, while logarithmic in size, allows incremental updates, wherein a short update key (single group element) is sufficient to compute the successive decryption key; our decryption key lets the client decrypt ciphertexts locked to any prior epoch. This leads to significant reduction is gas fees, for instance, only \$0.30 in the above setting. Moreover, ciphertexts are also compact (logarithmic in the total lifetime), and encryption and decryption are on the order of few milliseconds. Furthermore, we decentralize the trust among a number of servers, so as to tolerate up to a threshold number of (malicious) corruptions. Our construction is based on bilinear pairing, and adapts ideas from Canetti et al.'s binary tree encryption [Eurocypt 2003] and Naor et al.'s distributed pseudorandom functions [Eurocrypt 1999].

We propose the signature scheme Hawk, a concrete instantiation of proposals to use the Lattice Isomorphism Problem (LIP) as a foundation for cryptography that focuses on simplicity. This simplicity stems from LIP, which allows the use of lattices such as $\mathbb{Z}^n$ , leading to signature algorithms with no floats, no rejection sampling, and compact precomputed distributions. Such design features are desirable for constrained devices, and when computing signatures inside FHE or MPC. The most significant change from recent LIP proposals is the use of module lattices, reusing algorithms and ideas from NTRUSign and Falcon. Its simplicity makes Hawk competitive. We provide cryptanalysis with experimental evidence for the design of Hawk and implement two parameter sets, Hawk-512 and Hawk-1024. Signing using Hawk-512 and Hawk-1024 is four times faster than Falcon on x86 architectures, produces signatures that are about 15% more compact, and is slightly more secure against forgeries by lattice reduction attacks. When floating-points are unavailable, Hawk signs 15 times faster than Falcon. We provide a worst case to average case reduction for module LIP. For certain parametrisations of Hawk this applies to secret key recovery and we reduce signature forgery in the random oracle model to a new problem called the one more short vector problem.

Blind signatures are a fundamental cryptographic primitive with numerous practical applications. While there exist many practical blind signatures from number-theoretic assumptions, the situation is far less satisfactory from post-quantum assumptions. In this work, we provide the first overall practical, lattice-based blind signature, supporting an unbounded number of signature queries and additionally enjoying optimal round complexity. We provide a detailed estimate of parameters achieved -- we obtain a signature of size slightly above 45KB, for a core-SVP hardness of 109 bits. The run-times of the signer, user and verifier are also very small. Our scheme relies on the Gentry, Peikert and Vaikuntanathan signature [STOC'08] and non-interactive zero-knowledge proofs for linear relations with small unknowns, which are significantly more efficient than their general purpose counterparts. Its security stems from a new and arguably natural assumption which we introduce, called the one-more-ISIS assumption. This assumption can be seen as a lattice analogue of the one-more-RSA assumption by Bellare et al [JoC'03]. To gain confidence in our assumption, we provide a detailed analysis of diverse attack strategies.

We explore a bitwise modification in Ajtai's one-way function. Our main contribution is to define the higher-bit approximate inhomogeneous short integer solution (ISIS) problem and prove its reduction to the ISIS problem. In this new instance, our main idea is to discard low-weighted bits to gain compactness. As an application, we construct a bitwise version of a hash-and-sign signature in the random oracle model whose security relies on the (Ring)-LWE and (Ring)-ISIS assumptions. Our scheme is built from the hash-and-sign digital signature scheme based on the relaxed notion of approximate trapdoors introduced by Chen, Genise and Mukherjee (2019). Their work can be interpreted as a bitwise optimization of the work of Micciancio and Peikert (2012). We extend this idea and apply our technique to the scheme by discarding low-weighted bits in the public key. Our modification brings improvement in the public key size but also in the signature size when used in the right setting. However, constructions based on the higher-bit approximate ISIS save memory space at the expense of loosening security. Parameters must be set in regards with this trade-off.

A threshold public key encryption protocol is a public key system where the private key is distributed among $n$ different servers. It offers high security since no single server is entrusted to perform the decryption in its entirety. It is the core component of many multiparty computation protocols which involves mutually distrusting parties with common goals. It is even more useful when it is homomorphic, which means that public operations on ciphertexts translate to operations on the underlying plaintexts. In particular, Cramer, Damgård and Nielsen at Eurocrypt 2001 provided a new approach to multiparty computation from linearly homomorphic threshold encryption schemes. On the other hand, there has been recent interest in developing multiparty computations modulo $2^k$ for a certain integer $k$, that closely match data manipulated by a CPU. Multiparty computation would therefore benefit from an encryption scheme with such a message space that would support a distributed decryption. In this work, we provide the first threshold linearly homomorphic encryption whose message space is $\mathbf{Z}/2^k\mathbf{Z}$ for any $k$. It is inspired by Castagnos and Laguillaumie's encryption scheme from RSA 2015, but works with a class group of discriminant whose factorisation is unknown. Its natural structure à la Elgamal makes it possible to distribute the decryption among servers using linear integer secret sharing, allowing any access structure for the decryption policy. Furthermore its efficiency and its flexibility on the choice of the message space make it a good candidate for applications to multiparty computation.

The focus of this work are multi-signatures schemes in the synchronized setting. A multi-signature scheme allows multiple signatures for the same message but from independent signers to be compressed into one short aggregated signature, which allows verifying all of the signatures simultaneously. In the synchronized setting, the signing algorithm takes the current time step as an additional input. It is assumed that no signer signs more than one message per time step and we aim to aggregate signatures for the same message and same time step. This setting is particularly useful in the context of blockchains, where validators are naturally synchronized by the blocks they sign. We present Squirrel, a concretely efficient lattice-based multi-signature scheme in the synchronized setting that works for a bounded number of $2^{\tau}$ time steps and allows for aggregating up to $\rho$ signatures at each step, where both $\tau$ and $\rho$ are public parameters upon which the efficiency of our scheme depends. Squirrel allows for non-interactive aggregation of independent signatures and is proven secure in the random oracle model in the presence of rogue-key attacks assuming the hardness of the short integer solution problem in a polynomial ring. We provide a careful analysis of all parameters and show that Squirrel can be instantiated with good concrete efficiency. For $\tau = 24$ and $\rho = 4096$, a signer could sign a new message every 10 seconds for 5 years non-stop. Assuming the signer has a cache of 112 MB, signing takes 68 ms and verification of an aggregated signature takes 36 ms. The size of the public key is 1 KB, the size of an individual signature is 52 KB, and the size of an aggregated signature is 771 KB.

Witness encryption (WE) allows us to use an arbitrary NP statement $x$ as a public key to encrypt a message, and the witness $w$ serves as a decryption key. Security ensures that, when the statement $x$ is false, the encrypted message remains computationally hidden. WE appears to be significantly weaker than indistinguishability obfuscation (iO). Indeed, WE is closely related to a highly restricted form of iO that only guarantees security for null circuits (null iO). However, all current approaches towards constructing WE under nice assumptions go through iO. Such constructions are quite complex and are unlikely to lead to practically instantiable schemes. In this work, we revisit a very simple WE and null iO candidate of Chen, Vaikuntanathan and Wee (CRYPTO 2018). We show how to prove its security under a nice and easy-to-state assumption that we refer to as "evasive LWE" following Wee (EUROCRYPT 2022). Roughly speaking, the evasive LWE assumption says the following: assume we have some joint distributions over matrices $\mathbf{P}$, $\mathbf{S}$ and auxiliary information $\mathsf{aux}$ such that $$({\mathbf{S}\mathbf{B} + \mathbf{E}},{\mathbf{S} \mathbf{P} + \mathbf{E}'}, \mathsf{aux}) \approx_c ({\mathbf{U}},{\mathbf{U'}}, \mathsf{aux}),$$ for a uniformly random (and secret) matrix $\mathbf{B}$, where $\mathbf{U}, \mathbf{U}'$ are uniformly random matrices, and $\mathbf{E},\mathbf{E}'$ are chosen from the LWE error distribution with appropriate parameters. Then it must also be the case that: $$\mathbf{S}\mathbf{B} + \mathbf{E}, \mathbf{B}^{-1}(\mathbf{P}),\mathsf{aux}) \approx_c (\mathbf{U}, \mathbf{B}^{-1}(\mathbf{P}),\mathsf{aux}).$$ Essentially the above says that given $\mathbf{S}\mathbf{B} + \mathbf{E}$, getting the additional component $\mathbf{B}^{-1}(\mathbf{P})$ is no more useful than just getting the product $({\mathbf{S}\mathbf{B} + \mathbf{E}})\cdot \mathbf{B}^{-1}(\mathbf{P}) \approx \mathbf{S} \mathbf{P} + \mathbf{E}'$.

We propose Designated-Verifier Linkable Ring Signatures with unconditional anonymity, a cryptographic primitive that protects the privacy of signers in two ways: Firstly, it allows them to hide inside a ring (i.e. an anonymity set) they can create by collecting a set of public keys all of which must be used for verification. Secondly, it allows a designated entity to simulate signatures thus making it difficult for an adversary to deduce their identity from the content of the exchanged messages. Our scheme differs from similar proposals since the anonymity guarantees are unconditional.

In the current paper we investigate the possibility of designing secure blind signature scheme based on ElGamal signature equation. We define the generalized construction and analyze its security. We consider two types of schemes with the proposed construction, that cover all existing schemes. For schemes of the first type we provide generic ROS-style attack that violates unforgeability in the parallel setting. For schemes of the second type we prove that they do not provide either blindness, or unforgeability. As the result, we prove that all known ElGamal blind signature schemes are not secure. Moreover, these results show that the existence of secure ElGamal blind signature scheme is potentially possible only for small set of signature equations and requires the non-standard way of generating the first component of the signature.

Although the supersingular isogeny Diffie-Hellman (SIDH) protocol is one of the most promising post-quantum cryptosystems, it is significantly slower than its main counterparts due to the underlying large smooth-degree isogeny computation. In this work, we address the problem of evaluating and constructing a strategy for computing the large smooth-degree isogeny in the multi-processor setting by formulating them as scheduling problems with dependencies. The contribution of this work is two-fold. For the strategy evaluation, we transform strategies into task dependency graphs and apply precedence-constrained scheduling algorithms to them in order to find their costs. For the strategy construction, we construct strategies from smaller parts that are optimal solutions of integer programming representing the problem. We show via experiments that the proposed two techniques together offer more than 13% reduction in the strategy costs compared to the best current results by Hutchinson and Karabina presented at Indocrypt 2018.

