In a Multi-Client Functional Encryption (MCFE) scheme, $n$ clients each obtain a secret encryption key from a trusted authority. During each time step $t$, each client $i$ can encrypt its data using its secret key. The authority can use its master secret key to compute a functional key given a function $f$, and the functional key can be applied to a collection of $n$ clients’ ciphertexts encrypted to the same time step, resulting in the outcome of $f$ on the clients’ data. In this paper, we focus on MCFE for inner-product computations. If an MCFE scheme hides not only the clients’ data, but also the function $f$, we say it is function hiding. Although MCFE for inner-product computation has been extensively studied, how to achieve function privacy is still poorly understood. The very recent work of Agrawal et al. showed how to construct a function-hiding MCFE scheme for inner-product assuming standard bilinear group assumptions; however, they assume the existence of a random oracle and prove only a relaxed, selective security notion. An intriguing open question is whether we can achieve function-hiding MCFE for inner-product without random oracles. In this work, we are the first to show a function-hiding MCFE scheme for inner products, relying on standard bilinear group assumptions. Further, we prove adaptive security without the use of a random oracle. Our scheme also achieves succinct ciphertexts, that is, each coordinate in the plaintext vector encrypts to only $O(1$) group elements. Our main technical contribution is a new upgrade from single-input functional encryption for inner-products to a multi-client one. Our upgrade preserves function privacy, that is, if the original single-input scheme is function-hiding, so is the resulting multi-client construction. Further, this new upgrade allows us to obtain a conceptually simple construction.

CSI-FiSh is one of the most efficient isogeny-based signature schemes, which is proven to be secure in the Quantum Random Oracle Model (QROM). However, there is a bottleneck in CSI-FiSh in the threshold setting, which is that its public key needs to be generated by using $k-1$ secret keys. This leads to very inefficient threshold key generation protocols and also forces the parties to store $k-1$ secret shares. We present CSI-SharK, a new variant of $\textit{CSI}$-FiSh that has more $\textit{Shar}$ing-friendly $\textit{K}$eys and is as efficient as the original scheme. This is accomplished by modifying the public key of the ID protocol, used in the original CSI-FiSh, to the equal length Structured Public Key (SPK), generated by a $\textit{single}$ secret key, and then proving that the modified ID protocol and the resulting signature scheme remain secure in the QROM. We translate existing CSI-FiSh-based threshold signatures and Distributed Key Generation (DKG) protocols to the CSI-SharK setting. We find that DKG schemes based on CSI-SharK outperform the state-of-the-art actively secure DKG protocols from the literature by a factor of about $3$, while also strongly reducing the communication cost between the parties. We also uncover and discuss a flaw in the key generation of the actively secure CSI-FiSh based threshold signature $\textit{Sashimi}$, that can prevent parties from signing. Finally, we discuss how (distributed) key generation and signature schemes in the isogeny setting are strongly parallelizable and we show that by using $C$ independent CPU threads, the total runtime of such schemes can basically be reduced by a factor $C$. As multiple threads are standard in modern CPU architecture, this parallelizability is a strong incentive towards using isogeny-based (distributed) key generation and signature schemes in practical scenarios.

On-line/off-line encryption schemes enable the fast encryption of a message from a pre-computed coupon. The paradigm was put forward in the case of digital signatures. This work introduces a compact public-key additively homomorphic encryption scheme. The scheme is semantically secure under the decisional composite residuosity (DCR) assumption. Compared to Paillier cryptosystem, it merely requires one or two integer additions in the on-line phase and no increase in the ciphertext size. This work also introduces a compact on-line/off-line trapdoor commitment scheme featuring the same fast on-line phase. Finally, applications to chameleon signatures are presented.

This note introduces a public-key variant of TFHE. The output ciphertexts are of LWE type. Interestingly, the public key is shorter and the resulting ciphertexts are less noisy. The security of the scheme holds under the standard RLWE assumption. Several variations and extensions are also described.

In this paper we introduce a novel version of the Joye-Libert cryptosystem that allows users to decrypt without knowing the factorisation of the composite modulus. Then we use our construction as a building block for a threshold decryption protocol of the homomorphic Joye-Libert encryption scheme. Finally, we present several extensions of the threshold cryptosystem.

We cryptanalyse the isogeny-based public key encryption schemes SHealS and HealS, and the key exchange scheme HealSIDH of Fouotsa and Petit from Asiacrypt 2021.

We present an approach for designing fast public key encryption cryptosystems using random primitives and error permutation. An encryption speed of such systems allows to use them for “on-the-fly” public key encryption and makes them useful for real-time communications. A small error size allows to use this approach for designing digital signature schemes

Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalisation of Diffie-Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.

Wave is a provably EUF-CMA (existential unforgeability under adaptive chosen message attacks) digital signature scheme based on codes \cite{DST19a}. It is an hash-and-sign primitive and its security is built according to a GPV-like framework \cite{GPV08} under two assumptions related to coding theory: (i) the hardness of finding a word of prescribed Hamming weight and prescribed syndrome, and (ii) the pseudo-randomness of ternary generalized $(U|U+V)$ codes. Forgery attacks (i)---or message attacks---consist in solving the ternary decoding problem for large weight \cite{BCDL19}, while, to the best of our knowledge, key attacks (ii) will try to exhibit words that are characteristic of $(U|U+V)$ codes, which are called type-U or type-V codewords in the present paper. In the current state-of-the-art, the best known attacks both reduce to various flavours of Information Set Decoding (ISD) algorithms for different regime of parameters. In this paper we give estimates for the complexities of the best known ISD variants for those regimes. Maximizing the computational effort, thus the security, for both attacks lead to conflicting constraints on the parameters. We provide here a methodology to derive optimal trade-offs for selecting parameters for the Wave signature scheme achieving a given security. We apply this methodology to the current state-of-the-art and propose some effective parameters for Wave. For $\lambda=128$ bits of classical security, the signature is $737$ bytes long, scaling linearly with the security, and the public key size is $3.6$ Mbytes, scaling quadratically with the security.

We propose hinTS --- a new threshold signature scheme built on top of the widely used BLS signatures. Our scheme enjoys the following attractive features: \begin{itemize} \item A {\em silent setup} process where the joint public key of the parties is computed as a deterministic function of their locally computed public keys. \item Support for {\em dynamic} choice of thresholds and signers, after the silent setup, without further interaction. \item Support for {\em general} access policies; in particular, native support for {\em weighted} thresholds with zero additional overhead over standard threshold setting. \item Strong security guarantees, including proactive security and forward security. \end{itemize}We prove the security of our scheme in the algebraic group model and provide implementation and extensive evaluation. Our scheme outperforms all prior proposals that aim to avoid distributed key generation in terms of aggregation time, signature size, and verification time. As an example, the aggregation time for 1000 signers is under 0.5 seconds, while both signing and verification are constant time algorithms, taking roundly 1 ms and 17.5 ms respectively. The key technical contribution of our work involves the design of special-purpose succinct proofs to {\em efficiently} prove the well-formedness of aggregated public keys. Our solution uses public ``hints'' released by the signers as part of their public keys (hence the name hinTS).

This paper presents the first decentralized multi-authority attribute-based inner product functional encryption (MA-ABIPFE) schemes supporting vectors of a priori unbounded lengths. The notion of AB-IPFE, introduced by Abdalla et al. [ASIACRYPT 2020], combines the access control functionality of attribute-based encryption (ABE) with the possibility of evaluating linear functions on encrypted data. A decentralized MA-ABIPFE defined by Agrawal et al. [TCC 2021] essentially enhances the ABE component of AB-IPFE to the decentralized multi-authority setting where several authorities can independently issue user keys involving attributes under their control. In MA-ABIPFE for unbounded vectors (MA-ABUIPFE), encryptors can encrypt vectors of arbitrary length under access policies of their choice whereas authorities can issue secret keys to users involving attributes under their control and vectors of arbitrary lengths. Decryption works in the same way as for MA-ABIPFE provided the lengths of the vectors within the ciphertext and secret keys match. We present two MA-ABUIPFE schemes supporting access policies realizable by linear secret sharing schemes (LSSS), in the significantly faster prime-order bilinear groups under decisional assumptions based on the target groups which are known to be weaker compared to their counterparts based in the source groups. The proposed schemes demonstrate different trade-offs between versatility and underlying assumptions. The first scheme allows each authority to control a bounded number of attributes and is proven secure under the well-studied decisional bilinear Diffie-Hellman (DBDH) assumption. On the other hand, the second scheme allows authorities to control exponentially many attributes, that is, supports large attribute universe, and is proven secure under a non-interactive q-type variant of the DBDH assumption called L-DBDH, similar to what was used in prior large-universe multi-authority ABE (MA-ABE) construction. When compared with the only known MA-ABIPFE scheme due to Agrawal et al. [TCC 2021], our schemes offer significantly higher efficiency while offering greater flexibility and security under weaker assumptions at the same time. Moreover, unlike Agrawal et al., our schemes can support the appearance of the same attributes within an access policy arbitrarily many times. Since efficiency and practicality is the prime focus of this work, we prove the security of our constructions in the random oracle model against static adversaries similar to prior works on MA-ABE with similar motivations and assumptions. On the technical side, we extend the unbounded IPFE techniques of Dufour-Sans and Pointcheval [ACNS 2019] to the context of MA-ABUIPFE by introducing a novel hash-decomposition technique.

In this paper, we show how to use the Matrix Code Equivalence (MCE) problem as a new basis to construct signature schemes. This extends previous work on using isomorphism problems for signature schemes, a trend that has recently emerged in post-quantum cryptography. Our new formulation leverages a more general problem and allows for smaller data sizes, achieving competitive performance and great flexibility. Using MCE, we construct a zero-knowledge protocol which we turn into a signature scheme named Matrix Equivalence Digital Signature (MEDS). We provide an initial choice of parameters for MEDS, tailored to NIST's Category 1 security level, yielding public keys as small as 2.8 kB and signatures ranging from 18 kB to just around 6.5 kB, along with a reference implementation in C.

In post-quantum cryptography, hash-based signature schemes are attractive choices because of the weak assumptions. Most existing hash-based signature schemes are proven secure against post-quantum chosen message attacks (CMAs), where the adversaries are able to execute quantum computations and classically query to the signing oracle. In some cases, the signing oracle is also considered quantum-accessible, meaning that the adversaries are able to send queries with superpositions to the signing oracle. Considering this, Boneh and Zhandry [BZ13] propose a stronger security notion called existential unforgeability under quantum chosen message attacks (EUF-qCMA). We call it quantum-access security (or Q2 security in some literature). The quantum-access security of practical signature schemes is lacking in research, especially of the hash-based ones. In this paper, we analyze the quantum-access security of hash-based signature schemes in two directions. First, we show concrete quantum chosen message attacks (or superposition attacks) on existing hash-based signature schemes, such as SPHINCS and SPHINCS+. The complexity of the attacks is obviously lower than that of optimal classical chosen message attacks, implying that quantum chosen message attacks are more threatening than classical ones to these schemes. Second, we propose a simple variant of SPHINCS+ and give security proof against quantum chosen message attacks. As far as we know, it is the first practical hash-based stateless signature scheme against quantum chosen message attacks with concrete provable security.

In this paper, we study the compartment-based and hierarchical delegation of signing power of the verifiable accountable subgroup multi-signature (vASM). ASM is a multi-signature in which the participants are accountable for the resulting signature, and the number of participants is not fixed. After Micali et al.’s and Boneh et al.’s ASM schemes, the verifiable-ASM (vASM) scheme with a verifiable group setup and more efficient verification phase was proposed recently. The verifiable group setup in vASM verifies the participants at the group setup phase. In this work, we show that the vASM scheme can also be considered as a proxy signature in which an authorized user (original signer, designator) delegates her signing rights to a single (or a group of) unauthorized user(s) (proxy signer). Namely, we propose four new constructions with the properties and functionalities of an ideal proxy signature and a compartment-based/hierarchical structure. In the first construction, we apply the vASM scheme recursively; in the second one, we use Shamir’s secret sharing (SSS) scheme; in the third construction, we use SSS again but in a nested fashion. In the last one, we use the hierarchical threshold secret sharing (HTSS) scheme for delegation. Then, we show the affiliation of our constructions to proxy signatures and compare our constructions with each other in terms of efficiency and security. Finally we compare the vASM scheme with the existing pairing-based proxy signature schemes.

DME is a multivariate public key cryptosystem based on the composition of linear and exponential maps that allow the polynomials of the public key to be of a very high degree. A previous version of DME was presented to the NIST call (in the KEM category). The new version of DME adds one or two extra rounds of exponentials to the original two rounds. With this setting the composition gives a deterministic trapdoor one way permutation, which can be combined with an OAEP padding scheme for KEM and PSS00 for signature. In this paper we give the SUPERCOP timing of DME-OAEP and DME-PSS00 for three and four exponentials and compare them with NIST finalists. For NIST security level 5 the size of ciphertext and signature is only 64 bytes.