KEMTLS is a proposal for changing the TLS handshake to authenticate the handshake using long-term key encapsulation mechanism keys instead of signatures, motivated by trade-offs in the characteristics of post-quantum algorithms. Prior proofs of security of KEMTLS and its variant KEMTLS-PDK have been hand-written proofs in the reductionist model under computational assumptions. In this paper, we present computer-verified symbolic analyses of KEMTLS and KEMTLS-PDK using two distinct Tamarin models. In the first analysis, we adapt the detailed Tamarin model of TLS 1.3 by Cremers et al. (ACM CCS 2017), which closely follows the wire-format of the protocol specification, to KEMTLS(-PDK). We show that KEMTLS(-PDK) has equivalent security properties to the main handshake of TLS 1.3 proven in this model. We were able to fully automate this Tamarin proof, compared with the previous TLS 1.3 Tamarin model, which required a big manual proving effort; we also uncovered some inconsistencies in the previous model. In the second analysis, we present a novel Tamarin model of KEMTLS(-PDK), which closely follows the multi-stage key exchange security model from prior pen-and-paper proofs of KEMTLS(-PDK). The second approach is further away from the wire-format of the protocol specification but captures more subtleties in security definitions, like deniability and different levels of forward secrecy; it also identifies some flaws in the security claims from the pen-and-paper proofs. Our positive security results increase the confidence in the design of KEMTLS(-PDK). Moreover, viewing these models side-by-side allows us to comment on the trade-off in symbolic analysis between detail in protocol specification and granularity of security properties.

We present a bootstrapping procedure for the full-RNS variant of the approximate homomorphic-encryption scheme of Cheon et al., CKKS (Asiacrypt 17, SAC 18). Compared to the previously proposed procedures (Eurocrypt 18 & 19, CT-RSA 20), our bootstrapping procedure is more precise, more efficient (in terms of CPU cost and number of consumed levels), and is more reliable and 128-bit-secure. Unlike the previous approaches, it does not require the use of sparse secret-keys. Therefore, to the best of our knowledge, this is the first procedure that enables a highly efficient and precise bootstrapping with a low probability of failure for parameters that are 128-bit-secure under the most recent attacks on sparse R-LWE secrets. We achieve this efficiency and precision by introducing three novel contributions: (i) We propose a generic algorithm for homomorphic polynomial-evaluation that takes into account the approximate rescaling and is optimal in level consumption. (ii) We optimize the key-switch procedure and propose a new technique for linear transformations (\emph{double hoisting}). (iii) We propose a systematic approach to parameterize the bootstrapping, including a precise way to assess its failure probability. We implemented our improvements and bootstrapping procedure in the open-source Lattigo library. For example, bootstrapping a plaintext in $\mathbb{C}^{32768}$ takes 18 seconds, has an output coefficient modulus of 505 bits, a mean precision of 19.1 bits, and a failure probability of $2^{-15.58}$. Hence, we achieve 14.1$\times$ improvement in bootstrapped throughput (plaintext-bit per second), with respect to the previous best results, and we have a failure probability 468$\times$ smaller and ensure 128-bit security.

In 2020, Kudinov, Kiktenko, and Fedorov pointed out a flaw in the tight security proof of the $SPHINCS^{+}$ construction. This work gives a new tight security proof for $SPHINCS^{+}$. The flaw can be traced back to the security proof for the Winternitz one-time signature scheme (WOTS) used within $SPHINCS^{+}$. In this work, we give a standalone description of the WOTS variant used in SPHINCS+ that we call WOTS-TW. We provide a security proof for WOTS-TW and multi-instance WOTS-TW against non-adaptive chosen message attacks where the adversary only learns the public key after it made its signature query. Afterwards, we show that this is sufficient to give a tight security proof for $SPHINCS^{+}$. We recover almost the same bound for the security of $SPHINCS^{+}$, with only a factor $w$ loss compared to the previously claimed bound, where w is the Winternitz parameter that is commonly set to 16. On a more technical level, we introduce new lower bounds on the quantum query complexity for generic attacks against properties of cryptographic hash functions and analyse the constructions of tweakable hash functions used in $SPHINCS^{+}$ with regard to further security properties.

The qINDqCPA security notion for public-key encryption schemes by Gagliardoni et al. (PQCrypto'21) models security against adversaries which are able to obtain ciphertexts in superposition. Defining this security notion requires a special type of quantum operator. Known constructions differ in which keys are necessary to construct this operator, depending on properties of the encryption scheme. We argue—for the typical setting of securing communication between Alice and Bob—that in order to apply the notion, the quantum operator should be realizable for challengers knowing only the public key. This is already known to be the case for a wide range of public-key encryption schemes, in particular, those exhibiting the so-called recoverability property which allows to recover the message from a ciphertext using the randomness instead of the secret key. The open question is whether there are real-world public-key encryption schemes for which the notion is not applicable, considering the aforementioned observation on the keys known by the challenger. We answer this question in the affirmative by showing that applying the qINDqCPA security notion to the OAEP construction requires the challenger to know the secret key. We conclude that the qINDqCPA security notion might need to be refined to eventually yield a universally applicable PKE notion of quantum security with a quantum indistinguishability phase.

Time-lock puzzle schemes allow one to encrypt messages for the future. More concretely, one can efficiently generate a time-lock puzzle for a secret/solution $s$, such that $s$ remains hidden until a specified time $T$ has elapsed, even for any parallel adversaries. However, since computation on secrets within multiple puzzles can be performed only when \emph{all} of these puzzles are solved, the usage of classical time-lock puzzles is greatly limited. Homomorphic time-lock puzzle (HTLP) schemes were thus proposed to allow evaluating functions over puzzles directly without solving them. However, although efficient HTLP schemes exist, more improvements are still needed for practicability. In this paper, we improve HTLP schemes to broaden their application scenarios from the aspects of \emph{applicability} and \emph{verifiability}. In terms of applicability, we design the \emph{first} multiplicatively HTLP scheme with the solution space over $\mathbb{Z}_n^*$, which is more expressible than the original one, \eg representing integers. Then, to fit HTLP into scenarios requiring verifiability that is missing in existing schemes, we propose three \emph{simple} and \emph{fast} protocols for both the additively HTLP scheme and our multiplicatively HTLP scheme, respectively. The first two protocols allow a puzzle solver to convince others of the correctness of the solution or the invalidity of the puzzle so that others do not need to solve the puzzle themselves. The third protocol allows a puzzle generator to prove the validity of his puzzles. It is shown that a puzzle in our scheme is only $1.25$KB, and one multiplication on puzzles takes simply $0.01$ms. Meanwhile, the overhead of each protocol is less than $0.6$KB in communication and $40$ms in computation. Hence, HTLP still demonstrates excellent efficiency in both communication and computation with these versatile properties.

This paper deals with white-box implementations of the Elliptic Curve Digital Signature Algorithm (ECDSA): First, we consider attack paths to break such implementations. In particular, we provide a systematic overview of various fault attacks, to which ECDSA white-box implementations are especially susceptible. Then, we propose different mathematical countermeasures, mainly based on masking/blinding of sensitive variables, in order to prevent or at least make such attacks more difficult. We also briefly mention some typical implementational countermeasures and their challenges in the ECDSA white-box scenario. Our work has been initiated by the CHES challenge WhibOx Contest 2021, which consisted of designing and breaking white-box ECDSA implementations, so called challenges. We illustrate our results and findings by means of the submitted challenges and provide a comprehensive overview which challenge could be solved in which way. Furthermore, we analyze selected challenges in more details.

Resistance to key misuse attacks is a vital property for key encapsulation mechanisms（KEMs）in NIST-PQC standardization process. In key mismatch attack, the adversary recovers reused secret key with the help of an oracle $\mathcal{O}$ that indicates whether the shared key matches or not. Key mismatch attack is more powerful when fewer oracle queries are required. A series of works tried to reduce query times, Qin et al. [AISACRYPT 2021] gave a systematic approach to finding lower bound of oracle queries for a category of KEMs, including NIST’s third-round candidate Kyber and Saber. In this paper, we found the aforementioned bound can be bypassed by combining Qin et al. (AISACRYPT 2021)’s key mismatch attack with a standard lattice attack. In particular, we explicitly build the relationship between the number of queries to the oracle and the bit security of the lattice-based KEMs. Our attack is inspired by the fact that each oracle query reveals partial information of reused secrets, and affects the mean and the covariance parameter of secrets, making the attack on lattice easier. In addition, We quantify such effect in theory and estimate the security loss for all NIST second-round candidate KEMs.Specifically, Our improved attack reduces the number of queries for Kyber512 by 34% from 1312 queries with bit security 107 to 865 with bit security 32. For Kyber768 and Kyber1024, our improved attack reduces the number of queries by 29% and 27% with bit security is 32.

We present a much-improved practical protocol, based on the hardness of Module-SIS and Module-LWE problems, for proving knowledge of a short vector $s$ satisfying $As=t\bmod q$. The currently most-efficient technique for constructing such a proof works by showing that the $\ell_\infty$ norm of $s$ is small. It creates a commitment to a polynomial vector $m$ whose CRT coefficients are the coefficients of $s$ and then shows that (1) $A\cdot \mathsf{CRT}(m)=t\bmod\,q$ and (2) in the case that we want to prove that the $\ell_\infty$ norm is at most $1$, the polynomial product $(m - 1)\cdot m\cdot(m+1)$ equals to $0$. While these schemes are already quite good for practical applications, the requirement of using the CRT embedding and only being naturally adapted to proving the $\ell_\infty$-norm, somewhat hinders the efficiency of this approach. In this work, we show that there is a more direct and more efficient way to prove that the coefficients of $s$ have a small $\ell_2$ norm which does not require an equivocation with the $\ell_\infty$ norm, nor any conversion to the CRT representation. We observe that the inner product between two vectors $ r$ and $s$ can be made to appear as a coefficient of a product (or sum of products) between polynomials which are functions of $r$ and $s$. Thus, by using a polynomial product proof system and hiding all but one coefficient, we are able to prove knowledge of the inner product of two vectors modulo $q$. Using a cheap, approximate range proof, one can then lift the proof to be over $\mathbb{Z}$ instead of $\mathbb{Z}_q$. Our protocols for proving short norms work over all (interesting) polynomial rings, but are particularly efficient for rings like $\mathbb{Z}[X]/(X^n+1)$ in which the function relating the inner product of vectors and polynomial products happens to be a ``nice'' automorphism. The new proof system can be plugged into constructions of various lattice-based privacy primitives in a black-box manner. As examples, we instantiate a verifiable encryption scheme and a group signature scheme which are more than twice as compact as the previously best solutions.

Double-odd curves are curves with order equal to 2 modulo 4. A prime order group with complete formulas and a canonical encoding/decoding process could previously be built over a double-odd curve. In this paper, we reformulate such curves as a specific case of the Jacobi quartic. This allows using slightly faster formulas for point operations, as well as defining a more efficient encoding format, so that decoding and encoding have the same cost as classic point compression (decoding is one square root, encoding is one inversion). We define the prime-order groups jq255e and jq255s as the application of that modified encoding to the do255e and do255s groups. We furthermore define an optimized signature mechanism on these groups, that offers shorter signatures (48 bytes instead of the usual 64 bytes, for 128-bit security) and makes signature verification faster (down to less than 83000 cycles on an Intel x86 Coffee Lake core).

The verifiable encryption of bits is the main computational step that is needed to prepare ballots in many practical voting protocols. Its computational load can also be a practical bottleneck, preventing the deployment of some protocols or requiring the use of computing clusters. We investigate the question of producing many verifiably encrypted bits in an efficient and portable way, using as a baseline the protocol that is in use in essentially all modern voting systems and libraries supporting homomorphic voting, including ElectionGuard, a state-of-the-art open source voting SDK deployed in government elections. Combining fixed base exponentiation techniques and new encryption and ZK proof mechanisms, we obtain speed-ups by more than one order of magnitude against standard implementations. Our exploration requires balancing conflicting optimization strategies, and the use of asymptotically less efficient protocols that turn out to be very effective in practice. Several of our proposed improvements are now on the ElectionGuard roadmap.

A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a corresponding set of independently chosen receiver public keys. The resulting "multi-recipient ciphertext" can be then be reduced (by any 3rd party) to a shorter, receiver specific, "invidual ciphertext". Finally, to recover the $i$-th message in the batch from their indvidual ciphertext the $i$-th receiver only needs their own decryption key. A special case of mmPKE is multi-recipient PKE where all receivers are sent the same message. By treating (m)mPKE and their KEM counterparts as a stand-alone primitives we allow for more efficient constructions than trivially composing individual PKE/KEM instances. This is especially valuable in the post-quantum setting, where PKE/KEM ciphertexts and public keys tend to be far larger than their classic counterparts. In this work we describe a collection of new results around batched KEMs and PKE. We provide both classic and post-quantum proofs for all results. Our results are geared towards practical constructions and applications (for example in the domain of PQ-secure group messaging). Concretely, our results include a new non-adaptive to adaptive compiler for CPA-secure mKEMs resulting in public keys roughly half the size of the previous state-of-the-art [Hashimoto et.al., CCS'21]. We also prove their FO transform for mKEMs to be secure in the quantum random oracle model. We provide the first mKEM combiner as well as two mmPKE constructions. The first is an arbitrary message-length black-box construction from an mKEM (e.g. one produced by combining a PQ with a classic mKEM). The second is optimized for short messages and achieves hybrid PQ/classic security more directly. When encrypting $n$ short messages (e.g. as in several recent mmPKE applications) at 256-bits of security the mmPKE ciphertext are $144 n$ bytes shorter than the generic construction. Finally, we provide an optimized implementation of the (CCA secure) mKEM construction based on the NIST PQC winner Kyber and report benchmarks showing a significant speedup for batched encapsulation and up to 79% savings in ciphertext size compared to a naive solution.

We present experimental findings on the decoding failure rate (DFR) of BIKE, a fourth-round candidate in the NIST Post-Quantum Standardization process, at the 20-bit security level. We select parameters according to BIKE design principles and conduct a series of experiments. We directly compute the average DFR on a range of BIKE block sizes and identify both the waterfall and error floor regions of the DFR curve. We then study the influence on the average DFR of three sets $\mathcal{C}$, $\mathcal{N}$, and $2\mathcal{N}$ of near-codewords --- vectors of low weight that induce syndromes of low weight --- defined by Vasseur in 2021. We find that error vectors leading to decoding failures have small maximum support intersection with elements of these sets; further, the distribution of intersections is quite similar to that of sampling random error vectors and counting the intersections with $\mathcal{C}$, $\mathcal{N}$, and $2\mathcal{N}$. Our results indicate that these three sets are not sufficient in classifying vectors expected to cause decoding failures. Finally, we study the role of syndrome weight on the decoding behavior and conclude that the set of error vectors that lead to decoding failures differ from random vectors by having low syndrome weight.

This note discusses lattice-based cryptography over the field with $p= 2^{64} - 2^{32} + 1$ elements, with an eye to supporting lattice-based cryptography operations in virtual machines such as Miden VM that operate natively over this field. It discusses how to support Dilithium and Falcon, two lattice-based signature scheme recently selected by the NIST PQC project; and proposes parameters for efficient public key encryption and publicly re-randomizable commitments modulo $p$.

It can be tricky to trust elliptic curves standardized in a non-transparent way. To rectify this, we propose a systematic methodology for analyzing curves and statistically comparing them to the expected values of a large number of generic curves with the aim of identifying any deviations in the standard curves. For this purpose, we put together the largest publicly available database of standard curves. To identify unexpected properties of standard generation methods and curves, we simulate over 250 000 curves by mimicking the generation process of four standards. We compute 22 different properties of curves and analyze them with automated methods to pinpoint deviations in standard curves, pointing to possible weaknesses.

We show how to construct a completely generic UC-secure oblivious transfer scheme from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Our work is based on the work of Abdalla et al. at Asiacrypt 2013, where the authors formalize the notion of SPHF-friendly commitments, i.e. accepting an SPHF on the language of valid commitments (to allow implicit decommitment), and show how to construct from them a UC-secure oblivious transfer in a generic way. But Abdalla et al. only gave a DDH-based construction of SPHF-friendly commitment schemes, furthermore highly relying on pairings. In this work, we show how to generically construct an SPHF-friendly commitment scheme from a collision-resistant CH scheme and an SPHF-friendly CCA encryption scheme. This allows us to propose an instantiation of our schemes based on the DDH, as efficient as that of Abdalla et al., but without requiring any pairing. Interestingly, our generic framework also allows us to propose an instantiation based on the learning with errors (LWE) assumption. For the record, we finally propose a last instantiation based on the decisional composite residuosity (DCR) assumption.

In this work we propose time-deniable signatures (TDS), a new primitive that facilitates deniable authentication in protocols such as DKIM-signed email. As with traditional signatures, TDS provide strong authenticity for message content, at least for a sender-chosen period of time. Once this time period has elapsed, however, time-deniable signatures can be forged by any party who obtains a signature. This forgery property ensures that signatures serve a useful authentication purpose for a bounded time period, while also allowing signers to plausibly disavow the creation of older signed content. Most critically, and unlike many past proposals for deniable authentication, TDS do not require interaction with the receiver or the deployment of any persistent cryptographic infrastructure or services beyond the signing process (e.g., APIs to publish secrets or author timestamp certificates.) We first investigate the security definitions for time-deniability, demonstrating that past definitional attempts are insufficient (and indeed, allow for broken signature schemes.) We then propose an efficient construction of TDS based on well-studied assumptions.

The Hybrid Public Key Encryption (HPKE) scheme is an emerging standard currently under consideration by the Crypto Forum Research Group (CFRG) of the IETF as a candidate for formal approval. Of the four modes of HPKE, we analyse the authenticated mode HPKE_Auth in its single-shot encryption form as it contains what is, arguably, the most novel part of HPKE and has applications to other upcoming standards such as MLS. HPKE_Auth’s intended application domain is captured by a new primitive which we call Authenticated Public Key Encryption (APKE). We provide syntax and security definitions for APKE schemes, as well as for the related Authenticated Key Encapsulation Mechanisms (AKEMs). We prove security of the AKEM scheme DH-AKEM underlying HPKE_Auth based on the Gap Diffie-Hellman assumption and provide general AKEM/DEM composition theorems with which to argue about HPKE_Auth’s security. To this end, we also formally analyse HPKE_Auth’s key schedule and key derivation functions. To increase confidence in our results we use the automatic theorem proving tool CryptoVerif. All our bounds are quantitative and we discuss their practical implications for HPKE_Auth. As an independent contribution we propose the new framework of nominal groups that allows us to capture abstract syntactical and security properties of practical elliptic curves, including the Curve25519 and Curve448 based groups (which do not constitute cyclic groups).

This work investigates efficient multi-party signature schemes in the discrete logarithm setting. We focus on a concurrent model, in which an arbitrary number of signing sessions may occur in parallel. Our primary contributions are: (1) a modular framework for proving the security of Schnorr multisignature and threshold signature schemes, (2) an optimization of the two-round threshold signature scheme $\mathsf{FROST}$ that we call $\mathsf{FROST2}$, and (3) the application of our framework to prove the security of $\mathsf{FROST2}$ as well as a range of other multi-party schemes. We begin by demonstrating that our framework is applicable to multisignatures. We prove the security of a variant of the two-round $\mathsf{MuSig2}$ scheme with proofs of possession and a three-round multisignature $\mathsf{SimpleMuSig}$. We introduce a novel three-round threshold signature $\mathsf{SimpleTSig}$ and propose an optimization to the two-round $\mathsf{FROST}$ threshold scheme that we call $\mathsf{FROST2}$. $\mathsf{FROST2}$ reduces the number of scalar multiplications required during signing from linear in the number of signers to constant. We apply our framework to prove the security of $\mathsf{FROST2}$ under the one-more discrete logarithm assumption and $\mathsf{SimpleTSig}$ under the discrete logarithm assumption in the programmable random oracle model.

Consider a computer user who needs to update a piece of software installed on their computing device. To do so securely, a commonly accepted ad-hoc method stipulates that the old software version first retrieves the update information from the vendor's public repository, then checks that a cryptographic signature embedded into it verifies with the vendor's public key, and finally replaces itself with the new version. This updating method seems to be robust and lightweight, and to reliably ensure that no malicious third party (e.g., a distribution mirror) can inject harmful code into the update process. Unfortunately, recent prominent news reports (SolarWinds, Stuxnet, TikTok, Zoom, ...) suggest that nation state adversaries are broadening their efforts related to attacking software supply chains. This calls for a critical re-evaluation of the described signature based updating method with respect to the real-world security it provides against particularly powerful adversaries. We approach the setting by formalizing a cryptographic primitive that addresses specifically the secure software updating problem. We define strong, rigorous security models that capture forward security (stealing a vendor's key today doesn't allow modifying yesterday's software version) as well as a form of self-enforcement that helps protecting vendors against coercion attacks in which they are forced, e.g. by nation state actors, to misuse or disclose their keys. We note that the common signature based software authentication method described above meets neither the one nor the other goal, and thus represents a suboptimal solution. Hence, after formalizing the syntax and security of the new primitive, we propose novel, efficient, and provably secure constructions.

In this short note we explore a particular behaviour of the CSIDH key exchange that leads to a very special form of (shared) key control via the use of the quadratic twists. This peculiarity contained in CSIDH with regard to quadratic twists was already noted in the original CSDIH work and used in several subsequent papers but we believe spelling out this in the form of an attack might be useful to the wider community.