In this paper, we present a side-channel analysis (SCA) on key encapsulation mechanisms (KEMs) based on the Fujisaki–Okamoto (FO) transformation and its variants. Many post-quantum KEMs usually perform re-encryption during key decapsulation to achieve chosen-ciphertext attack (CCA) security. The side-channel leakage of re-encryption can be exploited to mount a key-recovery plaintext-checking attack (KR-PCA), even if the chosen-plaintext attack (CCA) secure decryption constructing the KEM is securely implemented. Herein, we propose an efficient side-channel-assisted KR-PCA on post-quantum KEMs, and achieve a key recovery with significantly fewer attack traces than existing ones in TCHES 2022 and 2023. The basic concept of the proposed attack is to introduce a new KR-PCA based on a multiple-valued (MV-)PC oracle and then implement a dedicated MV-PC oracle based on a multi-classification neural network (NN). The proposed attack is applicable to the NIST PQC selected algorithm Kyber and the similar lattice-based Saber, FrodoKEM and NTRU Prime, as well as SIKE. We also present how to realize a sufficiently reliable MV-PC oracle from NN model outputs that are not 100% accurate, and analyze the tradeoff between the key recovery success rate and the number of attack traces. We assess the feasibility of the proposed attack through attack experiments on three typical symmetric primitives to instantiate a random oracle (SHAKE, SHA3, and AES software). The proposed attack reduces the number of attack traces required for a reliable key recovery by up to 87% compared to the existing attacks against Kyber and other lattice-based KEMs, under the condition of 99.9999% success rate for key recovery. The proposed attack can also reduce the number of attack traces by 85% for SIKE.

Pairing-based cryptographic protocols are typically vulnerable to small-subgroup attacks in the absence of protective measures. To thwart them, one of feasible measures is to execute subgroup membership testings, which are generally considered expensive. Recently, Scott proposed an efficient method of subgroup membership testings for $\mathbb{G}_1$, $\mathbb{G}_2$ and $\mathbb{G}_T$ on the BLS family. In this paper, we generalize this method proposed by Scott and show that the new technique is applicable to a large class of pairing-friendly curves. In addition, we also confirm that the new method leads to a significant speedup for membership testings on many popular pairing-friendly curves.

Adaptor signatures are a novel cryptographic primitive with important applications for cryptocurrencies. They have been used to construct second layer solutions such as payment channels or cross-currency swaps. The basic idea of an adaptor signature scheme is to tie the signing process to the revelation of a secret value in the sense that, much like a regular signature scheme, an adaptor signature scheme can authenticate messages, but simultaneously leaks a secret to certain parties. Recently, Aumayr et al. provide the first formalization of adaptor signature schemes, and present provably secure constructions from ECDSA and Schnorr signatures. Unfortunately, the formalization and constructions given in this work have two limitations: (1) current schemes are limited to ECDSA and Schnorr signatures, and no generic transformation for constructing adaptor signatures is known; (2) they do not offer support for aggregated two-party signing, which can significantly reduce the blockchain footprint in applications of adaptor signatures. In this work, we address these two shortcomings. First, we show that signature schemes that are constructed from identification (ID) schemes, which additionally satisfy certain homomorphic properties, can generically be transformed into adaptor signature schemes. We further provide an impossibility result which proves that unique signature schemes (e.g., the BLS scheme) cannot be transformed into an adaptor signature scheme. In addition, we define two-party adaptor signature schemes with aggregatable public keys and show how to instantiate them via a generic transformation from ID-based signature schemes. Finally, we give instantiations of our generic transformations for the Schnorr, Katz-Wang and Guillou-Quisquater signature schemes.

Lattice-based cryptography has laid the foundation of various modern-day cryptosystems that cater to several applications, including post-quantum cryptography. For structured lattice-based schemes, polynomial arithmetic is a fundamental part. In several instances, the performance optimizations come from implementing compact multipliers due to the small range of the secret polynomial coefficients. However, this optimization does not easily translate to side-channel protected implementations since masking requires secret polynomial coefficients to be distributed over a large range. In this work, we address this problem and propose two novel generalized techniques, one for the number theoretic transform (NTT) based and another for the non-NTT-based polynomial arithmetic. Both these proposals enable masked polynomial multiplication while utilizing and retaining the small secret property. For demonstration, we used the proposed technique and instantiated masked multipliers for schoolbook as well as NTT-based polynomial multiplication. Both of these can utilize the compact multipliers used in the unmasked implementations. The schoolbook multiplication requires an extra polynomial accumulation along with the two polynomial multiplications for a first-order protected implementation. However, this cost is nothing compared to the area saved by utilizing the existing cheap multiplication units. We also extensively test the side-channel resistance of the proposed design through TVLA to guarantee its first-order security.

The NIST, in its recent competition on quantum-resilient confidentiality primitives, requested the submission of exclusively KEMs. The task of KEMs is to establish secure session keys that can drive, amongst others, public key encryption and TLS-like secure channels. In this work we test the KEM abstraction in the context of constructing cryptographic schemes that are not subsumed in the PKE and secure channels categories. We find that, when used to construct a key transport scheme or when used within a secure combiner, the KEM abstraction imposes certain inconvenient limits, the settling of which requires the addition of auxiliary symmetric primitives. We hence investigate generalizations of the KEM abstraction that allow a considerably simplified construction of the above primitives. In particular, we study VKEMs and KDFEMs, which augment classic KEMs by label inputs, encapsulation handle outputs, and key derivation features, and we demonstrate that they can be transformed into KEM combiners and key transport schemes without requiring auxiliary components. We finally show that all four finalist KEMs of the NIST competition are effectively KDFEMs. Our conclusion is that only very mild adjustments are necessary to significantly increase their versatility.

Secure computation enables mutually distrusting parties to jointly compute a function on their secret inputs, while revealing nothing beyond the function output. A long-running challenge is understanding the required communication complexity of such protocols---in particular, when communication can be sublinear in the circuit representation size of the desired function. For certain functions, such as Private Information Retrieval (PIR), this question extends to even sublinearity in the input size. We develop new techniques expanding the set of computational assumptions for sublinear communication in both settings: 1) [Circuit size] We present sublinear-communication protocols for secure evaluation of general layered circuits, given any 2-round rate-1 batch oblivious transfer (OT) protocol with a particular ``decomposability'' property. In particular, this condition can be shown to hold for the recent batch OT protocols of (Brakerski et al. Eurocrypt 2022), in turn yielding a new sublinear secure computation feasibility result: from Quadratic Residuosity (QR) together with polynomial-noise-rate Learning Parity with Noise (LPN). Our approach constitutes a departure from existing paths toward sublinear secure computation, all based on fully homomorphic encryption or homomorphic secret sharing. 2) [Input size.] We construct single-server PIR based on the Computational Diffie-Hellman (CDH) assumption, with polylogarithmic communication in the database input size $n$. Previous constructions from CDH required communication $\Omega(n)$. In hindsight, our construction comprises of a relatively simple combination of existing tools from the literature.

Laconic function evaluation (LFE) allows Alice to compress a large circuit $\mathbf{C}$ into a small digest $\mathsf{d}$. Given Alice's digest, Bob can encrypt some input $x$ under $\mathsf{d}$ in a way that enables Alice to recover $\mathbf{C}(x)$, without learning anything beyond that. The scheme is said to be $laconic$ if the size of $\mathsf{d}$, the runtime of the encryption algorithm, and the size of the ciphertext are all sublinear in the size of $\mathbf{C}$. Until now, all known LFE constructions have ciphertexts whose size depends on the $depth$ of the circuit $\mathbf{C}$, akin to the limitation of $levelled$ homomorphic encryption. In this work we close this gap and present the first LFE scheme (for Turing machines) with asymptotically optimal parameters. Our scheme assumes the existence of indistinguishability obfuscation and somewhere statistically binding hash functions. As further contributions, we show how our scheme enables a wide range of new applications, including two previously unknown constructions: • Non-interactive zero-knowledge (NIZK) proofs with optimal prover complexity. • Witness encryption and attribute-based encryption (ABE) for Turing machines from falsifiable assumptions.

We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures significantly more general adversarial strategies. In more detail, our adversary is not restricted to use an honest evaluation algorithm to run pirated software. Our results can be summarized as follows: 1. Definitions: We introduce the definition of PKE with secure key leasing and formalize a security notion that we call indistinguishability against key leasing attacks (IND-KLA security). We also define a one-wayness notion for PKE-SKL that we call OW-KLA security and show that an OW-KLA secure PKE-SKL scheme can be lifted to an IND-KLA secure one by using the (quantum) Goldreich-Levin lemma. 2. Constructing IND-KLA PKE with Secure Key Leasing: We provide a construction of OW-KLA secure PKE-SKL (which implies IND-KLA secure PKE-SKL as discussed above) by leveraging a PKE scheme that satisfies a new security notion that we call consistent or inconsistent security against key leasing attacks (CoIC-KLA security). We then construct a CoIC-KLA secure PKE scheme using 1-key Ciphertext-Policy Functional Encryption (CPFE) that in turn can be based on any IND-CPA secure PKE scheme. 3. Identity Based Encryption, Attribute Based Encryption and Functional Encryption with Secure Key Leasing: We provide definitions of secure key leasing in the context of advanced encryption schemes such as identity based encryption (IBE), attribute-based encryption (ABE) and functional encryption (FE). Then we provide constructions by combining the above PKE-SKL with standard IBE, ABE and FE schemes. Notably, our definitions allow the adversary to request distinguishing keys in the security game, namely, keys that distinguish the challenge bit by simply decrypting the challenge ciphertext, so long as it returns them (and they pass the validity test) before it sees the challenge ciphertext. All our constructions satisfy this stronger definition, albeit with the restriction that only a bounded number of such keys be allowed to the adversary in the IBE and ABE (but not FE) security games. Prior to our work, the notion of single decryptor encryption (SDE) has been studied in the context of PKE (Georgiou and Zhandry, Eprint 2020) and FE (Kitigawa and Nishimaki, Asiacrypt 2022) but all their constructions rely on strong assumptions including indistinguishability obfuscation. In contrast, our constructions do not require any additional assumptions, showing that PKE/IBE/ABE/FE can be upgraded to support secure key leasing for free.

The Deuring correspondence defines a bijection between isogenies of supersingular elliptic curves and ideals of maximal orders in a quaternion algebra. We present a new algorithm to translate ideals of prime-power norm to their corresponding isogenies --- a central task of the effective Deuring correspondence. The new method improves upon the algorithm introduced in 2021 by De Feo, Kohel, Leroux, Petit and Wesolowski as a building-block of the SQISign signature scheme. SQISign is the most compact post-quantum signature scheme currently known, but is several orders of magnitude slower than competitors, the main bottleneck of the computation being the ideal-to-isogeny translation. We implement the new algorithm and apply it to SQISign, achieving a more than two-fold speedup in key generation and signing with a new choice of parameter. Moreover, after adapting the state-of-the-art $\mathbb{F}_{p^2}$ multiplication algorithms by Longa to implement SQISign's underlying extension field arithmetic and adding various improvements, we push the total speedups to over three times for signing and four times for verification. In a second part of the article, we advance cryptanalysis by showing a very simple distinguisher against one of the assumptions used in SQISign. We present a way to impede the distinguisher through a few changes to the generic KLPT algorithm. We formulate a new assumption capturing these changes, and provide an analysis together with experimental evidence for its validity.

Blind signatures were originally introduced by Chaum (CRYPTO ’82) in the context of privacy-preserving electronic payment systems. Nowadays, the cryptographic primitive has also found applications in anonymous credentials and voting systems. However, many practical blind signature schemes have only been analysed in the game-based setting where a single signer is present. This is somewhat unsatisfactory as blind signatures are intended to be deployed in a setting with many signers. We address this in the following ways: – We formalise two variants of one-more-unforgeability of blind signatures in the Multi-Signer Setting. – We show that one-more-unforgeability in the Single-Signer Setting translates straightforwardly to the Multi-Signer Setting with a reduction loss proportional to the number of signers. – We identify a class of blind signature schemes which we call Key-Convertible where this reduction loss can be traded for an increased number of signing sessions in the Single-Signer Setting and show that many practical blind signature schemes such as blind BLS, blind Schnorr, blind Okamoto-Schnorr as well as two pairing-free, ROS immune schemes by Tessaro and Zhu (Eurocrypt’22) fulfil this property. – We further describe how the notion of key substitution attacks (Menezes and Smart, DCC’04) can be translated to blind signatures and provide a generic transformation of how they can be avoided.