We show a compiler that allows to prove the correct execution of RAM programs using any zero-knowledge system for circuit satisfiability. At the core of this work is an arithmetic circuit which verifies the consistency of a list of memory access tuples in zero-knowledge. Using such a circuit, we obtain the first constant-round and concretely efficient zero-knowledge proof protocol for RAM programs using any stateless zero-knowledge proof system for Boolean or arithmetic circuits. Both the communication complexity and the prover and verifier run times asymptotically scale linearly in the size of the memory and the run time of the RAM program; we demonstrate concrete efficiency with performance results of our C++ implementation. We concretely instantiate our construction with an efficient MPC-in-the-Head proof system, Limbo (ACM CCS 2021). The C++ implementation of our access protocol extends that of Limbo and provides interactive proofs with 40 bits of statistical security with an amortized cost of 0.42ms of prover time and 2.8KB of communication per memory access, independently of the size of the memory; with multi-threading, this cost is reduced to 0.12ms and 1.8KB respectively. This performance of our public-coin protocol approaches that of private-coin protocol BubbleRAM (ACM CCS 2020, 0.15ms and 1.5KB per access).

Code equivalence is a well-known concept in coding theory. Recently, literature saw an increased interest in this notion, due to the introduction of protocols based on the hardness of finding the equivalence between two linear codes. In this paper, we analyze the security of code equivalence, with a special focus on the hardest instances, in the interest of cryptographic usage. Our work stems from a thorough review of existing literature, identifies the various types of solvers for the problem, and provides a precise complexity analysis, where previously absent. Furthermore, we are able to improve on the state of the art, providing more efficient algorithm variations, for which we include numerical simulation data. Our results include also a dedicated method for solving code equivalence with a quantum algorithm, as well as a refinement of quantum Information-Set Decoding (ISD) algorithms. In the end, the goal of this paper is to provide a complete, single point of access, which can be used as a tool for designing schemes that rely on the code equivalence problem.

We define two metrics on vector spaces over a finite field using the linear complexity of finite sequences. We then develop coding theory notions for these metrics and study their properties. We give a Singleton-like bound as well as constructions of subspaces achieving this bound. We also provide an asymptotic Gilbert-Varshamov-like bound for random subspaces. We show how to reduce the problem of finding codewords with given Hamming weight into a problem of finding a vector of a given linear complexity. This implies that our new metric can be used for cryptography in a similar way to what is currently done in the code-based setting.

Many public-key cryptographic protocols, notably non-interactive key exchange (NIKE), require incoming public keys to be validated to mitigate some adaptive attacks. In CSIDH, an isogeny-based post-quantum NIKE, a key is deemed legitimate if the given Montgomery coefficient specifies a supersingular elliptic curve over the prime field. In this work, we survey the current supersingularity tests used for CSIDH key validation, and implement and measure two new alternative algorithms. Our implementation shows that we can determine supersingularity substantially faster, and using less memory, than the state-of-the-art.

The security of code-based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, already the most basic ISD algorithm by Prange suffers enormous width requirements caused by the quadratic description length of the underlying problem. Even if polynomial, this need for qubits is one of the biggest challenges considering the application of real quantum circuits in the near- to mid-term. In this work we overcome this issue by presenting the first hybrid ISD algorithms that allow to tailor the required qubits to any available amount while still providing quantum speedups of the form $T^\delta$, $0.5<\delta <1$, where $T$ is the running time of the purely classical procedure. Interestingly, when constraining the width of the circuit instead of its depth we are able to overcome previous optimality results on constraint quantum search. Further we give an implementation of the fully-fledged quantum ISD procedure and the classical co-processor using the quantum simulation library Qibo and SageMath.

Over the last years, the side-channel analysis of Post-Quantum Cryptography (PQC) candidates in the NIST standardization initiative has received increased attention. In particular, it has been shown that some post-quantum Key Encapsulation Mechanisms (KEMs) are vulnerable to Chosen-Ciphertext Side-Channel Attacks (CC-SCA). These powerful attacks target the re-encryption step in the Fujisaki-Okamoto (FO) transform, which is commonly used to achieve CCA security in such schemes. To sufficiently protect PQC KEMs on embedded devices against such a powerful CC-SCA, masking at increasingly higher order is required, which induces a considerable overhead. In this work, we propose to use a conceptually simple construction, the $\mathcal{E}t\mathcal{S}$ KEM, that alleviates the impact of CC-SCA. It uses the Encrypt-then-Sign ($\mathcal{E}t\mathcal{S}$) paradigm introduced by Zheng at ISW ’97 and further analyzed by An, Dodis and Rabin at EUROCRYPT ’02, and instantiates a postquantum authenticated KEM in the outsider-security model. While the construction is generic, we apply it to the CRYSTALS-Kyber KEM, relying on the CRYSTALS-Dilithium and Falcon signature schemes. We show that a CC-SCA-protected $\mathcal{E}t\mathcal{S}$ KEM version of CRYSTALS-Kyber requires less than 10% of the cycles required for the CC-SCA-protected FO-based KEM, at the cost of additional data/communication overhead. We additionally show that the cost of protecting the $\mathcal{E}t\mathcal{S}$ KEM against fault injection attacks, necessarily due to the added signature verification, remains negligible compared to the large cost of masking the FO transform at higher orders. Lastly, we discuss relevant embedded use cases for our $\mathcal{E}t\mathcal{S}$ KEM construction.

In this paper, we use genus theory to analyze the hardness of the decisional Diffie-Hellman problem for ideal class groups of imaginary quadratic orders acting on sets of elliptic curves through isogenies (DDH-CGA). Such actions are used in the Couveignes-Rostovtsev-Stolbunov protocol and in CSIDH. Concretely, genus theory equips every imaginary quadratic order $\mathcal{O}$ with a set of assigned characters $\chi : \text{cl}(\mathcal{O}) \to \{ \pm 1\}$, and for each such character and every secret ideal class $[\mathfrak{a}]$ connecting two public elliptic curves $E$ and $E' = [\mathfrak{a}] \star E$, we show how to compute $\chi([\mathfrak{a}])$ given only $E$ and $E'$, i.e. without knowledge of $[\mathfrak{a}]$. In practice, this breaks DDH-CGA as soon as the class number is even, which is true for a density $1$ subset of all imaginary quadratic orders. For instance, our attack works very efficiently for all supersingular elliptic curves over $\mathbb{F}_p$ with $p \equiv 1 \bmod 4$. Our method relies on computing Tate pairings and walking down isogeny volcanoes. We also show that these ideas carry over, at least partly, to abelian varieties of arbitrary dimension. This is an extended version of the paper that was presented at Crypto 2020.

This note presents some techniques to slightly reduce the size of EdDSA and ECDSA signatures without lowering their security or breaking compatibility with existing signers, at the cost of an increase in signature verification time; verifying a 64-byte Ed25519 signature truncated to 60 bytes has an average cost of 4.1 million cycles on 64-bit x86 (i.e. about 35 times the cost of verifying a normal, untruncated signature).

The standard model security of the Fiat-Shamir transform has been an active research area for many years. In breakthrough results, Canetti et al. (STOC'19) and Peikert-Shiehian (Crypto'19) showed that, under the Learning-With-Errors (LWE) assumption, it provides soundness by applying correlation-intractable (CI) hash functions to so-called trapdoor $\Sigma$-protocols. In order to be compatible with CI hash functions based on standard LWE assumptions with polynomial approximation factors, all known such protocols have been obtained via parallel repetitions of a basic protocol with binary challenges. In this paper, we consider languages related to Paillier's composite residuosity assumption (DCR) for which we give the first trapdoor $\Sigma$-protocols providing soundness in one shot, via exponentially large challenge spaces. This improvement is analogous to the one enabled by Schnorr over the original Fiat-Shamir protocol in the random oracle model. Using the correlation-intractable hash function paradigm, we then obtain simulation-sound NIZK arguments showing that an element of $\mathbb{Z}_{N^2}^\ast$ is a composite residue, which opens the door to space-efficient applications in the standard model. As a concrete example, we build logarithmic-size ring signatures (assuming a common reference string) with the shortest signature length among schemes based on standard assumptions in the standard model. We prove security under the DCR and LWE assumptions, while keeping the signature size comparable with that of random-oracle-based schemes.

Homomorphic encryption (HE) is being widely used for privacy-preserving computation. Since HE schemes only support polynomial operations, it is prevalent to use polynomial approximations of non-polynomial functions. We cannot monitor the intermediate values during the homomorphic evaluation; as a consequence, we should utilize polynomial approximations with sufficiently large approximation intervals to prevent the failure of the evaluation. However, the large approximation interval potentially accompanies computational overheads, and it is a serious bottleneck of HE application on real-world data. In this work, we introduce domain extension polynomials (DEPs) that extend the domain interval of functions by a factor of $k$ while preserving the feature of the original function on its original domain interval. By repeatedly iterating the domain-extension process with DEPs, we can extend with $O(\log{K})$ operations the domain of a given function by a factor of $K$ while the feature of the original function is preserved in its original domain interval. By using DEPs, we can efficiently evaluate in an encrypted state a function that converges at infinities, i.e., $\lim_{x\to\infty}f(x)$ and $\lim_{x\to-\infty}f(x)$ exist in $\mathbb{R}$. To uniformly approximate the function on $[-R,R]$, our method exploits $O(\log{R})$ operations and $O(1)$ memory. This is more efficient than the previous approach, the minimax approximation and Paterson-Stockmeyer algorithm, which uses $\Omega(\sqrt{R})$ multiplications and $\Omega(\sqrt{R})$ memory for the evaluation. As another application of DEPs, we also suggest a method to manage the risky outliers from a large interval $[-R,R]$ by using $O(\log{R})$ additional multiplications. As a real-world application, we trained the logistic regression classifier on large public datasets in an encrypted state by using our method. We exploit our method to the evaluation of the logistic function on large intervals, e.g., $[-7683,7683]$.

The lattice sieving algorithm based on list-decoding of Becker-Ducas-Gama-Laarhoven (SODA 2016) is currently at the center of cryptanalysis cost estimates of candidate lattice schemes for post-quantum standardization. Yet, only an idealized version of this algorithm has been carefully modelled, i.e. given an efficient list-decoding oracle for a perfectly random spherical code. In this work, we propose an experimental analysis of the actual algorithm. The difficulty lies in estimating the probabilistic defect with respect to perfectly random spherical codes for the task at hand. While it should be in principle infeasible to run the algorithm in cryptographically relevant dimensions, a few tricks allow to nevertheless measure experimentally the relevant quantity. Concretely, we conclude on an overhead factor of about $2^{6}$ on the number of gates in the RAM model compared to the idealized model for dimensions around $380$ after an appropriate re-parametrization. Part of this overhead can be traded for extra memory, at a costly rate. We also clarify that these overheads apply to an internal routine, and discuss how they can be partially mitigated in the whole attack.

Commitments to key-value maps (or, authenticated dictionaries) are an important building block in cryptographic applications, including cryptocurrencies and distributed file systems. In this work we study short commitments to key-value maps with two additional properties: double-hiding (both keys and values should be hidden) and homomorphism (we should be able to combine two commitments to obtain one that is the ``sum'' of their key-value openings). Furthermore, we require these commitments to be short and to support efficient transparent zero-knowledge arguments (i.e., without a trusted setup). As our main contribution, we show how to construct commitments with the properties above as well as efficient zero-knowledge arguments over them. We additionally discuss a range of practical optimizations that can be carried out depending on the application domain. Finally, we formally describe a specific application of commitments to key-value maps to scalable anonymous ledgers. We show how to extend QuisQuis (Fauzi et al., ASIACRYPT 2019). This results in an efficient, confidential multi-type system with a state whose size is independent of the number of transactions.

The NIST standardization process for post-quantum cryptography has been drawing the attention of researchers to the submitted candidates. One direction of research consists in implementing those candidates on embedded systems and that exposes them to physical attacks in return. The Classic McEliece cryptosystem, which is among the four finalists of round 3 in the Key Encapsulation Mechanism category, builds its security on the hardness of the syndrome decoding problem, which is a classic hard problem in code-based cryptography. This cryptosystem was recently targeted by a laser fault injection attack leading to message recovery. Regrettably, the attack setting is very restrictive and it does not tolerate any error in the faulty syndrome. Moreover, it depends on the very strong attacker model of laser fault injection, and does not apply to optimised implementations of the algorithm that make optimal usage of the machine words capacity. In this article, we propose a to change the angle and perform a message-recovery attack that relies on side-channel information only. We improve on the previously published work in several key aspects. First, we show that side-channel information, obtained with power consumption analysis, is sufficient to obtain an integer syndrome, as required by the attack framework. This is done by leveraging classic machine learning techniques that recover the Hamming weight information very accurately. Second, we put forward a computationally-efficient method, based on a simple dot product and information-set decoding algorithms, to recover the message from the, possibly inaccurate, recovered integer syndrome. Finally, we present a masking countermeasure against the proposed attack.

Recently, Chaum et al. (ACNS'21) introduced $\mathcal{S}_{leeve}$, which describes an extra security layer for signature schemes, i.e., ECDSA. This distinctive feature is a new key generation mechanism, allowing users to generate a ''back up key'' securely nested inside the secret key of a signature scheme. Using this novel construction, the ''back up key'', which is secret, can be used to generate a ''proof of ownership'', i.e., only the rightful owner of this secret key can generate such a proof. This design offers a quantum secure fallback, i.e., a brand new quantum resistant signature, ready to be used, nested in the ECDSA secret key. In this work, we rely on the original $\mathcal{S}_{leeve}$ definition to generalize the construction to a modular design based on Tweakable Hash Functions, thus yielding a cleaner design of the primitive. Furthermore, we provide a thorough security analysis taking into account the security of the ECDSA signature scheme, which is lacking in the original work. Finally, we provide an analysis based on formal methods using Verifpal assuring the security guarantees our construction provides.

A decentralized multi-authority anonymous authentication scheme that is suitable for IoT and blockchains is proposed, in which a prover and a verifier are non-interactive. The proposed scheme can treat dynamically increasing/decreasing independent attribute authorities. When an entity wants the authorities to issue attribute credentials, the authorities only have to generate digital signatures on her global identity. Two security definitions are given; resistance against eavesdrop-and-collude attacks that cause misauthentication, and anonymity for privacy protection. Then a construction of our scheme is described under a principle of ``commit-to-ID'' to attain resistance against the collusion attacks. There are two building blocks; the structure-preserving signature scheme and the Groth-Sahai non-interactive proof system, the both of which are in the setting of bilinear groups. The proposed scheme is proved to be secure in the standard model.

The genus is an efficiently computable arithmetic invariant for lattices up to isomorphism. Given the recent proposals of basing cryptography on the lattice isomorphism problem, it is of cryptographic interest to classify relevant families of lattices according to their genus. We propose such a classification for q-ary lattices, and also study their distribution. In particular, for an odd prime q, we show that random q-ary lattices are mostly concentrated on two genera. Because the genus is local, this also provides information on the distribution for general odd q. The case of q a power of 2 is also studied, although we only achieve a partial classification.

Mix-nets are protocols that allow a set of senders to send messages anonymously. Faonio et al. (ASIACRYPT’19) showed how to instantiate mix-net protocols based on Public-Verifiable Re-randomizable Replayable CCA-secure (Rand-RCCA) PKE schemes. The bottleneck of their approach is that public-verifiable Rand-RCCA PKEs are less efficient than typical CPA-secure re-randomizable PKEs. In this paper, we revisit their mix-net protocol, showing how to get rid of the cumbersome public-verifiability property, and we give a more efficient instantiation for the mix-net protocol based on a (non publicly-verifiable) Rand-RCCA scheme. Additionally, we give a more careful security analysis of their mix-net protocol.

NTRU lattices are a class of polynomial rings which allow for compact and efficient representations of the lattice basis, thereby offering very good performance characteristics for the asymmetric algorithms that use them. Signature algorithms based on NTRU lattices have fast signature generation and verification, and relatively small signatures, public keys and private keys. A few lattice-based cryptographic schemes entail, generally during the key generation, solving the NTRU equation: $$ f G - g F = q \mod x^n + 1 $$ Here $f$ and $g$ are fixed, the goal is to compute solutions $F$ and $G$ to the equation, and all the polynomials are in $\mathbb{Z}[x]/(x^n + 1)$. The existing methods for solving this equation are quite cumbersome: their time and space complexities are at least cubic and quadratic in the dimension $n$, and for typical parameters they therefore require several megabytes of RAM and take more than a second on a typical laptop, precluding onboard key generation in embedded systems such as smart cards. In this work, we present two new algorithms for solving the NTRU equation. Both algorithms make a repeated use of the field norm in tower of fields; it allows them to be faster and more compact than existing algorithms by factors $\tilde O(n)$. For lattice-based schemes considered in practice, this reduces both the computation time and RAM usage by factors at least 100, making key pair generation within range of smart card abilities.

The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of `structured' LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by adding cyclic structure to Module LWE. The proposed construction is both more efficient than Module LWE and conjecturally more secure than Ring LWE, the best of both worlds. We show that the security reductions expected for an LWE problem hold, namely a reduction from certain structured lattice problems to the hardness of the decision variant of the CLWE problem. As a contribution of theoretic interest, we view CLWE as the first variant of Ring LWE which supports non-commutative multiplication operations. This ring structure compares favorably with Module LWE, and naturally allows a larger message space for error correction coding.

CCA-like game-based security definitions capture confidentiality by asking an adversary to distinguish between honestly computed encryptions of chosen plaintexts. In the context of voting systems, such guarantees have been shown to be sufficient to prove ballot privacy (Asiacrypt'12). In this paper, we observe that they fall short when one seeks to obtain receipt-freeness, that is, when corrupted voters who submit chosen ciphertexts encrypting their vote must be prevented from proving how they voted to a third party. Since no known encryption security notion can lead to a receipt-free ballot submission process, we address this challenge by proposing a novel publicly verifiable encryption primitive coined Traceable Receipt-free Encryption (TREnc) and a new notion of traceable CCA security filling the definitional gap underlined above. We propose two TREnc instances, one generic achieving stronger guarantees for the purpose of relating it to existing building blocks, and a dedicated one based on SXDH. Both support the encryption of group elements in the standard model, while previously proposed encryption schemes aiming at offering receipt-freeness only support a polynomial-size message space, or security in the generic group model. Eventually, we demonstrate how a TREnc can be used to build receipt-free voting protocols, by following a standard blueprint.

This work introduces new key recovery attacks against the Rainbow signature scheme, which is one of the three finalist signature schemes still in the NIST Post-Quantum Cryptography standardization project. The new attacks outperform previously known attacks for all the parameter sets submitted to NIST and make a key-recovery practical for the SL 1 parameters. Concretely, given a Rainbow public key for the SL 1 parameters of the second-round submission, our attack returns the corresponding secret key after on average 53 hours (one weekend) of computation time on a standard laptop.

The Support-Minors (SM) method has opened new routes to attack multivariate schemes with rank properties that were previ- ously impossible to exploit, as shown by the recent attacks of Tao at al. (CRYPTO 2021) and Beullens (EUROCRYPT 2021) on the Round 3 NIST candidates GeMSS and Rainbow respectively. In this paper, we study this SM approach more in depth and we propose a greatly improved attack on GeMSS based on this Support-Minors method. Even though GeMSS was already affected by Tao's attack, our attack affects it even more and makes it completely unfeasible to repair the scheme by simply increasing the size of its parameters or even applying the recent projection technique from Øygarden et al. (PQCrypto 2021) whose purpose was to make GeMSS immune to Tao's attack. For instance, our attack on the GeMSS128 parameter set has estimated time complexity 2^72 , and repairing the scheme by applying projection would result in a signature with slower signing time by an impractical factor of 2^14 . Another contribution is to suggest optimizations that can reduce memory access costs for an XL strategy on a large SM system using the Block-Wiedemann algorithm as subroutine when these costs are a concern. In a memory cost model based on the one provided by Bernstein et al. (https://ntruprime.cr.yp.to/nist/ntruprime-20201007.pdf), we show that the rectangular MinRank attack of Beullens may indeed reduce the security for all Round 3 Rainbow parameter sets below their targeted security strengths, contradicting the lower bound claimed by the Rainbow team using the same memory cost model (https://troll.iis.sinica.edu.tw/by-publ/recent/response-ward.pdf).

This work proposes a new two-stage lattice two-stage sampling technique, generalizing the prior two-stage sampling method of Gentry, Peikert, and Vaikuntanathan (STOC '08). By using our new technique as a key building block, we can significantly improve security and efficiency of the current state of the arts of simulation-based functional encryption. Particularly, our functional encryption achieves $(Q,\poly)$ simulation-based semi-adaptive security that allows arbitrary pre- and post-challenge key queries, and has succinct ciphertexts with only an additive $O(Q)$ overhead. Additionally, our two-stage sampling technique can derive new feasibilities of indistinguishability-based adaptively-secure $\IB$-$\FE$ for inner products and semi-adaptively-secure $\AB$-$\FE$ for inner products, breaking several technical limitations of the recent work by Abdalla, Catalano, Gay, and Ursu (Asiacrypt '20).