Mass surveillance targets many users at the same time with the goal of learning as much as possible. Intuitively, breaking many users’ cryptography simultaneously should be at least as hard as that of only breaking a single one, but ideally security degradation is gradual: an adversary ought to work harder to break more. Bellare, Ristenpart and Tessaro (Crypto’12) introduced the notion of multi-instance security to capture the related concept for password hashing with salts. Auerbach, Giacon and Kiltz (Eurocrypt’20) motivated the study of public key encryption (PKE) in the multi-instance setting, yet their technical results are exclusively stated in terms of key encapsulation mechanisms (KEMs), leaving a considerable gap. We investigate the multi-instance security of public key encryption. Our contributions are twofold. Firstly, we define and compare possible security notions for multi-instance PKE, where we include PKE schemes whose correctness is not perfect. Secondly, we observe that, in general, a hybrid encryption scheme of a multi-instance secure KEM and an arbitrary data encapsulation mechanism (DEM) is unlikely to inherit the KEM’s multi-instance security. Yet, we show how with a suitable information-theoretic DEM, and a computationally secure key derivation function if need be, inheritance is possible. As far as we are aware, ours is the first inheritance result in the challenging multi-bit scenario.

Predicate inner product functional encryption (P-IPFE) is essentially attribute-based IPFE (AB-IPFE) which additionally hides attributes associated to ciphertexts. In a P-IPFE, a message x is encrypted under an attribute w and a secret key is generated for a pair (y, v) such that recovery of ⟨x, y⟩ requires the vectors w, v to satisfy a linear relation. We call a P-IPFE unbounded if it can encrypt unbounded length attributes and message vectors. • zero predicate IPFE. We construct the first unbounded zero predicate IPFE (UZP-IPFE) which recovers ⟨x,y⟩ if ⟨w,v⟩ = 0. This construction is inspired by the unbounded IPFE of Tomida and Takashima (ASIACRYPT 2018) and the unbounded zero inner product encryption of Okamoto and Takashima (ASIACRYPT 2012). The UZP-IPFE stands secure against general attackers capable of decrypting the challenge ciphertext. Concretely, it provides full attribute-hiding security in the indistinguishability-based semi-adaptive model under the standard symmetric external Diffie-Hellman assumption. • non-zero predicate IPFE. We present the first unbounded non-zero predicate IPFE (UNP-IPFE) that successfully recovers ⟨x, y⟩ if ⟨w, v⟩ ≠ 0. We generically transform an unbounded quadratic FE (UQFE) scheme to weak attribute-hiding UNP-IPFE in both public and secret key settings. Interestingly, our secret key simulation secure UNP-IPFE has succinct secret keys and is constructed from a novel succinct UQFE that we build in the random oracle model. We leave the problem of constructing a succinct public key UNP-IPFE or UQFE in the standard model as an important open problem.

Bootstrapping parameters for the approximate homomorphic-encryption scheme of Cheon et al., CKKS (Asiacrypt 17), are usually instantiated using sparse secrets to be efficient. However, using sparse secrets constrains the range of practical parameters within a tight interval, as they must support a large enough depth for the bootstrapping circuit but also be secure with respect to the sparsity of their secret. We present a bootstrapping procedure for the CKKS scheme that combines both dense and sparse secrets. Our construction enables the use of parameters for which the homomorphic capacity is based on a dense secret, yet with a bootstrapping complexity that remains the one of a sparse secret and with a large security margin. Moreover, this also enables us to easily parameterize the bootstrapping circuit so that it has a negligible failure probability that, to the best of our knowledge, has never been achieved for the CKKS scheme. When using the parameters of previous works, our bootstrapping procedures enables a faster procedure with an increased precision and lower failure probability. For example we are able to bootstrapp a plaintext of $\mathbb{C}^{32768}$ in 20.2 sec, with 32.11 bits of precision, 285 bits of modulus remaining, a failure probability of $2^{-138.7}$ and 128 bit security.

The hardness of solving the quadratic residuosity problem is the basis for establishing the security of many cryptographic schemes. Two of these are the public key encryption scheme and the identity-based encryption scheme proposed by Cocks. In this paper, we introduce a new computational problem: the problem of distinguishing between the Jacobi symbols of the solutions of a quadratic congruence modulo an RSA integer. We show that the security of the two encryption schemes is equivalent to the hardness of this problem, while the quadratic residuosity problem reduces to this new problem. We then specialize the problem to roots of quadratic residues and establish several computational indistinguishability relationships.

It is known that the agreement property of the Byzantine consensus problem among $n$ processes can be violated in a non-synchronous system if the number of faulty processes exceeds $t_0 = n / 3 - 1$. In this paper, we investigate the accountable Byzantine consensus problem in non-synchronous systems: the problem of solving Byzantine consensus whenever possible (e.g., when the number of faulty processes does not exceed $t_0$) and allowing correct processes to obtain proof of culpability of (at least) $t_0 + 1$ faulty processes whenever correct processes disagree. We present four complementary contributions: 1) We introduce $ABC$: a simple yet efficient transformation of any Byzantine consensus protocol to an accountable one. $ABC$ introduces an overhead of (1) only two all-to-all communication rounds and $O(n^2)$ additional bits in executions with up to $t_0$ faults (i.e., in the common case). 2) We define the accountability complexity, a complexity metric representing the number of accountability-specific messages that correct processes must send. Furthermore, we prove a tight lower bound. In particular, we show that any accountable Byzantine consensus algorithm incurs cubic accountability complexity. Moreover, we illustrate that the bound is tight by applying the $ABC$ transformation to any Byzantine consensus protocol. 3) We demonstrate that, when applied to an optimal Byzantine consensus protocol, $ABC$ constructs an accountable Byzantine consensus protocol that is (1) optimal in solving consensus whenever consensus is solvable with respect to the communication complexity, and (2) optimal in obtaining accountability whenever disagreement occurs with respect to the accountability complexity. 4) We generalize $ABC$ to other distributed computing problems besides the classic consensus problem. We characterize a class of agreement tasks, including reliable and consistent broadcast, that $ABC$ renders accountable.

Bounded-collusion identity-based encryption (BC-IBE) is a variant of identity-based encryption, where an adversary obtains user secrete keys corresponding to at most $d$ identities. From results of existing work, it is proven that BC-IBE can be constructed from public key encryption (PKE) with several properties. In particular, we focus on post-quantum PKE schemes submitted to the NIST PQC competition, as the underlying PKE of BC-IBE schemes. This is because post-quantum cryptography is one of active research areas, due to recent advancement of developing quantum computers. Hence, it is reasonable to consider converting such PKE schemes into encryption schemes with additional functionalities. By using existing generic constructions of BC-IBE, those post-quantum PKE schemes are transformed into BC-IBE with non-compact public parameter. In this paper, we propose generic constructions of BC-IBE whose public parameter-size is more compact, and it is possible to apply many post-quantum PKE schemes secure against chosen plaintext attacks, into our generic constructions. To this end, we construct BC-IBE schemes from a group testing perspective, while existing ones are constructed by employing error-correcting codes or cover-free families. As a result, we can obtain BC-IBE schemes with more compact public parameter, which are constructed from the NIST PQC PKE schemes.

Post-quantum signature schemes based on the MPC-in-the-Head (MPCitH) paradigm are recently attracting significant attention as their security solely depends on the one-wayness of the underlying primitive, providing diversity for the hardness assumption in post-quantum cryptography. Recent MPCitH-friendly ciphers have been designed using simple algebraic S-boxes operating on a large field in order to improve the performance of the resulting signature schemes. Due to their simple algebraic structures, their security against algebraic attacks should be comprehensively studied. In this paper, we refine algebraic cryptanalysis of power mapping based S-boxes over binary extension fields, and cryptographic primitives based on such S-boxes. In particular, for the Gröbner basis attack over $\mathbb{F}_2$, we experimentally show that the exact number of Boolean quadratic equations obtained from the underlying S-boxes is critical to correctly estimate the theoretic complexity based on the degree of regularity. Similarly, it turns out that the XL attack might be faster when all possible quadratic equations are found and used from the S-boxes. This refined cryptanalysis leads to more precise algebraic analysis of cryptographic primitives based on algebraic S-boxes. Considering the refined algebraic cryptanalysis, we propose a new one-way function, dubbed $\mathsf{AIM}$, as an MPCitH-friendly symmetric primitive with high resistance to algebraic attacks. The security of $\mathsf{AIM}$ is comprehensively analyzed with respect to algebraic, statistical, quantum, and generic attacks. $\mathsf{AIM}$ is combined with the BN++ proof system, yielding a new signature scheme, dubbed $\mathsf{AIMer}$. Our implementation shows that $\mathsf{AIMer}$ outperforms existing signature schemes based on symmetric primitives in terms of signature size and signing time.

Incompressible encryption, recently proposed by Guan, Wichs and Zhandry (EUROCRYPT'22), is a novel encryption paradigm geared towards providing strong long-term security guarantees against adversaries with bounded long-term memory. Given that the adversary forgets just a small fraction of a ciphertext, this notion provides strong security for the message encrypted therein, even if, at some point in the future, the entire secret key is exposed. This comes at the price of having potentially very large ciphertexts. Thus, an important efficiency measure for incompressible encryption is the message-to-ciphertext ratio (also called the rate). Guan et al. provided a low-rate instantiation of this notion from standard assumptions and a rate-1 instantiation from indistinguishability obfuscation (iO). In this work, we propose a simple framework to build rate-1 incompressible encryption from standard assumptions. Our construction can be realized from, e.g. the DDH and additionally the DCR or the LWE assumptions.

We present a tightly secure identity-based signature (IBS) scheme based on the supersingular isogeny problems. Although Shaw and Dutta proposed an isogeny-based IBS scheme with provable security, the security reduction is non-tight. For an IBS scheme with concrete security, the tightness of its security reduction affects the key size and signature size. Hence, it is reasonable to focus on a tight security proof for an isogeny-based IBS scheme. In this paper, we propose an isogeny-based IBS scheme based on the lossy CSI-FiSh signature scheme and give a tight security reduction for this scheme. While the existing isogeny-based IBS has the square-root advantage loss in the security proof, the security proof for our IBS scheme avoids such advantage loss, due to the properties of lossy CSI-FiSh.

The Bitcoin architecture heavily relies on the ECDSA signature scheme which is broken by quantum adversaries as the secret key can be computed from the public key in quantum polynomial time. To mitigate this attack, bitcoins can be paid to the hash of a public key (P2PKH). However, the first payment reveals the public key so all bitcoins attached to it must be spent at the same time (i.e. the remaining amount must be transferred to a new wallet). Some problems remain with this approach: the owners are vulnerable against rushing adversaries between the time the signature is made public and the time it is committed to the blockchain. Additionally, there is no equivalent mechanism for threshold signatures. Finally, no formal analysis of P2PKH has been done. In this paper, we formalize the security notion of a digital signature with a hidden public key and we propose and prove the security of a generic transformation that converts a classical signature to a post-quantum one that can be used only once. We compare it with P2PKH. Namely, our proposal relies on pre-image resistance instead of collision resistance as for P2PKH, so allows for shorter hashes. Additionally, we propose the notion of a delay signature to address the problem of the rushing adversary when used with a public ledger and discuss the advantages and disadvantages of our approach. We further extend our results to threshold signatures.

As for any cryptographic algorithm, the deployment of post-quantum CCA-secure public-key encryption schemes may come with the need to be protected against side-channel attacks. For existing post-quantum schemes that have not been developed with leakage in mind, recent results showed that the cost of these protections can make their implementations more expensive by orders of magnitude. In this paper, we describe a new design, coined \(\texttt{POLKA}\), that is specifically tailored for this purpose. It leverages various ingredients in order to enable efficient side-channel protected implementations such as: (i) the rigidity property (which intuitively means that de-randomized encryption and decryption are injective functions) to avoid the very leaky re-encryption step of the Fujisaki-Okamoto transform, (ii) the randomization of the decryption thanks to the incorporation of a dummy ciphertext, removing the adversary’s control of its intermediate computations and making these computations ephemeral, (iii) key-homomorphic computations that can be masked against side-channel attacks with overheads that scale linearly in the number of shares, (iv) hard physical learning problem to argue about the security of some critical unmasked operations. Furthermore, we use an explicit rejection mechanism (returning an error symbol for invalid ciphertexts) to avoid the additional leakage caused by implicit rejection. As a result, all the operations of \(\texttt{POLKA}\) can be protected against leakage in a much cheaper way than state-of-the-art designs, opening the way towards schemes that are both quantum-safe and leakage-resistant.

Blind signatures allow a signer to issue signatures on messages chosen by the signature recipient. The main property is that the recipient's message is hidden from the signer. There are many applications, including Chaum's e-cash system and Privacy Pass, where no special distribution of the signed message is required, and the message can be random. Interestingly, existing notions do not consider this practical use case separately. In this paper, we show that constraining the recipient's choice over the message distribution spawns a surprising new primitive that improves the well-established state-of-the-art. We formalize this concept by introducing the notion of non-interactive blind signatures (${\sf NIBS}$). Informally, the signer can create a presignature with a specific recipient in mind, identifiable via a public key. The recipient can use her secret key to finalize it and receive a blind signature on a random message determined by the finalization process. The key idea is that online interaction between the signer and recipient is unnecessary. We show an efficient instantiation of ${\sf NIBS}$ in the random oracle model from signatures on equivalence classes. The exciting part is that, in this case, for the recipient's public key, we can use preexisting keys for Schnorr, ECDSA signatures, El-Gamal encryption scheme, or even the Diffie-Hellman key exchange. Reusing preexisting public keys allows us to distribute anonymous tokens similarly to cryptocurrency airdropping. Additional contributions include tagged non-interactive blind signatures (${\sf TNIBS}$) and their efficient instantiation. A generic construction in the random oracle or common reference string model based on verifiable random functions, standard signatures, and non-interactive proof systems.

We propose and analyze a simple strategy for constructing 1-key constrained pseudorandom functions (CPRFs) from homomorphic secret sharing. In the process, we obtain the following contributions. First, we identify desirable properties for the underlying HSS scheme for our strategy to work. Second, we show that (most) recent existing HSS schemes satisfy these properties, leading to instantiations of CPRFs for various constraints and from various assumptions. Notably, we obtain the first (1-key selectively secure, private) CPRFs for inner-product and (1-key selectively secure) CPRFs for NC 1 from the DCR assumption, and more. Lastly, we revisit two applications of HSS, equipped with these additional properties, to secure computation: we obtain secure computation in the silent preprocessing model with one party being able to precompute its whole preprocessing material before even knowing the other party, and we construct one-sided statistically secure computation with sublinear communication for restricted forms of computation.

We investigate a new class of fault-injection attacks against the CSIDH family of cryptographic group actions. Our disorientation attacks effectively flip the direction of some isogeny steps. We achieve this by faulting a specific subroutine, connected to the Legendre symbol or Elligator computations performed during the evaluation of the group action. These subroutines are present in almost all known CSIDH implementations. Post-processing a set of faulty samples allows us to infer constraints on the secret key. The details are implementation specific, but we show that in many cases, it is possible to recover the full secret key with only a modest number of successful fault injections and modest computational resources. We provide full details for attacking the original CSIDH proof-of-concept software as well as the CTIDH constant-time implementation. Finally, we present a set of lightweight countermeasures against the attack and discuss their security.

We propose how to homomorphically evaluate arbitrary univariate and bivariate integer functions such as division. A prior work proposed by Okada et al. (WISTP'18) uses polynomial evaluations such that the scheme is still compatible with the SIMD operations in BFV and BGV, and is implemented with the input domain size $\mathbb{Z}_{257}$. However, the scheme of Okada et al. requires the quadratic number of plaintext-ciphertext multiplications and ciphertext-ciphertext additions in the input domain size, and although these operations are more lightweight than the ciphertext-ciphertext multiplication, the quadratic complexity makes handling larger inputs quite inefficient. In this work, first we improve the prior work and also propose a new approach that exploits the packing method to handle the larger input domain size instead of enabling the SIMD operation, thus making it possible to work with the larger input domain size, e.g., $\mathbb{Z}_{2^{15}}$ in a reasonably efficient way. In addition, we show how to slightly extend the input domain size to $\mathbb{Z}_{2^{16}}$ with a relatively moderate overhead. Further we show another approach to handling the larger input domain size by using two ciphertexts to encrypt one integer plaintext and applying our techniques for uni/bivariate function evaluation. We implement the prior work of Okada et al., our improved scheme of Okada et al., and our new scheme in PALISADE with the input domain size $\mathbb{Z}_{2^{15}}$, and confirm that the estimated run-times of the prior work and our improved scheme of the prior work are still about 117 days and 59 days respectively while our new scheme can be computed in 307 seconds.

In this paper, we consider the new version of tropical cryptography protocol, i.e the tropical version of ElGamal encryption. We follow the ideas and modify the classical El Gamal encryption using tropical matrices and matrix power in tropical algebra. Then we also provide a toy example for the reader’s understanding.

We consider the McEliece cryptosystem with a binary Goppa code $C \subset \mathbb{F}_2^n$ specified by an irreducible Goppa polynomial $g(x) \in \mathbb{F}_{2^m}[X]$ and Goppa points $(\alpha_1, \ldots, \alpha_n) \in \mathbb{F}_{2^m}^n$. Since $g(x)$ together with the Goppa points allow for efficient decoding, these parameters form McEliece secret keys. Such a Goppa code $C$ is an $(n-tm)$-dimensional subspace of $\mathbb{F}_2^n$, and therefore $C$ has co-dimension $tm$. For typical McEliece instantiations we have $tm \approx \frac n 4$. We show that given more than $tm$ entries of the Goppa point vector $(\alpha_1, \ldots, \alpha_n)$ allows to recover the Goppa polynomial $g(x)$ and the remaining entries in polynomial time. Hence, in case $tm \approx \frac n 4$ roughly a fourth of a McEliece secret key is sufficient to recover the full key efficiently. Let us give some illustrative numerical examples. For \textsc{ClassicMcEliece} with $(n,t,m)=(3488,64,12)$ on input $64\cdot 12+1=769$ Goppa points, we recover the remaining $3488-769=2719$ Goppa points in $\mathbb{F}_{2^{12}}$ and the degree-$64$ Goppa polynomial $g(x) \in \mathbb{F}_{2^{12}}[x]$ in $60$ secs. For \textsc{ClassicMcEliece} with $(n,t,m)=(8192,128,13)$ on input $128\cdot 13+1=1665$ Goppa points, we recover the remaining $8192-1665=6529$ Goppa points in $\mathbb{F}_{2^{13}}$ and the degree-$128$ Goppa polynomial $g(x) \in \mathbb{F}_{2^{13}}[x]$ in $288$ secs. Our results also extend to the case of erroneous Goppa points, but in this case our algorithms are no longer polynomial time.

A \emph{witness map} deterministically maps a witness $w$ of some NP statement $x$ into computationally sound proof that $x$ is true, with respect to a public common reference string (CRS). In other words, it is a deterministic, non-interactive, computationally sound proof system in the CRS model. A \emph{unique witness map} (UWM) ensures that for any fixed statement $x$, the witness map should output the same \emph{unique} proof for $x$, no matter what witness $w$ it is applied to. More generally a \emph{compact witness map} (CWM) can only output one of at most $2^\alpha$ proofs for any given statement $x$, where $\alpha$ is some compactness parameter. Such compact/unique witness maps were proposed recently by Chakraborty, Prabhakaran and Wichs (PKC '20) as a tool for building tamper-resilient signatures, who showed how to construct UWMs from indistinguishability obfuscation (iO). In this work, we study CWMs and UWMs as primitives of independent interest and present a number of interesting connections to various notions in cryptography. \begin{itemize} \item First, we show that UWMs lie somewhere between witness PRFs (Zhandry; TCC '16) and iO -- they imply the former and are implied by the latter. In particular, we show that a relaxation of UWMs to the ``designated verifier (dv-UWM)'' setting is \emph{equivalent} to witness PRFs. Moreover, we consider two flavors of such dv-UWMs, which correspond to two flavors of witness PRFs previously considered in the literature, and show that they are all in fact equivalent to each other in terms of feasibility. \item Next, we consider CWMs that are extremely compact, with $\alpha = O(\log \kappa)$, where $\kappa$ is the security parameter. We show that such CWMs imply \emph{pseudo-UWMs} where the witness map is allowed to be \emph{pseudo-deterministic} -- i.e., for every true statement $x$, there is a unique proof such that, on any witness $w$, the witness map outputs this proof with $1-1/p(\lambda)$ probability, for a polynomial $p$ that we can set arbitrarily large. \item Lastly, we consider CWMs that are mildly compact, with $\alpha = p(\lambda)$ for some a-priori fixed polynomial $p$, independent of the length of the statement $x$ or witness $w$. Such CWMs are implied by succinct non-interactive arguments (SNARGs). We show that such CWMs imply NIZKs, and therefore lie somewhere between NIZKs and SNARGs. \end{itemize}

As online group communication scenarios become more and more common these years, malicious or unpleasant messages are much easier to spread on the internet. Message franking is a crucial cryptographic mechanism designed for content moderation in online end-to-end messaging systems, allowing the receiver of a malicious message to report the message to the moderator. Unfortunately, the existing message franking schemes only consider 1-1 communication scenarios. In this paper, we systematically explore message franking in group communication scenarios. We introduce the notion of asymmetric group message franking (AGMF), and formalize its security requirements. Then, we provide a framework of constructing AGMF from a new primitive, called $\text{HPS-KEM}^{\rm{\Sigma}}$. We also give a construction of $\text{HPS-KEM}^{\rm{\Sigma}}$ based on the DDH assumption. Plugging the concrete $\text{HPS-KEM}^{\rm{\Sigma}}$ scheme into our AGMF framework, we obtain a DDH-based AGMF scheme, which supports message franking in group communication scenarios.

We give the first examples of public-key encryption schemes which can be proven to achieve multi-challenge, multi-user CCA security via reductions that are tight in time, advantage, and memory. Our constructions are obtained by applying the KEM-DEM paradigm to variants of Hashed ElGamal and the Fujisaki-Okamoto transformation that are augmented by adding uniformly random strings to their ciphertexts and/or keys. The reductions carefully combine recent proof techniques introduced by Bhattacharyya’20 and Ghoshal- Ghosal-Jaeger-Tessaro’22. Our proofs for the augmented ECIES version of Hashed-ElGamal make use of a new computational Diffie-Hellman assumption wherein the adversary is given access to a pairing to a random group, which we believe may be of independent interest.

A *functional commitment* scheme enables a user to concisely commit to a function from a specified family, then later concisely and verifiably reveal values of the function at desired inputs. Useful special cases, which have seen applications across cryptography, include vector commitments and polynomial commitments. To date, functional commitments have been constructed (under falsifiable assumptions) only for functions that are essentially *linear*, with one recent exception that works for arbitrarily complex functions. However, that scheme operates in a strong and non-standard model, requiring an online, trusted authority to generate special keys for any opened function inputs. In this work, we give the first functional commitment scheme for nonlinear functions---indeed, for *all functions* of any bounded complexity---under a standard setup and a falsifiable assumption. Specifically, the setup is ``transparent,'' requiring only public randomness (and not any trusted entity), and the assumption is the hardness of the standard Short Integer Solution (SIS) lattice problem. Our construction also has other attractive features, including: *stateless updates* via generic composability; excellent *asymptotic efficiency* for the verifier, and also for the committer in important special cases like vector and polynomial commitments, via preprocessing; and *post-quantum security*, since it is based on SIS.

We consider a transform, called Derive-then-Derandomize, that hardens a given signature scheme against randomness failure and implementation error. We prove that it works. We then give a general lemma showing indifferentiability of Shrink-MD, a class of constructions that apply a shrinking output transform to an MD-style hash function. Armed with these tools, we give new proofs for the widely standardized and used EdDSA signature scheme, improving prior work in two ways: (1) we give proofs for the case that the hash function is an MD-style one, reflecting the use of SHA512 in the NIST standard, and (2) we improve the tightness of the reduction so that one has guarantees for group sizes in actual use.

This paper presents a code-based signature scheme based on the well-known syndrome decoding (SD) problem. The scheme builds upon a recent line of research which uses the Multi-Party-Computation-in-the-Head (MPCitH) approach to construct efficient zero-knowledge proofs, such as Syndrome Decoding in the Head (SDitH), and builds signature schemes from them using the Fiat-Shamir transform. At the heart of our proposal is a new approach, Hypercube-MPCitH, to amplify the soundness of any MPC protocol that uses additive secret sharing. An MPCitH protocol with $N$ parties can be repeated $D$ times using parallel composition to reach the same soundness as a protocol run with $N^D$ parties. However, the former comes with $D$ times higher communication costs, often mainly contributed by the usage of $D$ `auxiliary' states (which in general have a significantly bigger impact on size than random states). Instead of that, we begin by generating $N^D$ shares, arranged into a $D$-dimensional hypercube of side $N$ containing only one `auxiliary' state. We derive from this hypercube $D$ sharings of size $N$ which are used to run $D$ instances of an $N$ party MPC protocol. Hypercube-MPCitH leads to a protocol with $1/N^D$ soundness error, requiring $N^D$ offline computation, but with only $N\cdot D$ online computation, and only $1$ `auxiliary'. As the (potentially offline) share generation phase is generally inexpensive, this leads to trade-offs that are superior to just using parallel composition. Our novel method of share generation and aggregation not only improves certain MPCitH protocols in general but also shows in concrete improvements of signature schemes. Specifically, we apply it to the work of Feneuil, Joux, and Rivain (CRYPTO'22) on code-based signatures, and obtain a new signature scheme that achieves a 8.1x improvement in global runtime and a 30x improvement in online runtime for their shortest signatures size (8,481 Bytes). It is also possible to leverage the fact that most computations are offline to define parameter sets leading to smaller signatures: 6,784 Bytes for 26 ms offline and 5,689 Bytes for 320 ms offline. For NIST security level 1, online signature cost is around 3 million cycles ($<$1 ms on commodity processors), regardless of signature size.