Falcon is a very efficient and compact lattice-based signature finalist of the NIST's Post-Quantum standardization campaign. This work assesses Falcon's side-channel resistance by analyzing two vulnerabilities, namely the pre-image computation and the trapdoor sampling. The first attack is an improvement of Karabulut and Aysu (DAC 2021). It overcomes several difficulties inherent to the structure of the stored key like the Fourier representation and directly recovers the key with a limited number of traces and a reduced complexity. The main part of this paper is dedicated to our second attack: we show that a simple power analysis during the signature execution could provide the exact value of the output of a subroutine called the base sampler. This intermediate value does not directly lead to the secret and we had to adapt the so-called hidden parallelepiped attack initially introduced by Nguyen and Regev in Eurocrypt 2006 and reused by Ducas and Nguyen in Asiacrypt 2012. We extensively quantify the resources for our attacks and experimentally demonstrate them with Falcon's reference implementation on the ELMO simulator (McCann, Oswald and Whitnall USENIX 2017) and on a Chipwhisperer Lite with STM32F3 target (ARM Cortex M4). These new attacks highlight the need for side-channel protection for one of the three finalists of NIST's standardization campaign by pointing out the vulnerable parts and quantifying the resources of the attacks.

In multi-client functional encryption (MC-FE) for predicate queries, clients generate ciphertexts of attributes $x_1, \ldots, x_n$ binding with a time period $T$ and store them on a cloud server, and the cloud server receives a token corresponding to a predicate $f$ from a trusted center and learns whether $f(x_1, \ldots, x_n) = 1$ or not by running the query algorithm on the multiple ciphertexts of the same time period. MC-FE for predicates can be used for a network event or medical data monitoring system based on time series data gathered by multiple clients. In this paper, we propose efficient MC-FE schemes that support conjunctive equality or range queries on encrypted data in the multi-client settings. First, we propose an efficient multi-client hidden vector encryption (MC-HVE) scheme in bilinear groups and prove the selective strong attribute hiding security with static corruptions. Our MC-HVE scheme is very efficient since a token is composed of four group elements, a ciphertext consists of $O(n)$ group elements, and the query algorithm only requires four pairing operations. Second, we propose an efficient multi-client range query encryption (MC-RQE) scheme and prove the weak attribute hiding security with static corruptions. Since our MC-RQE scheme uses a binary tree, it is efficient since a ciphertext consists of $O(n \log D)$ group elements and a token consists of $O(n \log D)$ group elements where $D$ is the maximum value of the range.

Verifiable random functions (VRFs) are a useful extension of pseudorandom functions for which it is possible to generate a proof that a certain image is indeed the correct function value (relative to a public verification key). Due to their strong soundness requirements on such proofs, VRFs are notoriously hard to construct, and existing constructions suffer either from complex proofs (for function images), or rely on complex and non-standard assumptions. In this work, we attempt to explain this phenomenon. We show that for a large class of pairing-based VRFs, it is not possible to obtain short proofs and a reduction to a simple assumption simultaneously. Since the class of "consecutively verifiable" VRFs we consider contains in particular the VRF of Lysyanskaya and that of Dodis-Yampolskiy, our results explain the large proof size, resp. the complex assumption of these VRFs.

This study proposes a chosen-ciphertext side-channel attack against a lattice-based key encapsulation mechanism (KEM), the third-round candidate of the national institute of standards and technology (NIST) standardization project. Unlike existing attacks that target operations such as inverse NTT and message encoding/decoding, we target Barrett Reduction in the decapsulation phase of CRYSTALS-KYBER to obtain a secret key. We show that a sensitive variable-dependent leakage of Barrett Reduction exposes an entire secret key. The results of experiments conducted on the ARM Cortex-M4 microcontroller accomplish a success rate of 100%. We only need six chosen ciphertexts for KYBER512 and KYBER768 and eight chosen ciphertexts for KYBER1024. We also show that the m4 scheme of the pqm4 library, an implementation with the ARM Cortex-M4 specific optimization (typically in assembly), is vulnerable to the proposed attack. In this scheme, six, nine, and twelve chosen ciphertexts are required for KYBER512, KYBER768, and KYBER1024, respectively.

This paper presents a new public key cryptography scheme using multivariate polynomials over a finite field. Each multivariate polynomial from the public key is obtained by secretly and repeatedly composing affine transformations with series of quadratic polynomials (in a single variable). The main drawback of this scheme is the length of the public key.

Verifying security of advanced cryptographic primitives such as attribute-based encryption (ABE) is often difficult. In this work, we show how to break eleven schemes: two single-authority and nine multi-authority (MA) ABE schemes. Notably, we break DAC-MACS, a highly-cited multi-authority scheme, published at TIFS. This suggests that, indeed, verifying security of complex schemes is complicated, and may require simpler tools. The multi-authority attacks also illustrate that mistakes are made in transforming single-authority schemes into multi-authority ones. To simplify verifying security, we systematize our methods to a linear approach to analyzing generic security of ABE. Our approach is not only useful in analyzing existing schemes, but can also be applied during the design and reviewing of new schemes. As such, it can prevent the employment of insecure (MA-)ABE schemes in the future.

We study $(\ell,\ell)$-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The $(\ell,\ell)$-isogeny graph has cycles of small length that can be used to break the collision resistance assumption of the genus two isogeny hash function suggested by Takashima. Algorithms for computing $(2,2)$-isogenies on the level of Jacobians and $(3,3)$-isogenies on the level of Kummers are used to develop a genus two version of the supersingular isogeny Diffie--Hellman protocol of Jao and de~Feo. The genus two isogeny Diffie--Hellman protocol achieves the same level of security as SIDH but uses a prime with a third of the bit length.

The lattice-based cryptography is considered a strong candidate amongst many other proposed quantum-safe schemes for the currently deployed asymmetric cryptosystems that do not seem to stay secure when quantum computers come into play. Lattice-based algorithms possess a time-consuming operation of polynomial multiplication. As it is relatively the highest time-consuming operation in lattice-based cryptosystems, one can obtain fast polynomial multiplication by using number theoretic transform (NTT). In this paper, we focus on and develop a radix-3 NTT polynomial multiplication and compute its computational complexity. In addition, utilizing the ring structure, we propose two parameter sets of CRYSTALS-KYBER, one of the four round-three finalists in the NIST Post-Quantum Competition.

Anonymous attribute-based credentials (ABCs) are a powerful tool allowing users to authenticate while maintaining privacy. When instantiated from structure-preserving signatures on equivalence classes (SPS-EQ) we obtain a controlled form of malleability, and hence increased functionality and privacy for the user. Existing constructions consider equivalence classes on the message space, allowing the joint randomization of credentials and the corresponding signatures on them. In this work, we additionally consider equivalence classes on the signing-key space. In this regard, we obtain a signer-hiding notion, where the issuing organization is not revealed when a user shows a credential. To achieve this, we instantiate the ABC framework of Fuchsbauer, Hanser, and Slamanig (FHS19, Journal of Cryptology '19) with a recent SPS-EQ scheme (ASIACRYPT '19) modified to support a fully adaptive NIZK from the framework of Couteau and Hartmann (CRYPTO '20). We also show how to obtain mercurial signatures (CT-RSA '19), extending the application of our construction to anonymous delegatable credentials. To further increase functionality and efficiency, we augment the set-commitment scheme of FHS19 to support openings on attribute sets disjoint from those possessed by the user, while integrating a proof of exponentiation to allow for a more efficient verifier. Instantiating in the CRS model, we obtain an efficient credential system, anonymous under malicious organization keys, with increased expressiveness and privacy, proven secure in the standard model.

The seminal work of Heninger and Shacham (Crypto 2009) demonstrated a method for reconstructing secret RSA keys from artial information of the key components. In this paper we further investigate this approach but apply it to a different context that appears in some side-channel attacks. We assume a fixed-window exponentiation algorithm that leaks the equivalence between digits, without leaking the value of the digits themselves. We explain how to exploit the side-channel information with the Heninger-Shacham algorithm. To analyse the complexity of the approach, we model the attack as a Markov process and experimentally validate the accuracy of the model. Our model shows that the attack is feasible in the commonly used case where the window size is 5.

A ring signature is a digital signature scheme that allows identifying a group of possible signers without revealing the identity of the actual signer. In this paper, we first present a post-quantum sigma protocol for a ring that relies on the supersingular isogeny-based interactive zero-knowledge identification scheme proposed by De Feo, Jao, and Plût in 2014. Then, we construct a ring signature from the proposed sigma protocol for a ring by applying the Fiat-Shamir transform. In order to reduce the size of exchanges, we use Merkle trees and show that the signature size increases logarithmically in the size of the ring. The security proofs and complexity analyses of the proposed protocols are also provided.

The LESS signature scheme, introduced in 2020, represented a fresh start for code-based signatures. In this paper we explore advanced functionalities for signature schemes, stemming from the work of LESS. First, we adapt a recent protocol of Beullens et al. to obtain a construction for (linkable) ring signatures. Then, we realize an identity-based signature scheme following the traditional approach by Joye and Neven. Our performance numbers confirm that signature schemes based on the code equivalence problem have considerable potential for practical applications.

In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Groebner bases methods. Our main results include a connection between the solving degree and the last fall degree and one between the degree of regularity and the Castelnuovo-Mumford regularity.

Isogeny-based cryptography is a promising approach for post-quantum cryptography. The best-known protocol following that approach is the supersingular isogeny Diffie-Hellman protocol (SIDH); this protocol was turned into the CCA-secure key encapsulation mechanism SIKE, which was submitted to and remains in the third round of NIST's post-quantum standardization process as an ``alternate'' candidate. Isogeny-based cryptography generally relies on the conjectured hardness of computing an isogeny between two isogenous elliptic curves, and most cryptanalytic work referenced on SIKE's webpage exclusively focuses on that problem. Interestingly, the hardness of this problem is sufficient for neither SIDH nor SIKE. In particular, these protocols reveal additional information on the secret isogeny, in the form of images of specific torsion points through the isogeny. This paper surveys existing cryptanalysis approaches exploiting this often called ``torsion point information'', summarizes their current impact on SIKE and related algorithms, and suggests some research directions that might lead to further impact.

Multi-Key fully homomorphic encryption (MKFHE) allows computations on data encrypted by different parties. One disadvantage of previous MKFHE schemes is that the ciphertext size increases linearly or squarely with respect to the number of parties. It incurs a heavy communication and computation burden for the homomorphic evaluation, especially when the number of involved parties is large. In this paper, we propose the first method to construct MKFHE scheme while keeping the size of the ciphertext and corresponding evaluation key to be independent of the number of parties during the homomorphic evaluation. Specifically, we construct efficient compact MKFHE schemes with various advantages. On the one hand, we show how to construct compact MKFHE schemes which support the homomorphic encryption of ring elements and are friendly to floating point numbers. On the other hand, we give a compact MKFHE scheme that supports high efficient bootstrapping. In our paper, we show a novel method to reduce the cost of generating these evaluation keys from a quadratic time to a linear time with respect to the number of parties.

Over the past decade, cryptocurrency has been undergoing a rapid development. Digital wallet, as the tool to store and manage the cryptographic keys, is the primary entrance for the public to access cryptocurrency assets. Hierarchical Deterministic Wallet (HDW), proposed in Bitcoin Improvement Proposal 32 (BIP32), has attracted much attention and been widely used in the community, due to its virtues such as easy backup/recovery, convenient cold-address management, and supporting trust-less audits and applications in hierarchical organizations. While HDW allows the wallet owner to generate and manage his keys conveniently, Stealth Address (SA) allows a payer to generate fresh address (i.e., public key) for the receiver without any interaction, so that users can achieve ``one coin each address" in a very convenient manner, which is widely regarded as a simple but effective way to protect user privacy. Consequently, SA has also attracted much attention and been widely used in the community. However, as so far, there is not a secure wallet algorithm that provides the virtues of both HDW and SA. Actually, even for standalone HDW, to the best of our knowledge, there is no strict definition of syntax and models that captures the functionality and security (i.e., safety of coins and privacy of users) requirements that practical scenarios in cryptocurrency impose on wallet. As a result, the existing wallet algorithms either have (potential) security flaws or lack crucial functionality features. In this work, we formally define the syntax and security models of Hierarchical Deterministic Wallet supporting Stealth Address (HDWSA), capturing the functionality and security (including safety and privacy) requirements imposed by the practice in cryptocurrency, which include all the versatile functionalities that lead to the popularity of HDW and SA as well as all the security guarantees that underlie these functionalities. We propose a concrete HDWSA construction and prove its security in the random oracle model. We implement our scheme and the experimental results show that the efficiency is suitable for typical cryptocurrency settings.

Cryptosystems have been developed over the years under the typical prevalent setting which assumes that the receiver’s key is kept secure from the adversary, and that the choice of the message to be sent is freely performed by the sender and is kept secure from the adversary as well. Under these fundamental and basic operational assumptions, modern Cryptography has flourished over the last half a century or so, with amazing achievements: New systems (including public-key Cryptography), beautiful and useful models (including security definitions such as semantic security), and new primitives (such as zero-knowledge proofs) have been developed. Furthermore, these fundamental achievements have been translated into actual working systems, and span many of the daily human activities over the Internet. However, in recent years, there is an overgrowing pressure from many governments to allow the government itself access to keys and messages of encryption systems (under various names: escrow encryption, emergency access, communication decency acts, etc.). Numerous non-direct arguments against such policies have been raised, such as "the bad guys can utilize other encryption system" so all other cryptosystems have to be declared illegal, or that "allowing the government access is an ill-advised policy since it creates a natural weak systems security point, which may attract others (to masquerade as the government)." It has remained a fundamental open issue, though, to show directly that the above mentioned efforts by a government (called here “a dictator” for brevity) which mandate breaking of the basic operational assumption (and disallowing other cryptosystems), is, in fact, a futile exercise. This is a direct technical point which needs to be made and has not been made to date. In this work, as a technical demonstration of the futility of the dictator’s demands, we invent the notion of “Anamorphic Encryption” which shows that even if the dictator gets the keys and the messages used in the system (before anything is sent) and no other system is allowed, there is a covert way within the context of well established public-key cryptosystems for an entity to immediately (with no latency) send piggybacked secure messages which are, in spite of the stringent dictator conditions, hidden from the dictator itself! We feel that this may be an important direct technical argument against the nature of governments’ attempts to police the use of strong cryptographic systems, and we hope to stimulate further works in this direction.

This work describes the Mitaka signature scheme: a new hash-and-sign signature scheme over NTRU lattices which can be seen as a variant of NIST finalist Falcon. It achieves comparable efficiency but is considerably simpler, online/offline, and easier to parallelize and protect against side-channels, thus offering significant advantages from an implementation standpoint. It is also much more versatile in terms of parameter selection. We obtain this signature scheme by replacing the FFO lattice Gaussian sampler in Falcon by the ``hybrid'' sampler of Ducas and Prest, for which we carry out a detailed and corrected security analysis. In principle, such a change can result in a substantial security loss, but we show that this loss can be largely mitigated using new techniques in key generation that allow us to construct much higher quality lattice trapdoors for the hybrid sampler relatively cheaply. This new approach can also be instantiated on a wide variety of base fields, in contrast with Falcon's restriction to power-of-two cyclotomics. We also introduce a new lattice Gaussian sampler with the same quality and efficiency, but which is moreover compatible with the integral matrix Gram root technique of Ducas et al., allowing us to avoid floating point arithmetic. This makes it possible to realize the same signature scheme as Mitaka efficiently on platforms with poor support for floating point numbers. Finally, we describe a provably secure masking of Mitaka. More precisely, we introduce novel gadgets that allow provable masking at any order at much lower cost than previous masking techniques for Gaussian sampling-based signature schemes, for cheap and dependable side-channel protection.

An important theme in research on attribute-based encryption (ABE) is minimizing the sizes of the secret keys and ciphertexts. In this work, we present two new ABE schemes with *constant-size* secret keys, that is, the key size is independent of the sizes of policies or attributes, and dependent only on the security parameter lambda. * We construct the first key-policy ABE scheme for circuits with constant-size secret keys, |sk_f|=poly(lambda), which concretely consist of only three group elements. The previous state-of-the-art construction by [Boneh et al., Eurocrypt '14] has key size polynomial in the maximum depth d of the policy circuits, |sk_f|=poly(d,lambda). Our new scheme removes this dependency of key size on d while keeping the ciphertext size the same, which grows linearly in the attribute length and polynomially in the maximal depth, |ct|=|x|poly(d,lambda). * We present the first ciphertext-policy ABE scheme for Boolean formulae that simultaneously has constant-size keys and succinct ciphertexts of size independent of the policy formulae, in particular, |sk_f|=poly(lambda) and |ct_x|=poly(|x|,lambda). Concretely, each secret key consists of only two group elements. Previous ciphertext-policy ABE schemes either have succinct ciphertexts but non constant-size keys [Agrawal--Yamada, Eurocrypt '20; Agrawal--Wichs--Yamada, TCC '20], or constant-size keys but large ciphertexts that grow with the policy size, as well as the attribute length. Our second construction is the first ABE scheme achieving *double succinctness*, where both keys and ciphertexts are smaller than the corresponding attributes and policies tied to them. Our constructions feature new ways of combining lattices with pairing groups for building ABE and are proven selectively secure based on LWE and in the generic (pairing) group model. We further show that when replacing the LWE assumption with its adaptive variant introduced in [Quach--Wee--Wichs FOCS '18] the constructions become adaptively secure.

Anonymous attestation for secure hardware platforms leverages tailored group signature schemes and assumes the hardware to be trusted. Yet, there is an ever increasing concern on the trustworthiness of hardware components and embedded systems. A subverted hardware may, for example, use its signatures to exfiltrate identifying information or even the signing key. In this paper we focus on Enhanced Privacy ID (EPID)---a popular anonymous attestation scheme used in commodity secure hardware platforms like Intel SGX. We define and instantiate a \emph{subversion resilient} EPID scheme (or SR-EPID). In a nutshell, SR-EPID provides the same functionality and security guarantees of the original EPID, despite potentially subverted hardware. In our design, a ``sanitizer'' ensures no covert channel between the hardware and the outside world both during enrollment and during attestation (i.e., when signatures are produced). We design a practical SR-EPID scheme secure against adaptive corruptions and based on a novel combination of malleable NIZKs and hash functions modeled as random oracles. Our approach has a number of advantages over alternative designs. Namely, the sanitizer bears no secret information---hence, a memory leak does not erode security. Further, the role of sanitizer may be distributed in a cascade fashion among several parties so that sanitization becomes effective as long as one of the parties has access to a good source of randomness. Also, we keep the signing protocol non-interactive, thereby minimizing latency during signature generation.

We consider the use of supersingular abelian surfaces in cryptography. Several generalisations of well-known cryptographic schemes and constructions based on supersingular elliptic curves to the 2-dimensional setting of superspecial abelian surfaces have been proposed. The computational assumptions in the superspecial 2-dimensional case can be reduced to the corresponding 1-dimensional problems via a product decomposition by observing that every superspecial abelian surface is non-simple and separably isogenous to a product of supersingular elliptic curves. Instead, we propose to use supersingular non-superspecial isogeny graphs where such a product decomposition does not have a computable description via separable isogenies. We study the advantages and investigate security concerns of the move to supersingular non-superspecial abelian surfaces.

Side-stepping the protection provided by cryptography, exfiltration attacks are becoming a considerable real-world threat. With the goal of mitigating the exfiltration of cryptographic keys, big-key cryptosystems have been developed over the past few years. These systems come with very large secret keys which are thus hard to exfiltrate. Typically, in such systems, the setup time must be large as it generates the large secret key. However, subsequently, the encryption and decryption operations, that must be performed repeatedly, are required to be efficient. Specifically, the encryption uses only a small public key and the decryption only accesses small ciphertext-dependent parts of the full secret key. Nonetheless, these schemes require decryption to have access to the entire secret key. Thus, using such big-key cryptosystems necessitate that users carry around large secret keys on their devices, which can be a hassle and in some cases might also render exfiltration easy. With the goal of removing this problem, in this work, we initiate the study of big-key identity-based encryption (bk-IBE). In such a system, the master secret key is allowed to be large but we require that the identity-based secret keys are short. This allows users to use the identity-based short keys as the ephemeral secret keys that can be more easily carried around and allow for decrypting ciphertexts matching a particular identity, e.g. messages that were encrypted on a particular date. In particular: -We build a new definitional framework for bk-IBE capturing a range of applications. In the case when the exfiltration is small our definition promises stronger security --- namely, an adversary can break semantic security for only a few identities, proportional to the amount of leakage it gets. In contrast, in the catastrophic case where a large fraction of the master secret key has been ex-filtrated, we can still resort to a guarantee that the ciphertexts generated for a randomly chosen identity (or, an identity with enough entropy) remain protected. We demonstrate how this framework captures the best possible security guarantees. -We show the first construction of such a bk-IBE offering strong security properties. Our construction is based on standard assumptions on groups with bilinear pairings and brings together techniques from seemingly different contexts such as leakage resilient cryptography, reusable two-round MPC, and laconic oblivious transfer. We expect our techniques to be of independent interest.

Code-based cryptography received attention after the NIST started the post-quantum cryptography standardization process in 2016. A central NP-hard problem is the binary syndrome decoding problem, on which the security of many code-based cryptosystems lies. The best known methods to solve this problem all stem from the information-set decoding strategy, first introduced by Prange in 1962. A recent line of work considers augmented versions of this strategy, with hints typically provided by side-channel information. In this work, we consider the integer syndrome decoding problem, where the integer syndrome is available but might be noisy. We study how the performance of the decoder is affected by the noise. We provide experimental results on cryptographic parameters for the BIKE and Classic McEliece cryptosystems, which are finalist and alternate candidates for the third round of the NIST standardization process, respectively.