In this work, we present a novel generic construction for a Distributed Key Generation (DKG) scheme. Our generic construction relies on three modular cryptographic building blocks. The first is an aggregatable Verifiable Secret Sharing (AgVSS) scheme, the second is a Non-Interactive Key Exchange (NIKE) scheme, and the third is a secure hash function. We give formal definitions for the AgVSS and NIKE schemes, as well as concrete constructions. The utility of this generic construction is flexibility; i.e., any aggregatable VSS and NIKE scheme can be employed, and the construction will remain secure. To prove the security of our generic construction, we introduce formalized game based notions of security for DKGs, building upon existing notions in the literature. However, these prior security notions either were presented informally, omitted important requirements, or assumed certain algebraic structure of the underlying scheme. Our security notions make no such assumption of underlying algebraic structure, and explicitly consider details such as participant consistency, communication patterns, and key validity. Further, our security notions imply simulatability with respect to a target key generation scheme without rewinding. Hence, any construction that is proven secure using our security notions additionally imply UC security. We then present STORM, a concrete instantiation of our generic construction that is secure in the discrete logarithm setting in the random oracle model. STORM is more efficient than related DKG schemes in the literature. Because of its simple design and composability, it is a practical choice for real world settings and standardization efforts.

Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a notoriously hard task, despite several isogeny-based protocols relying on such an object. A trusted setup is often proposed as a workaround, but several aspects remain unclear. In this work, we develop the tools necessary to practically run such a distributed trusted-setup ceremony. Our key contribution is the first statistically zero-knowledge proof of isogeny knowledge that is compatible with any base field. To prove statistical ZK, we introduce isogeny graphs with Borel level structure and prove they have the Ramanujan property. Then, we analyze the security of a distributed trusted-setup protocol based on our ZK proof in the simplified universal composability framework. Lastly, we develop an optimized implementation of the ZK proof, and we propose a strategy to concretely deploy the trusted-setup protocol.

Blind signatures are a fundamental tool for privacy-preserving applications. Known constructions of concurrently secure blind signature schemes either are prohibitively inefficient or rely on non-standard assumptions, even in the random oracle model. A recent line of work (ASIACRYPT `21, CRYPTO `22) initiated the study of concretely efficient schemes based on well-understood assumptions in the random oracle model. However, these schemes still have several major drawbacks: 1) The signer is required to keep state; 2) The computation grows linearly with the number of signing interactions, making the schemes impractical; 3) The schemes require at least five moves of interaction. In this paper, we introduce a blind signature scheme that eliminates all of the above drawbacks at the same time. Namely, we show a round-optimal, concretely efficient, concurrently secure, and stateless blind signature scheme in which communication and computation are independent of the number of signing interactions. Our construction also naturally generalizes to the partially blind signature setting. Our scheme is based on the CDH assumption in the asymmetric pairing setting and can be instantiated using a standard BLS curve. We obtain signature and communication sizes of 9KB and 36KB, respectively. To further improve the efficiency of our scheme, we show how to obtain a scheme with better amortized communication efficiency. Our approach batches the issuing of signatures for multiple messages.

In this work we apply the Type-Safe (TS) generic group model, recently introduced by Zhandry (2022), to the more general setting of group actions and extend it to the universal composability (UC) framework of Canetti (2000). We then relax this resulting model, that we call UC-TS, to define an algebraic action framework (UC-AA), where the adversaries can behave algebraically, similarly to the algebraic group model (AGM), but for group actions. Finally, we instantiate UC-AA with isogeny-based assumptions, obtaining the Explicit-Isogeny model, UC-EI, and show that, under certain assumptions, UC-EI is less restricting that UC-AGM. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure protocol described by Lai et al. (2021), hence providing the first concretely efficient two-round isogeny-based OT protocol in the random oracle model against malicious adversaries.

This paper gives new constructions of two-round multi-signatures and threshold signatures for which security relies solely on either the hardness of the (plain) discrete logarithm problem or the hardness of RSA, in addition to assuming random oracles. Their signing protocol is partially non-interactive, i.e., the first round of the signing protocol is independent of the message being signed. We obtain our constructions by generalizing the most efficient discrete- logarithm based schemes, MuSig2 (Nick, Ruffing, and Seurin, CRYPTO ’21) and FROST (Komlo and Goldberg, SAC ’20), to work with suitably defined linear hash functions. While the original schemes rely on the stronger and more controversial one-more discrete logarithm assumption, we show that suitable instantiations of the hash functions enable security to be based on either the plain discrete logarithm assumption or on RSA. The signatures produced by our schemes are equivalent to those obtained from Okamoto’s identification schemes (CRYPTO ’92). More abstractly, our results suggest a general framework to transform schemes secure under OMDL into ones secure under the plain DL assumption and, with some restrictions, under RSA.

Re-randomizable Replayable CCA-secure public key encryption (Rand-RCCA PKE) schemes guarantee security against chosen-ciphertext attacks while ensuring the useful property of re-randomizable ciphertexts. We introduce the notion of multi-user and multi-ciphertext Rand-RCCA PKE and we give the first construction of such a PKE scheme with an almost tight security reduction to a standard assumption. Our construction is structure preserving and can be instantiated over Type-1 pairing groups. Technically, our work borrows ideas from the state of the art Rand-RCCA PKE scheme of Faonio et al. (ASIACRYPT’19) and the adaptive partitioning technique of Hofheinz (EUROCRYPT’17). Additionally, we show (1) how to turn our scheme into a publicly-verifiable (pv) Rand-RCCA scheme and (2) that plugging our pv-Rand-RCCA PKE scheme into the MixNet protocol of Faonio et al. we can obtain the first almost tightly-secure MixNet protocol.

We present a pairing-based traitor tracing scheme for $N$ users with$$ |\mathsf{pk}| = |\mathsf{ct}| = O(N^{1/3}), \quad |\mathsf{sk}| = O(1). $$This is the first pairing-based scheme to achieve ${|\mathsf{pk}|\cdot|\mathsf{sk}|\cdot|\mathsf{ct}|=o(N)}$. Our construction relies on the (bilateral) $k$-Lin assumption, and achieves private tracing and full collusion resistance. Our result simultaneously improves upon the sizes of $\mathsf{pk},\mathsf{ct}$ in Boneh–Sahai–Waters [Eurocrypt '06] and the size of $\mathsf{sk}$ in Zhandry [Crypto '20], while further eliminating the reliance on the generic group model in the latter work.

Lattice-based cryptography is one of the leading proposals for post-quantum cryptography. The Shortest Vector Problem (SVP) is arguably the most important problem for the cryptanalysis of lattice-based cryptography, and many lattice-based schemes have security claims based on its hardness. The best quantum algorithm for the SVP is due to Laarhoven [Laa16 PhD] and runs in (heuristic) time $2^{0.2653d + o(d)}$. In this article, we present an improvement over Laarhoven's result and present an algorithm that has a (heuristic) running time of $2^{0.2570 d + o(d)}$ where $d$ is the lattice dimension. We also present time-memory trade-offs where we quantify the amount of quantum memory and quantum random access memory of our algorithm. The core idea is to replace Grover's algorithm used in [Laa16 PhD] in a key part of the sieving algorithm by a quantum random walk in which we add a layer of local sensitive filtering.

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. SIDH is a compact and efficient isogeny-based key exchange, and SIKE, which is the SIDH-based key encapsulation mechanism, remains the NIST PQC Round 4. However, by the brilliant attack provided by Castryck and Decru, the original SIDH is broken in polynomial time (with heuristics). To break the original SIDH, there are three important pieces of information in the public key: information about the endomorphism ring of a starting curve, some image points under a cyclic hidden isogeny, and the degree of the isogeny. In this paper, we proposed the new isogeny-based scheme named \textit{masked-degree SIDH}. This scheme is the variant of SIDH that masks most information about degrees of hidden isogenies, and the first trial against Castryck--Decru attack. The main idea to cover degrees is to use many primes to compute isogenies that allow the degree to be more flexible. Though the size of the prime $p$ for this scheme is slightly larger than that of SIDH, this scheme resists current attacks using degrees of isogenies like the attack of Castryck and Decru. The most effective attack for masked-degree SIDH has $\tilde{O}(p^{1/(8\log_2{(\log_2{p})})})$ time complexity with classical computers and $\tilde{O}(p^{1/(16\log_2{(\log_2{p})})})$ time complexity with quantum computers in our analysis.

Hierarchical Identity Based Encryption (HIBE) is a well studied, versatile tool used in many cryptographic protocols. Yet, since the performance of all known HIBE constructions is broadly considered prohibitive, some real-world applications avoid relying on HIBE at the expense of security. A prominent example for this is secure messaging: Strongly secure messaging protocols are provably equivalent to Key-Updatable Key Encapsulation Mechanisms (KU-KEMs; Balli et al., Asiacrypt 2020); so far, all KU-KEM constructions rely on adaptive unbounded-depth HIBE (Poettering and Rösler, Jaeger and Stepanovs, both CRYPTO 2018). By weakening security requirements for better efficiency, many messaging protocols dispense with using HIBE. In this work, we aim to gain better efficiency without sacrificing security. For this, we observe that applications like messaging only need a restricted variant of HIBE for strong security. This variant, that we call Unique-Path Identity Based Encryption (UPIBE), restricts HIBE by requiring that each secret key can delegate at most one subordinate secret key. However, in contrast to fixed secret key delegation in Forward-Secure Public Key Encryption, the delegation in UPIBE, as in HIBE, is uniquely determined by variable identity strings from an exponentially large space. We investigate this mild but surprisingly effective restriction and show that it offers substantial complexity and performance advantages. More concretely, we generically build bounded-depth UPIBE from only bounded-collusion IBE in the standard model; and we generically build adaptive unbounded-depth UPIBE from only selective bounded-depth HIBE in the random oracle model. These results significantly extend the range of underlying assumptions and efficient instantiations. We conclude with a rigorous performance evaluation of our UPIBE design. Beyond solving challenging open problems by reducing complexity and improving efficiency of KU-KEM and strongly secure messaging protocols, we offer a new definitional perspective on the bounded-collusion setting.

We extend and consolidate the security justification for the Dilithium signature scheme. In particular, we identify a subtle but crucial gap that appears in several ROM and QROM security proofs for signature schemes that are based on the Fiat-Shamir with aborts paradigm, including Dilithium. The gap lies in the CMA-to-NMA reduction and was uncovered when trying to formalize a variant of the QROM security proof by Kiltz, Lyubashevsky, and Schaffner (Eurocrypt 2018). The gap was confirmed by the authors, and there seems to be no simple patch for it. We provide new, fixed proofs for the affected CMA-to-NMA reduction, both for the ROM and the QROM, and we perform a concrete security analysis for the case of Dilithium to show that the claimed security level is still valid after addressing the gap. Furthermore, we offer a fully mechanized ROM proof for the CMA-security of Dilithium in the EasyCrypt proof assistant. Our formalization includes several new tools and techniques of independent interest for future formal verification results.

A private puncturable pseudorandom function (PRF) enables one to create a constrained version of a PRF key, which can be used to evaluate the PRF at all but some punctured points. In addition, the constrained key reveals no information about the punctured points and the PRF values on them. Existing constructions of private puncturable PRFs are only proven to be secure against a restricted adversary that must commit to the punctured points before viewing any information. It is an open problem to achieve the more natural adaptive security, where the adversary can make all its choices on-the-fly. In this work, we solve the problem by constructing an adaptively secure private puncturable PRF from standard lattice assumptions. To achieve this goal, we present a new primitive called explainable hash, which allows one to reprogram the hash function on a given input. The new primitive may find further applications in constructing more cryptographic schemes with adaptive security. Besides, our construction has collusion resistant pseudorandomness, which requires that even given multiple constrained keys, no one could learn the values of the PRF at the punctured points. Private puncturable PRFs with collusion resistant pseudorandomness were only known from multilinear maps or indistinguishability obfuscations in previous works, and we provide the first solution from standard lattice assumptions.

Besides the well-known class of Koblitz curves over binary fields, the class of Koblitz curves $E_b: y^2=x^3+b/\mathbb{F}_p$ over prime fields with $p\equiv 1 \pmod 3$ is also of some practical interest. By refining a classical result of Rajwade for the cardinality of $E_b(\mathbb{F}_p)$, we obtain a simple formula of $\#E_b(\mathbb{F}_p)$ in terms of the norm on the ring $\mathbb{Z}[\omega]$ of Eisenstein integers, that is, for some $\pi \in \mathbb{Z}[\omega]$ with $N(\pi)=p$ and some unit $u\in \mathbb{Z}[\omega]$, \[ \#E_b(\mathbb{F}_p)=N(\pi+u) \] holds. This establishes an interesting relation between the number of points on this class of curves and the number of elements of their underlying fields, they are given by the norm of two integers of $\mathbb{Z}[\omega]$ whose difference is just a unit. It is also interesting to note that such relationship has already been derived for the case of Koblitz curves over binary fields. Some tools that are useful in the computation of cubic residues are also developed.