The ability to trust a system to act safely and securely strongly relies on the integrity of the software that it runs. To guarantee authenticity of the software one can include cryptographic data such as digital signatures on application images that can only be generated by trusted parties. These are typically based on cryptographic primitives such as Rivest-Shamir-Adleman (RSA) or Elliptic-Curve Cryptography (ECC), whose security will be lost whenever a large enough quantum computer is built. For that reason, migration towards Post-Quantum Cryptography (PQC) is necessary. This paper investigates the practical impact of migrating the secure boot flow on a Vehicle Network Processor (S32G274A) towards PQC. We create a low-memory fault-attack- resistant implementation of the Dilithium signature verification algorithm and evaluate its impact on the boot flow.

Threshold signature schemes enable distribution of the signature issuing capability to multiple users, to mitigate the threat of signing key compromise. Though a classic primitive, these signatures have witnessed a surge of interest in recent times due to relevance to modern applications like blockchains and cryptocurrencies. In this work, we study round-optimal threshold signatures in the post- quantum regime and improve the only known lattice-based construction by Boneh et al [CRYPTO’18] as follows: • Efficiency. We reduce the amount of noise flooding used in the construction from $2^{\Omega(\lambda)}$ down to $\sqrt{Q}$, where $Q$ is the bound on the number of generated signatures and $\lambda$ is the security parameter. By using lattice hardness assumptions over polynomial rings, this allows to decrease the signature bit-lengths from $\widetilde{O}(\lambda^3)$ to~$\widetilde{O}(\lambda)$, bringing them significantly closer to practice. Our improvement relies on a careful analysis using Rényi divergence rather than statistical distance in the security proof. • Instantiation. The construction of Boneh et al requires a standard signature scheme to be evaluated homomorphically. To instantiate this, we provide a homomorphism-friendly variant of Lyubashevsky’s signature [EUROCRYPT ’12] which achieves low circuit depth by being “rejection-free” and uses an optimal, moderate noise flooding of $\sqrt{Q}$, matching the above. • Towards Adaptive Security. The construction of Boneh et al satisfies only selective security, where all the corrupted parties must be announced before any signing query is made. We improve this in two ways: in the Random Oracle Model, we obtain partial adaptivity where signing queries can be made before the corrupted parties are announced but the set of corrupted parties must be announced all at once. In the standard model, we obtain full adaptivity, where parties can be corrupted at any time but this construction is in a weaker pre-processing model where signers must be provided correlated randomness of length proportional to the number of signatures, in an offline preprocessing phase.

Functional Encryption (FE) allows users who hold a specific decryption key, to learn a specific function of encrypted data while the actual plaintexts remain private. While FE is still in its infancy, it is our strong belief that in the years to come, this remarkable cryptographic primitive will have matured to the degree that will make it an integral part of access control systems, especially cloud-based ones. To this end, we believe it is of great importance to provide not only theoretical and generic constructions but also concrete instantiations of FE schemes from well-studied cryptographic assumptions. Therefore, in this paper, we undertake the task of presenting two instantiations of the generic work presented in [8] from the Decisional Diffie-Hellman (DDH) problem that also satisfies the property of verifiable decryption. Moreover, we present a novel multi-input FE (MIFE) scheme, that can be instantiated from Regev's cryptosystem, and thus remains secure even against quantum adversaries. Finally, we provide a multi-party computation (MPC) protocol that allows our MIFE construction to be deployed in the multi-client mode

We investigate the security assumptions behind three public-key quantum money schemes. Aaronson and Christiano proposed a scheme based on hidden subspaces of the vector space $\mathbb{F}_2^n$ in 2012. It was conjectured by Pena et al in 2015 that the hard problem underlying the scheme can be solved in quasi-polynomial time. We confirm this conjecture by giving a polynomial time quantum algorithm for the underlying problem. Our algorithm is based on computing the Zariski tangent space of a random point in the hidden subspace. Zhandry proposed a scheme based on multivariate hash functions in 2017. We give a polynomial time quantum algorithm for cloning a money state with high probability. Our algorithm uses the verification circuit of the scheme to produce a banknote from a given serial number. Kane proposed a scheme based on modular forms in 2018. The underlying hard problem in Kane's scheme is cloning a quantum state that represents an eigenvector of a set of Hecke operators. We give a polynomial time quantum reduction from this hard problem to a linear algebra problem. The latter problem is much easier to understand, and we hope that our reduction opens new avenues to future cryptanalyses of this scheme.

Unlike conventional ABE systems, which support Boolean attributes (with only 2 states: "1" and "0", or "Present" and "Absent"), weighted Attribute-based encryption schemes also support numerical values attached to attributes, and each terminal node of the access structure contains a threshold for a minimum weight. We propose a weighted ABE system, with access policy of logarithmic expansion, by dividing each weighted attribute in sub-attributes. On top of that, we show that the decryption can be parallelized, leading to a notable improvement in running time, compared to the serial version.

In a set membership proof, the public information consists of a set of elements and a commitment. The prover then produces a zero-knowledge proof showing that the commitment is indeed to some element from the set. This primitive is closely related to concepts like ring signatures and ``one-out-of-many'' proofs that underlie many anonymity and privacy protocols. The main result of this work is a new succinct lattice-based set membership proof whose size is logarithmic in the size of the set. We also give a transformation of our set membership proof to a ring signature scheme. The ring signature size is also logarithmic in the size of the public key set and has size $16$ KB for a set of $2^5$ elements, and $22$ KB for a set of size $2^{25}$. At an approximately $128$-bit security level, these outputs are between 1.5X and 7X smaller than the current state of the art succinct ring signatures of Beullens et al. (Asiacrypt 2020) and Esgin et al. (CCS 2019). We then show that our ring signature, combined with a few other techniques and optimizations, can be turned into a fairly efficient Monero-like confidential transaction system based on the MatRiCT framework of Esgin et al. (CCS 2019). With our new techniques, we are able to reduce the transaction proof size by factors of about 4X - 10X over the aforementioned work. For example, a transaction with two inputs and two outputs, where each input is hidden among $2^{15}$ other accounts, requires approximately $30$KB in our protocol.

In 2018, the longest vector problem and closest vector problem in local fields were introduced, as the p-adic analogues of the shortest vector problem and closest vector problem in lattices of Euclidean spaces. They are considered to be hard and useful in constructing cryptographic primitives, but no applications in cryptography were given. In this paper, we construct the first signature scheme and public-key encryption cryptosystem based on p-adic lattice by proposing a trapdoor function with the orthogonal basis of p-adic lattice. These cryptographic schemes have reasonable key size and efficiency, which shows that p-adic lattice can be a new alternative to construct cryptographic primitives and well worth studying.

With the recent shift to post-quantum algorithms it becomes increasingly important to provide precise bit-security estimates for code-based cryptography such as McEliece and quasi-cyclic schemes like BIKE and HQC. While there has been significant progress on information set decoding (ISD) algorithms within the last decade, it is still unclear to which extent this affects current cryptographic security estimates. We provide the first concrete implementations for representation-based ISD, such as May-Meurer-Thomae (MMT) or Becker-Joux-May-Meurer (BJMM), that are parameter-optimized for the McEliece and quasi-cyclic setting. Although MMT and BJMM consume more memory than naive ISD algorithms like Prange, we demonstrate that these algorithms lead to significant speedups for practical cryptanalysis on medium-sized instances (around 60 bit). More concretely, we provide data for the record computations of McEliece-1223 and McEliece-1284 (old record: 1161), and for the quasi-cyclic setting up to code length 2918 (before: 1938). Based on our record computations we extrapolate to the bit-security level of the proposed BIKE, HQC and McEliece parameters in NIST's standardization process. For BIKE/HQC, we also show how to transfer the Decoding-One-Out-of-Many (DOOM) technique to MMT/BJMM. Although we achieve significant DOOM speedups, our estimates confirm the bit-security levels of BIKE and HQC. For the proposed McEliece round-3 parameter sets of 192 and 256 bit, however, our extrapolation indicates a security level overestimate by roughly 20 and 10 bits, respectively, i.e., the high-security McEliece instantiations may be a bit less secure than desired.

MPC-in-the-head based zero-knowledge proofs allow one to prove knowledge of a preimage for a circuit defined over a finite field F. In recent proofs the soundness depends on the size F, and small fields require more parallel repetitions, and therefore produce larger proofs. In this paper we develop and systematically apply lifting strategies to such proof protocols in order to increase soundness and reduce proof size. The strategies are (i) lifting parts of the protocol to extension fields of F, (ii) using reverse- multiplication friendly embeddings to pack elements of F into a larger field and (iii) to use an alternative circuit representation. Using a combination of these strategies at different points in the protocol, we design two new proof systems well suited to small circuits defined over small fields. As a case study we consider efficient constructions of post-quantum signatures, where a signature is a proof of knowledge of a one-way function preimage, and two commonly used one-way functions are defined over small fields (AES and LowMC). We find that carefully applying these lifting strategies gives shorter signatures than the state-of-the-art: our AES-based signatures are 1.3x shorter than Banquet (PKC 2021) and our LowMC-based signatures are almost 2x shorter than the NIST-candidate algorithm Picnic3. We implement our schemes and provide benchmarks. Finally, we also give other optimizations: some generally applicable to this class of proofs, and some specific to the circuits we focused on.

Identifying the concrete hardness of the discrete logarithm problem is crucial for instantiating a vast range of cryptographic schemes. Towards this goal, Corrigan-Gibbs and Kogan (EUROCRYPT '18) extended the generic-group model for capturing "preprocessing" algorithms, offering a tradeoff between the space $S$ required for storing their preprocessing information, the time $T$ required for their online phase, and their success probability. Corrigan-Gibbs and Kogan proved an upper bound of $\widetilde{O}(S T^2/N)$ on the success probability of any such algorithm, where $N$ is the prime order of the group, matching the known preprocessing algorithms. However, the known algorithms assume the availability of truly random hash functions, without taking into account the space required for storing them as part of the preprocessing information, and the time required for evaluating them in essentially each and every step of the online phase. This led Corrigan-Gibbs and Kogan to pose the open problem of designing a discrete-logarithm preprocessing algorithm that is fully constructive in the sense that it relies on explicit hash functions whose description lengths and evaluation times are taken into account in the algorithm's space-time tradeoff. We present a fully constructive discrete-logarithm preprocessing algorithm with an asymptotically optimal space-time tradeoff (i.e., with success probability $\widetilde{\Omega}(S T^2/N)$). In addition, we obtain an algorithm that settles the corresponding tradeoff for the computational Diffie-Hellman problem. Our approach is based on derandomization techniques that provide rather weak independence guarantees. On the one hand, we show that such guarantees can be realized in our setting with only a minor efficiency overhead. On the other hand, exploiting such weak guarantees requires a more subtle and in-depth analysis of the underlying combinatorial structure compared to that of the known preprocessing algorithms and their analyses.