We propose a REinforced modified Dual-Ouroboros based on Gabidulin codes, shortly called REDOG. This is a code-based cryptosystem based on the well-known rank metric codes, Gabidulin codes. The public key sizes of REDOG are 14KB, 33KB, 63KB at the security levels of 128, 192, 256 bits respectively. There is no decoding failure in decryption. REDOG is IND-CPA. As a new result, we give the performance results of implementing REDOG including the time for Key generation, encryption, and decryption for each security level.

An oblivious pseudorandom function, or OPRF, is an important primitive that is used to build many advanced cryptographic protocols. Despite its relevance, very few post-quantum solutions exist. In this work, we propose a novel OPRF protocol that is post-quantum, verifiable, round-optimal, and moderately compact. Our protocol is based on a previous SIDH-based construction by Boneh, Kogan, and Woo, which was later shown to be insecure due to an attack on its one-more unpredictability. We first propose an efficient countermeasure against this attack by redefining the PRF function to use irrational isogenies. This prevents a malicious user from independently evaluating the PRF. The SIDH-based construction by Boneh, Kogan, and Woo is also vulnerable to the recent attacks on SIDH. We thus demonstrate how to efficiently incorporate the countermeasures against such attacks to obtain a secure OPRF protocol. To achieve this, we also propose the first proof of isogeny knowledge that is compatible with masked torsion points, which may be of independent interest. Lastly, we design a novel non-interactive proof of knowledge of parallel isogenies, which reduces the number of communication rounds of the OPRF to the theoretically-optimal two. Putting everything together, we obtain the most compact post-quantum verifiable OPRF protocol.

Verifiable random functions (VRFs) are essentially pseudorandom functions for which selected outputs can be proved correct and unique, without compromising the security of other outputs. VRFs have numerous applications across cryptography, and in particular they have recently been used to implement committee selection in the Algorand protocol. Elliptic Curve VRF (ECVRF) is an elegant construction, originally due to Papadopoulos et al., that is now under consideration by the Internet Research Task Force. Prior work proved that ECVRF possesses the main desired security properties of a VRF, under suitable assumptions. However, several recent versions of ECVRF include changes that make some of these proofs inapplicable. Moreover, the prior analysis holds only for *classical* attackers, in the random-oracle model (ROM); it says nothing about whether any of the desired properties hold against *quantum* attacks, in the quantumly accessible ROM. We note that certain important properties of ECVRF, like uniqueness, do *not* rely on assumptions that are known to be broken by quantum computers, so it is plausible that these properties could hold even in the quantum setting. This work provides a multi-faceted security analysis of recent versions of ECVRF, in both the classical and quantum settings. First, we motivate and formally define new security properties for VRFs, like non-malleability and binding, and prove that recent versions of ECVRF satisfy them (under standard assumptions). Second, we identify a subtle obstruction in proving that recent versions of ECVRF have *uniqueness* via prior indifferentiability definitions and theorems, even in the classical setting. Third, we fill this gap by defining a stronger notion called *relative indifferentiability*, and extend prior work to show that a standard domain extender used in ECVRF satisfies this notion, in both the classical and quantum settings. This final contribution is of independent interest and we believe it should be applicable elsewhere.

All known instantiations for fully homomorphic encryption (FHE) produce noisy ciphertexts and rely on a technique called bootstrapping to reduce the noise so as to enable an arbitrary number of homomorphic operations. Bootstrapping is the main performance bottleneck and arguably the biggest obstacle to widespread adoption of FHE. Among the FHE schemes, TFHE and its variations present the appealing property of having a bootstrapping procedure---as well as its extension to programmable bootstrapping---that is relatively light-weight. The essential operations consist of a series of multiplications in $(Z/qZ)[X]/(X^N+1)$. While the NTT is seemingly the natural candidate for evaluating these multiplications in a fast and exact way, it restricts the possible choices for $q$ and $N$. To the authors' knowledge, all current implementations of TFHE with $q$ a power of two actually employ the FFT over the complex numbers instead. This introduces real numbers to the otherwise purely discrete algorithms, including all the drawbacks of the need to approximate them using finite precision. This work studies the avenues available to apply the NTT in the context of TFHE-like schemes. In particular, it considers various combinations of coefficient rings and quotient polynomials that are compatible with the requirements of the underlying scheme. Importantly, this work provides methods for adapting the (programmable) bootstrapping to quotient polynomials beyond power-of-two cyclotomics. As a side effect, it also demonstrates how this may enhance the programmability of the bootstrapping.

The post-quantum security of cryptographic schemes assumes that the quantum adversary only receives the classical result of computations with the secret key. Further, it is unknown whether the post-quantum secure schemes still remain secure if the adversary can obtain a superposition state of the results. In this paper, we formalize one class of public-key encryption schemes named oracle-masked schemes. Then we define the plaintext extraction procedure for those schemes and this procedure simulates the quantum-accessible decryption oracle with a certain loss. The construction of the plaintext extraction procedure does not need to take the secret key as input. Based on this property, we prove the IND-qCCA security of the Fujisaki-Okamoto (FO) transformation in the quantum random oracle model (QROM) and our security proof is tighter than the proof given by Zhandry (Crypto 2019). We also give the first IND-qCCA security proof of the REACT transformation in the QROM. Furthermore, our formalization can be applied to prove the IND-qCCA security of key encapsulation mechanisms with explicit rejection. As an example, we present the IND-qCCA security proof of $\textsf{T}_{\textsf{CH}}$ transformation, proposed by Huguenin-Dumittan and Vaudenay (Eurocrypt 2022), in the QROM.

Existing lattice signature schemes are much less efficient than encryption schemes due to the rejection sampling paradigm. We give a new construction which avoids rejection sampling by using temporary public keys and structured secrets in a Bliss type scheme. Structured secrets also improve existing lattice encryption schemes to nearly the same extreme efficiency. Our signing algorithm is comparative with this optimized encryption efficiency. Our signature scheme allows the same key pair work as an encryption scheme. For lightweight implementation, our techniques allow integrating of public-key encryption and signature in a simple circuit which only needs to do small integer additions as the main part of computation.

Ciphertext-policy attribute-based encryption is a versatile primitive that has been considered extensively to securely manage data in practice. Especially completely unbounded schemes are attractive, because they do not restrict the sets of attributes and policies. So far, any such schemes that support negations in the access policy or that have online/offline extensions have an inefficient decryption algorithm. In this work, we propose GLUE (Generalized, Large-universe, Unbounded and Expressive), which is a novel scheme that allows for the efficient implementation of the decryption while allowing the support of both negations and online/offline extensions. We achieve these properties simultaneously by uncovering an underlying dependency between encryption and decryption, which allows for a flexible trade-off in their efficiency. For the security proof, we devise a new technique that enables us to generalize multiple existing schemes. As a result, we obtain a completely unbounded scheme supporting negations that, to the best of our knowledge, outperforms all existing such schemes in the decryption algorithm.

Decentralized multi-authority attribute-based encryption (𝖬𝖠-𝖠𝖡𝖤) is a distributed generalization of standard (ciphertext-policy) attribute-based encryption where there is no trusted central authority: any party can become an authority and issue private keys, and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. We present the first multi-authority attribute-based encryption schemes that are provably fully adaptively secure. Namely, our construction is secure against an attacker that may corrupt some of the authorities as well as perform key queries adaptively throughout the life-time of the system. Our main construction relies on a prime order bilinear group where the 𝑘-linear assumption holds as well as on a random oracle. Along the way, we present a conceptually simpler construction relying on a composite order bilinear group with standard subgroup decision assumptions as well as on a random oracle. Prior to this work, there was no construction that could resist adaptive corruptions of authorities, no matter the assumptions used. In fact, we point out that even standard complexity leveraging style arguments do not work in the multi-authority setting.

The lattice isomorphism problem (LIP) asks one to find an isometry between two lattices. It has recently been proposed as a foundation for cryptography in two independent works [Ducas & van Woerden, EUROCRYPT 2022, Bennett et al. preprint 2021]. This problem is the lattice variant of the code equivalence problem, on which the notion of the hull of a code can lead to devastating attacks. In this work we study the cryptanalytic role of an adaptation of the hull to the lattice setting, namely, the $s$-hull. We first show that the $s$-hull is not helpful for creating an arithmetic distinguisher. More specifically, the genus of the $s$-hull can be efficiently predicted from $s$ and the original genus and therefore carries no extra information. However, we also show that the hull can be helpful for geometric attacks: for certain lattices the minimal distance of the hull is relatively smaller than that of the original lattice, and this can be exploited. The attack cost remains exponential, but the constant in the exponent is halved. This second result gives a counterexample to the general hardness conjecture of LIP proposed by Ducas & van Woerden. Our results suggests that one should be very considerate about the geometry of hulls when instantiating LIP for cryptography. They also point to unimodular lattices as attractive options, as they are equal to their dual and their hulls, leaving only the original lattice to an attacker. Remarkably, this is already the case in proposed instantiations, namely the trivial lattice $\mathbb{Z}^n$ and the Barnes-Wall lattices.

In 2020, Bernard and Roux-Langlois introduced the Twisted-PHS algorithm to solve Approx-SVP for ideal lattices on any number field, based on the PHS algorithm by Pellet-Mary, Hanrot and Stehlé. They performed experiments for prime conductors cyclotomic fields of degrees at most 70, one of the main bottlenecks being the computation of a log-$\mathcal{S}$-unit lattice which requires subexponential time. Our main contribution is to extend these experiments to cyclotomic fields of degree up to $210$ for most conductors $m$. Building upon new results from Bernard and Kučera on the Stickelberger ideal, we use explicit generators to construct full-rank log-$\mathcal{S}$-unit sublattices fulfilling the role of approximating the full Twisted-PHS lattice. In our best approximate regime, our results show that the Twisted-PHS algorithm outperforms, over our experimental range, the CDW algorithm by Cramer, Ducas and Wesolowski, and sometimes beats its asymptotic volumetric lower bound. Additionally, we use these explicit Stickelberger generators to remove almost all quantum steps in the CDW algorithm, under the mild restriction that the plus part of the class number verifies $h^+_{m}\leq O(\sqrt{m})$.

Hecht and Scolnik proposed key agreement using rectangular matrices and determinants. This report describes an attack.

Kyber is a key-encapsulation mechanism (KEM) that was recently selected by NIST in its PQC standardization process; it is also the only scheme to be selected in the context of public-key encryption (PKE) and key establishment. The main security target for KEMs, and their associated PKE schemes, in the NIST PQC context has been IND-CCA security. However, some important modern applications also require their underlying KEMs/PKE schemes to provide anonymity (Bellare et al., ASIACRYPT 2001). Examples of such applications include anonymous credential systems, cryptocurrencies, broadcast encryption schemes, authenticated key exchange, and auction protocols. It is hence important to analyze the compatibility of NIST's new PQC standard in such "beyond IND-CCA" applications. Some starting steps were taken by Grubbs et al. (EUROCRYPT 2022) and Xagawa (EUROCRYPT 2022) wherein they studied the anonymity properties of most NIST PQC third round candidate KEMs. Unfortunately, they were unable to show the anonymity of Kyber because of certain technical barriers. In this paper, we overcome said barriers and resolve the open problems posed by Grubbs et al. (EUROCRYPT 2022) and Xagawa (EUROCRYPT 2022) by establishing the anonymity of Kyber, and the (hybrid) PKE schemes derived from it, in a post-quantum setting. Along the way, we also provide an approach to obtain tight IND-CCA security proofs for Kyber with concrete bounds; this resolves another issue identified by the aforementioned works related to the post-quantum IND-CCA security claims of Kyber from a provable security point-of-view. Our results also extend to Saber, a NIST PQC third round finalist, in a similar fashion.

In CT-RSA 2020, P3S was proposed as the first policy-based sanitizable signature scheme which allows the signer to designate future message sanitizers by defining an access policy relative to their attributes rather than their keys. However, since P3S utilizes a policy-based chameleon hash (PCH), it does not achieve unlinkability which is a required notion in privacy-preserving applications. Moreover, P3S requires running a procedure to share the secret trapdoor information for PCH with each new sanitizer before sanitizing a new message. We further observe that in order to maintain the transparency in P3S’s multiple-sanitizers setting, the signature size should grow linearly with the number of sanitizers. In this work, we propose an unlinkable policy-based sanitizable signature scheme (UP3S) where we employ a rerandomizable digital signature scheme and a traceable attribute-based signature scheme as its building blocks. Compared to P3S, UP3S achieves unlinkability, does not require new secrets to be shared with future sanitizers prior to sanitizing each message, and has a fixed signature size for a given sanitization policy. We define and formally prove the security notions of the generic scheme, propose an instantiation of UP3S utilizing the Pointcheval-Sanders rerandomizable signature scheme and DTABS traceable attribute-based signature scheme, and analyze its efficiency. Finally, we compare UP3S with P3S in terms of the features of the procedures, scalability, and security models.

Studies of linear codes in terms of finite projective geometries form traditional direction in Coding Theory. Some applications of projective geometries are known. Noncommutative groups and semigroups defined in terms of projective geometries can serve as platforms of protocols of Post Quantum Cryptography. We introduce an idea of public keys of Multivariate Cryptography given by quadratic public rules generated via walks on incidence substructures of projective geometry with vertexes from two largest Schubert cells. It differs from the known algorithms of Code Based Cryptography and can be considered as the first attempt to combine ideas of this area with the approach of Multivariate Cryptography.

The elliptic curve family of schemes has the lowest computational latency, memory use, energy consumption, and bandwidth requirements, making it the most preferred public key method for adoption into network protocols. Being suitable for embedded devices and applicable for key exchange and authentication, ECC is assuming a prominent position in the field of IoT cryptography. The attractive properties of the relatively new curve Curve448 contribute to its inclusion in the TLS1.3 protocol and pique the interest of academics and engineers aiming at studying and optimizing the schemes. When addressing low-end IoT devices, however, the literature indicates little work on these curves. In this paper, we present an efficient design for both protocols based on Montgomery curve Curve448 and its birationally equivalent Edwards curve Ed448 used for key agreement and digital signature algorithm, specifically the X448 function and the Ed448 DSA, relying on efficient low-level arithmetic operations targeting the ARM-based Cortex-M4 platform. Our design performs point multiplication, the base of the Elliptic Curve Diffie-Hellman (ECDH), in 3,2KCCs, resulting in more than 48% improvement compared to the best previous work based on Curve448, and performs sign and verify, the main operations of the Edwards-curves Digital Signature Algorithm (EdDSA), in 6,038KCCs and 7,404KCCs, showing a speedup of around 11% compared to the counterparts. We present novel modular multiplication and squaring architectures reaching ~25% and ~35% faster runtime than the previous best-reported results, respectively, based on Curve448 key exchange counterparts, and ~13% and ~25% better latency results than the Ed448-based digital signature counterparts targeting Cortex-M4 platform.

In this paper, we consider tight multi-user security under adaptive corruptions, where the adversary can adaptively corrupt some users and obtain their secret keys. We propose generic constructions for a bunch of primitives, and the instantiations from the matrix decision Diffie-Hellman (MDDH) assumptions yield the following schemes: (1) the first digital signature (SIG) scheme achieving almost tight strong EUF-CMA security in the multi-user setting with adaptive corruptions in the standard model; (2) the first public-key encryption (PKE) scheme achieving almost tight IND-CCA security in the multi-user multi-challenge setting with adaptive corruptions in the standard model; (3) the first signcryption (SC) scheme achieving almost tight privacy and authenticity under CCA attacks in the multi-user multi-challenge setting with adaptive corruptions in the standard model. As byproducts, our SIG and SC naturally derive the first strongly secure message authentication code (MAC) and the first authenticated encryption (AE) schemes achieving almost tight multi-user security under adaptive corruptions in the standard model. We further optimize constructions of SC, MAC and AE to admit better efficiency. Furthermore, we consider key leakages besides corruptions, as a natural strengthening of tight multi-user security under adaptive corruptions. This security considers a more natural and more complete "all-or-part-or-nothing" setting, where secret keys of users are either fully exposed to adversary ("all"), or completely hidden to adversary ("nothing"), or partially leaked to adversary ("part"), and it protects the uncorrupted users even with bounded key leakages. All our schemes additionally support bounded key leakages and enjoy full compactness. This yields the first SIG, PKE, SC, MAC, AE schemes achieving almost tight multi-user security under both adaptive corruptions and leakages.

The Schnorr signature scheme is an efficient digital signature scheme with short signature lengths, i.e., $4k$-bit signatures for $k$ bits of security. A Schnorr signature $\sigma$ over a group of size $p\approx 2^{2k}$ consists of a tuple $(s,e)$, where $e \in \{0,1\}^{2k}$ is a hash output and $s\in \mathbb{Z}_p$ must be computed using the secret key. While the hash output $e$ requires $2k$ bits to encode, Schnorr proposed that it might be possible to truncate the hash value without adversely impacting security. In this paper, we prove that short Schnorr signatures of length $3k$ bits provide $k$ bits of multi-user security in the (Shoup's) generic group model and the programmable random oracle model. We further analyze the multi-user security of key-prefixed short Schnorr signatures against preprocessing attacks, showing that it is possible to obtain secure signatures of length $3k + \log S$ bits. Here, $S$ denotes the size of the hint generated by our preprocessing attacker, e.g., if $S=2^{k/2}$, then we would obtain $3.5k$-bit signatures. Our techniques easily generalize to several other Fiat-Shamir-based signature schemes, allowing us to establish analogous results for Chaum-Pedersen signatures and Katz-Wang signatures. As a building block, we also analyze the $1$-out-of-$N$ discrete-log problem in the generic group model, with and without preprocessing.

The pair encodings framework is an important result in the simplified design of complex attribute-based encryption schemes. In particular, it reduces the effort of proving security of a scheme to proving security of the associated pair encoding, which can then be transformed into a provably secure pairing-based encryption scheme with a compiler. Especially the symbolic property, as introduced by Agrawal and Chase (EUROCRYPT '17), has proven to be a valuable security notion that is both simple to verify and applies to many schemes. Nevertheless, several practical extensions using full-domain hashes or employing multiple authorities cannot be instantiated with this compiler, and therefore still require complicated proof techniques. In this work, we present the first compiler for attribute-based encryption schemes that supports such extensions. To this end, we generalize the definitions of pair encodings and the symbolic property. With our compiler, we flexibly instantiate any pair encodings that satisfy this new notion of the symbolic property in any pairing-friendly groups, and generically prove the resulting scheme to be selectively secure. To illustrate the effectiveness of our new compiler, we give several new multi-authority and hash-based constructions.

We propose a countermeasure to the Castryck-Decru attack on SIDH. The attack heavily relies on the images of torsion points. The main input to our countermeasure consists in masking the torsion point images in SIDH in a way they are not exploitable in the attack, but can be used to complete the key exchange. This comes with a change in the form the field characteristic and a considerable increase in the parameter sizes.

Attribute-based encryption (ABE) generalizes public-key encryption and enables fine-grained control to encrypted data. However, ABE upends the traditional trust model of public-key encryption by requiring a single trusted authority to issue decryption keys. If an adversary compromises the central authority and exfiltrates its secret key, then the adversary can decrypt every ciphertext in the system. This work introduces registered ABE, a primitive that allows users to generate secret keys on their own and then register the associated public key with a "key curator" along with their attributes. The key curator aggregates the public keys from the different users into a single compact master public key. To decrypt, users occasionally need to obtain helper decryption keys from the key curator which they combine with their own secret keys. We require that the size of the aggregated public key, the helper decryption keys, the ciphertexts, as well as the encryption/decryption times to be polylogarithmic in the number of registered users. Moreover, the key curator is entirely transparent and maintains no secrets. Registered ABE generalizes the notion of registration-based encryption (RBE) introduced by Garg et al. (TCC 2018), who focused on the simpler setting of identity-based encryption. We construct a registered ABE scheme that supports an a priori bounded number of users and policies that can be described by a linear secret sharing scheme (e.g., monotone Boolean formulas) from assumptions on composite-order pairing groups. Our approach deviates sharply from previous techniques for constructing RBE and only makes black-box use of cryptography. All existing RBE constructions (a weaker notion than registered ABE) rely on heavy non-black-box techniques. The encryption and decryption costs of our construction are comparable to those of vanilla pairing-based ABE. Two limitations of our scheme are that it requires a structured reference string whose size scales quadratically with the number of users (and linearly with the size of the attribute universe) and the running time of registration scales linearly with the number of users. Finally, as a feasibility result, we construct a registered ABE scheme that supports general policies and an arbitrary number of users from indistinguishability obfuscation and somewhere statistically binding hash functions.

When multiple users have power or rights, there is always the risk of corruption or abuse. Whereas there is no solution to avoid those malicious behaviors, from the users themselves or from external adversaries, one can strongly deter them with tracing capabilities that will later help to revoke the rights or negatively impact the reputation. On the other hand, privacy is an important issue in many applications, which seems in contradiction with traceability. In this paper, we first extend usual tracing techniques based on codes so that not just one contributor can be traced but the full collusion. In a second step, we embed suitable codes into a set $\mathcal V$ of vectors in such a way that, given a vector $\mathbf U \in \mathsf{span}(\mathcal V)$, the underlying code can be used to efficiently find a minimal subset $\mathcal X \subseteq \mathcal V$ such that $\mathbf U \in \mathsf{span}(\mathcal X)$. To meet privacy requirements, we then make the vectors of $\mathsf{span}(\mathcal V)$ anonymous while keeping the efficient tracing mechanism. As an interesting application, we formally define the notion of linearly-homomorphic group signatures and propose a construction from our codes: multiple signatures can be combined to sign any linear subspace in an anonymous way, but a tracing authority is able to trace back all the contributors involved in the signatures of that subspace.

Secure communication is gained by combining encryption with authentication. In real-world applications encryption commonly takes the form of KEM-DEM hybrid encryption, which is combined with ideal authentication. The pivotal question is how weak the employed key encapsulation mechanism (KEM) is allowed to be to still yield universally composable (UC) secure communication when paired with symmetric encryption and ideal authentication. This question has so far been addressed for public-key encryption (PKE) only, showing that encryption does not need to be stronger than sender-binding CPA, which binds the CPA secure ciphertext non-malleably to the sender ID. For hybrid encryption, prior research unanimously reaches for CCA2 secure encryption which is unnecessarily strong. Answering this research question is vital to develop more efficient and feasible protocols for real-world secure communication and thus enable more communication to be conducted securely. In this paper we use ideas from the PKE setting to develop new answers for hybrid encryption. We develop a new and significantly weaker security notion—sender-binding CPA for KEMs—which is still strong enough for secure communication. By using game-based notions as building blocks, we attain secure communication in the form of ideal functionalities with proofs in the UC-framework. Secure communication is reached in both the classic as well as session context by adding authentication and one-time/replayable CCA secure symmetric encryption respectively. We furthermore provide an efficient post-quantum secure LWE-based construction in the standard model giving an indication of the real-world benefit resulting from our new security notion. Overall we manage to make significant progress on discovering the minimal security requirements for hybrid encryption components to facilitate secure communication.

The understanding of directionality for updatable encryption (UE) schemes is important, but not yet completed in the literature. We show that security in the backward-leak uni-directional key updates setting is equivalent to the no-directional one. Combining with the work of Jiang (ASIACRYPT 2020) and Nishimaki (PKC 2022), it is showed that the backward-leak notion is the strongest one among all known key update notions and more relevant in practice. We propose two novel generic constructions of UE schemes that are secure in the backward-leak uni-directional key update setting from public key encryption (PKE) schemes: the first one requires a key and message homomorphic PKE scheme and the second one requires a bootstrappable PKE scheme. These PKE can be constructed based on standard assumptions (such as the Decisional Diffie-Hellman and Learning With Errors assumptions).

Functional encryption features secret keys, each associated with a key function $f$, which allow to directly recover $f(x)$ from an encryption of $x$, without learning anything more about $x$. This property is particularly useful when delegating data processing to a third party as it allows the latter to perfom its task while ensuring minimum data leakage. However, this generic term conceals a great diversity in the cryptographic constructions that strongly differ according to the functions $f$ they support. A recent series of works has focused on the ability to search a pattern within a data stream, which can be expressed as a function $f$. One of the conclusions of these works was that this function $f$ was not supported by the current state-of-the-art, which incited their authors to propose a new primitive called Stream Encryption supporting Pattern Matching (SEPM). Some concrete constructions were proposed but with some limitations such as selective security or reliance on non-standard assumptions. In this paper, we revisit the relations between this primitive and two major subclasses of functional encryption, namely Hidden Vector Encryption (HVE) and Inner Product Encryption (IPE). We indeed first exhibit a generic transformation from HVE to SEPM, which immediately yields new efficient SEPM constructions with better features than existing ones. We then revisit the relations between HVE and IPE and show that we can actually do better than the transformation proposed by Katz, Sahai and Waters in their seminal paper on predicate encryption. This allows to fully leverage the vast state-of-the-art on IPE which contains adaptively secure constructions proven under standard assumptions. This results in countless new SEPM constructions, with all the features one can wish for. Beyond that, we believe that our work sheds a new light on the relations between IPE schemes and HVE schemes and in particular shows that some of the former are more suitable to construct the latter.

SQISign is an isogeny-based signature scheme that has short keys and signatures and is expected to be a post-quantum scheme. Its security depends on the hardness of the problem to find an isogeny between given two elliptic curves over $\mathbb{F}_{p^2}$, where $p$ is a large prime. For efficiency reasons, a public key in SQISign is taken from a set of supersingular elliptic curves with a particular property. In this paper, we investigate the security related to public keys in SQISign. First, we show some properties of the set of public keys. Next, we show that a key generation procedure used in implementing SQISign could not generate all public keys and propose a modification for the procedure. In addition, we confirm the latter result through an experiment.

In CRYPTO 2012, Zhandry developed generic semi-constant oracle technique and proved security of an identity-based encryption scheme, GPV-IBE, and full domain hash (FDH) signature scheme in the quantum random oracle model (QROM). However, the reduction provided by Zhandry incurred a quadratic reduction loss. In this work, we provide a much tighter proof, with linear reduntion loss, for the FDH, probabilistc FDH (PFDH), and GPV-IBE in the QROM. Our proof is based on the measure-and-reprogram technique developed by Don, Fehr, Majenz and Schaffner.

Encryption satisfying CCA2 security is commonly known to be unnecessarily strong for realizing secure channels. Moreover, CCA2 constructions in the standard model are far from being competitive practical alternatives to constructions via random oracle. A promising research area to alleviate this problem are weaker security notions—like IND-RCCA secure encryption or IND-atag-wCCA secure tag-based encryption—which are still able to facilitate secure message transfer (SMT) via authenticated channels. In this paper we introduce the concept of sender-binding encryption (SBE), unifying prior approaches of SMT construction in the universal composability (UC) model. We furthermore develop the corresponding non-trivial security notion of IND-SB-CPA and formally prove that it suffices for realizing SMT in conjunction with authenticated channels. Our notion is the weakest so far in the sense that it generically implies the weakest prior notions—RCCA and atag-wCCA—without additional assumptions, while the reverse is not true. A direct consequence is that IND-stag-wCCA, which is strictly weaker than IND-atag-wCCA but stronger than our IND-SB-CPA, can be used to construct a secure channel. Finally, we give an efficient IND-SB-CPA secure construction in the standard model from IND-CPA secure double receiver encryption (DRE) based on McEliece. This shows that IND-SB-CPA security yields simpler and more efficient constructions in the standard model than the weakest prior notions, i.e., IND-atag-wCCA and IND-stag-wCCA.

We give a construction of a 2-round blind signature scheme based on the hardness of standard lattice problems (Ring/Module-SIS/LWE and NTRU) with a signature size of 22 KB. The protocol is round-optimal and has a transcript size that can be as small as 60 KB. This blind signature is around $4$ times shorter than the most compact lattice-based scheme based on standard assumptions of del Pino and Katsumata (Crypto 2022) and around $2$ times shorter than the scheme of Agrawal et al. (CCS 2022) based on their newly-proposed one-more-SIS assumption. We also give a construction of a ``keyed-verification'' blind signature scheme in which the verifier and the signer need to share a secret key. The signature size in this case is only $48$ bytes, but more work needs to be done to explore the efficiency of the protocol which generates the signature.

Ring signatures enable a user to sign messages on behalf of an arbitrary set of users, called the ring. The anonymity property guarantees that the signature does not reveal which member of the ring signed the message. The notion of linkable ring signatures (LRS) is an extension of the concept of ring signatures such that there is a public way of determining whether two signatures have been produced by the same signer. Lattice-based LRS is an important and active research line since lattice-based cryptography has attracted more attention due to its distinctive features, especially the quantum-resistant. However, all the existing lattice-based LRS relied on random oracle heuristics, i.e., no lattice-based LRS in the standard model has been introduced so far. In this paper, we present a lattice-based LRS scheme in the standard model. Toward our goal, we present a lattice basis extending algorithm which is the key ingredient in our construction, that may be of indepen- dent interest

Since the invention of Bitcoin, cryptocurrencies have gained huge popularity. Crypto wallet, as the tool to store and manage the cryptographic keys, is the primary entrance for the public to access cryptocurrency funds. Deterministic wallet is an advanced wallet mech- anism that has been proposed to achieve some appealing virtues, such as low-maintenance, easy backup and recovery, supporting functionali- ties required by cryptocurrencies, and so on. But deterministic wallets still have a long way to be practical in quantum world, and there are also some gaps in the classic world, since there are the following prob- lems waiting to be solved. Firstly, the relying on the state, i.e., stateful. The stateful deterministic wallet scheme must internally maintain and keep refreshing synchronously a state which makes the implementation in practice become more complex. And once one of the states is leaked, thereafter the security notion of unlinkability is cannot be guaranteed (referred to as the weak security notion of forward unlinkability). The second problem is vulnerable. There are security shortfalls in previous works, they suffer a vulnerability when a minor fault happens (say, one derived key is compromised somehow), then the damage is not limited to the leaked derived key, instead, it spreads to the master key and the whole system collapses. Thirdly, the falling short in supporting hot/cold setting. The hot/cold setting is a widely adopted method to effectively reduce the exposure chance of secret keys and hence improving the se- curity of the deterministic wallet system. The last problem is the relying on the weak security notion of unforgeability, in which the adversary is only allowed to query and forge the signatures w.r.t. the public keys that were assigned by the challenger. In this work, we present a new deterministic wallet scheme in quantum world, which is stateless, supports hot/cold setting, satisfiies stronger security notions, and is more efficient. In particular, we reformalize the syntax and security models for deterministic wallets, capturing the func- tionality and security requirements imposed by the practice in cryptocur- rency. Then we propose a deterministic wallet construction and prove its security in the quantum random oracle model. Finally, we show our wal- let scheme is more practicable by analyzing an instantiation of our wallet scheme based on the signature scheme Falcon.

In this paper we study linearization proposed on ePrint 2021/583, that's addressed to entropic quasigroups cryptography. We show how this attack can be avoided and actually linearization can be used to build valid cryptosystems.

In this work, we consider the formal verification of the public-key encryption scheme of Saber, one of the selected few post-quantum cipher suites currently considered for potential standardization. We formally verify this public-key encryption scheme's IND-CPA security and $\delta$-correctness properties, i.e., the properties required to transform the public-key encryption scheme into an IND-CCA2 secure and $\delta$-correct key encapsulation mechanism, in EasyCrypt. To this end, we initially devise hand-written proofs for these properties that are significantly more detailed and meticulous than the presently existing proofs. Subsequently, these hand-written proofs serve as a guideline for the formal verification. The results of this endeavor comprise hand-written and computer-verified proofs which demonstrate that Saber's public-key encryption scheme indeed satisfies the desired security and correctness properties.

This paper describes a formalization of the specification and the algorithm of the cryptographic scheme CRYSTALS-KYBER as well as the verification of its (1 − δ)-correctness proof. During the formalization, a problem in the correctness proof was uncovered. In order to amend this issue, a necessary property on the modulus parameter of the CRYSTALS-KYBER algorithm was introduced. This property is already implicitly fulfilled by the structure of the modulus prime used in the number theoretic transform (NTT). The NTT and its convolution theorem in the case of CRYSTALS-KYBER was formalized as well. The formalization was realized in the theorem prover Isabelle.

Selective opening (SO) security is one of the most important security notions of public key encryption (PKE) in a multi-user setting. Even though messages and random coins used in some ciphertexts are leaked, SO security guarantees the confidentiality of the other ciphertexts. Actually, it is shown that there exist PKE schemes which meet the standard security such as indistinguishability against chosen ciphertext attacks (IND-CCA security) but do not meet SO security against chosen ciphertext attacks. Hence, it is important to consider SO security in the multi-user setting. On the other hand, many researchers have studied cryptosystems in the security model where adversaries can submit quantum superposition queries (i.e., quantum queries) to oracles. In particular, IND-CCA secure PKE and KEM schemes in the quantum random oracle model have been intensively studied so far. In this paper, we show that two kinds of constructions of hybrid encryption schemes meet simulation-based SO security against chosen ciphertext attacks (SIM-SO-CCA security) in the quantum random oracle model or the quantum ideal cipher model. The first scheme is constructed from any IND-CCA secure KEM and any simulatable data encapsulation mechanism (DEM). The second one is constructed from any IND-CCA secure KEM based on Fujisaki-Okamoto transformation and any strongly unforgeable message authentication code (MAC). We can apply any IND-CCA secure KEM scheme to the first one if the underlying DEM scheme meets simulatability, whereas we can apply strongly unforgeable MAC to the second one if the underlying KEM is based on Fujisaki-Okamoto transformation.

We consider actions of a group or a semigroup on a set, which generalize the setup of discrete logarithm based cryptosystems. Such cryptographic group actions have gained increasing attention recently in the context of isogeny-based cryptography. We introduce generic algorithms for the semigroup action problem and discuss lower and upper bounds. Also, we investigate Pohlig-Hellman type attacks in a general sense. In particular, we consider reductions provided by non-invertible elements in a semigroup, and we deal with subgroups in the case of group actions.

Computation on ciphertexts of all known fully homomorphic encryption (FHE) schemes induces some noise, which, if too large, will destroy the plaintext. Therefore, the bootstrapping technique that re-encrypts a ciphertext and reduces the noise level remains the only known way of building FHE schemes for arbitrary unbounded computations. The bootstrapping step is also the major efficiency bottleneck in current FHE schemes. A promising direction towards improving concrete efficiency is to exploit the bootstrapping process to perform useful computation while reducing the noise at the same time. We show a bootstrapping algorithm, which embeds a lookup table and evaluates arbitrary functions of the plaintext while reducing the noise. Depending on the choice of parameters, the resulting homomorphic encryption scheme may be either an exact FHE or homomorphic encryption for approximate arithmetic. Since we can evaluate arbitrary functions over the plaintext space, we can use the natural homomorphism of Regev encryption to compute affine functions without bootstrapping almost for free. Consequently, our algorithms are particularly suitable for arithmetic circuits over a finite field with many additions and scalar multiplication gates. We achieve significant speedups when compared to binary circuit-based FHE. For example, we achieve 280-1200x speedups when computing an affine function of size 784 followed by any univariate function when compared to FHE schemes that compute binary circuits. With our bootstrapping algorithm, we can efficiently convert between arithmetic and boolean plaintexts and extend the plaintext space using the Chinese remainder theorem. Furthermore, we can run the computation in an exact and approximate mode where we trade-off the size of the plaintext space with approximation error. We provide a tight error analysis and show several parameter sets for our bootstrapping. Finally, we implement our algorithm and provide extensive tests. We demonstrate our algorithms by evaluating different neural networks in several parameter and accuracy settings.

The SIDH protocol is an isogeny-based key exchange protocol using supersingular isogenies, designed by Jao and De Feo in 2011. The protocol underlies the SIKE algorithm which advanced to the fourth round of NIST's post-quantum standardization project in May 2022. The algorithm was considered very promising: indeed the most significant attacks against SIDH were meet-in-the-middle variants with exponential complexity, and torsion point attacks which only applied to unbalanced parameters (and in particular, not to SIKE). This security picture dramatically changed in August 2022 with new attacks by Castryck-Decru, Maino-Martindale and Robert. Like prior attacks on unbalanced versions, these new attacks exploit torsion point information provided in the SIDH protocol. Crucially however, the new attacks embed the isogeny problem into a similar isogeny problem in a higher dimension to also affect the balanced parameters. As a result of these works, the SIKE algorithm is now fully broken both in theory and in practice. Given the considerable interest attracted by SIKE and related protocols in recent years, it is natural to seek countermeasures to the new attacks. In this paper, we introduce two such countermeasures based on partially hiding the isogeny degrees and torsion point information in the SIDH protocol. We present a preliminary analysis of the resulting schemes including non-trivial generalizations of prior attacks. Based on this analysis we suggest parameters for our M-SIDH variant with public key sizes of 4434, 7037 and 9750 bytes respectively for NIST security levels 1, 3, 5.

We define a new primitive that we call a somewhere statistically binding (SSB) commitment scheme, which is a generalization of dual-mode commitments but has similarities with SSB hash functions (Hubacek and Wichs, ITCS 2015) without local opening. In (existing) SSB hash functions, one can compute a hash of a vector v that is statistically binding in one coordinate of v. Meanwhile, in SSB commitment schemes, a commitment of a vector v is statistically binding in some coordinates of v and is statistically hiding in the other coordinates. The set of indices where binding holds is predetermined but known only to the commitment key generator. We show that the primitive can be instantiated by generalizing the succinct Extended Multi-Pedersen commitment scheme (González et al., Asiacrypt 2015). We further introduce the notion of functional SSB commitment schemes and, importantly, use it to get an efficient quasi-adaptive NIZK for arithmetic circuits and efficient oblivious database queries.

Recently, Chen et al. (ASIACRYPT 2021) introduced a notion called hierarchical integrated signature and encryption (HISE), which provides a new principle for combining public key schemes. It uses a single public key for both signature and encryption schemes, and one can derive a decryption key from the signing key but not vice versa. Whereas, they left the dual notion where the signing key can be derived from the decryption key as an open problem. In this paper, we resolve the problem by formalizing the notion called hierarchical integrated encryption and signature (HIES). Similar to HISE, it features a unique public key for both encryption and signature components and has a two-level key derivation mechanism, but reverses the hierarchy between signing key and decryption key, i.e. one can derive a signing key from the decryption key but not vice versa. This property enables secure delegation of signing capacity in the public key reuse setting. We present a generic construction of HIES from constrained identity-based encryption. Furthermore, we instantiate our generic HIES construction and implement it. The experimental result demonstrates that our HIES scheme is comparable to the best Cartesian product combined public-key scheme in terms of efficiency, and is superior in having richer functionality as well as retaining merits of key reuse.