In this paper we propose a new cryptanalytic method against block ciphers, which combines both algebraic and statistical techniques. More specifically, we show how to use algebraic relations arising from differential characteristics to speed up and improve key-recovery differntial attacks against block ciphers. To illustrate the new technique, we apply algebraic techniques to mount differential attacks against round reduced variants of Present-128.

\begin{document} Ciphers $y=C(x, k)$ and $Y=C_{1}(X, K)$ are isomorphic if there exists invertible computable in both directions map $y \leftrightarrow Y$, $x \leftrightarrow X$, $k \leftrightarrow K$. Cipher is vulnerable if and only if isomorphic cipher is vulnerable. Instead of computing the key of a cipher it is sufficient to find suitable isomorphic cipher and compute its key. If $\varphi $ is arbitrary substitution and $T$ is round substitution, its conjugate $T_{1}=\varphi T\varphi ^{ - 1}$ is cipher isomorphism. Conjugate substitutions have the same cycle type. Conjugation can be composed with affine maps. Combining conjugation and affine equivalence, sometimes we can transform non-linear special $S$-box to conjugate affine substitution $S_{1}$. Usually for given $S$, $S_{1}$ there are many different auxiliary substitutions $\varphi $. Conjugate diffusion map and XOR operation become non-linear, but taking appropriate $\varphi $ we can get large probabilities of differentials and linear sums of diffusion map and XOR. For example AES substitution (as finite field inverting) is approximately conjugate with bit changing substitution. That conjugate substitution has differentials and linear sums of probability 1. Corresponding byte substitution $\varphi $ defines non-linear conjugate diffusion map and non-linear conjugate to XOR operation with round key. Probabilities of differentials (biases of linear sums) of byte substitution of conjugate diffusion map are 8-12 times more then corresponding values of original $S$-box. Probabilities of differentials of conjugate XOR with the round key byte depends on the round key and can be 1 for some key bytes.

We analyse the Double-Mix Merkle-Damgaard construction (DMMD) used in the AURORA family of hash functions. We show that DMMD falls short of providing the expected level of security. Specically, we are able to find 2nd pre-images for AURORA-512 in time 2^{291}, and collisions in time 2^{234.4}. A limited-memory variant finds collisions in time 2^{249}.

In this note, we present a 2nd-preimage attack on AURORA-512, which is one of the candidates for SHA-3. Our attack can generate 2nd-preimages of any given message, in particular, the attack complexity becomes optimal when the message length is 9 blocks or more. In such a case, the attack complexity is approximately $2^{290}$ AURORA-512 operations, which is less than the brute force attack on AURORA-512, namely, $2^{512-\log_2{9}}\approx2^{508}$. Our attack exploits some weakness in the mode of operation.

CryptMT v3 is a stream cipher submitted to eStream project, and has entered the third evaluation phase. Any attack has not been found until now. In this paper, we mainly discuss the security of the state initialization process of CryptMT v3. For the key and IV setup function $f_K$, we can construct a probabilistic testing algorithm $A^{f_K}$ with a distinguishing probability 1, which indicates that for each key $K$, $f_K$ is a non-PRF. However, we have not found any non-randomness about the keystream output.

In this note, we present a collision attack on AURORA-512, which is one of the candidates for SHA-3. The attack complexity is approximately $2^{236}$ AURORA-512 operations, which is less than the birthday bound of AURORA-512, namely, $2^{256}$. Our attack exploits some weakness in the mode of operation.

This paper shows the complete linear probability distribution of MARS' s-box. The best bias is $\dfrac{84}{2^9}$ ($=2^{-2.61}$), while the designers' estimation is $\dfrac{64}{2^9}$ and the best previously known bias is $\dfrac{82}{2^9}$.

Cryptanalytic time memory tradeoff algorithms are generic one-way function inversion techniques that utilize pre-computation. Even though the online time complexity is known up to a small multiplicative factor for any tradeoff algorithm, false alarms pose a major obstacle in its accurate assessment. In this work, we study the expected pre-image size for an iteration of functions and use the result to analyze the cost incurred by false alarms. We are able to present the expected online time complexities for the Hellman tradeoff and the rainbow table method in a manner that takes false alarms into account. We also analyze the effects of the checkpoint method in reducing false alarm costs. The ability to accurately compute the online time complexities will allow one to choose their tradeoff parameters more optimally, before starting the expensive pre-computation process.

The security of cascade blockcipher encryption is an important and well-studied problem in theoretical cryptography with practical implications. It is well-known that double encryption improves the security only marginally, leaving triple encryption as the shortest reasonable cascade. In a recent paper, Bellare and Rogaway showed that in the ideal cipher model, triple encryption is significantly more secure than single and double encryption, stating the security of longer cascades as an open question. In this paper, we propose a new lemma on the indistinguishability of systems extending Maurer's theory of random systems. In addition to being of independent interest, it allows us to compactly rephrase Bellare and Rogaway's proof strategy in this framework, thus making the argument more abstract and hence easy to follow. As a result, this allows us to address the security of longer cascades as well as some errors in their paper. Our result implies that for blockciphers with smaller key space than message space (e.g. DES), longer cascades improve the security of the encryption up to a certain limit. This partially answers the open question mentioned above.

Message Authentication Codes (MACs) are central algorithms deployed in virtually every security protocol in common usage. In these protocols, the integrity and authenticity of messages rely entirely on the security of the MAC; we examine cases in which this security is lost. In this paper, we examine the notion of “reforgeability” for MACs. We first give a definition for this new notion, then examine some of the most widely-used and well-known MACs under our definition. We show that for each of these MACs there exists an attack that allows efficient forgeries after the first one is obtained, and we show that simply making these schemes stateful is usually insufficient. For those schemes where adding state is effective, we go one step further to examine how counter misuse affects the security of the MAC, finding, in many cases, simply repeating a single counter value yields complete insecurity. These issues motivated the design of a new scheme, WMAC, which has a number of desirable properties. It is as efficient as the fastest MACs, resists counter misuse, and has tags which may be truncated to the desired length without affecting security (currently, the fastest MACs do not have this property), making it resistant to reforging attacks and arguably the best MAC for constrained environments.

Digital Enhanced Cordless Telecommunications (DECT) is a standard for connecting cordless telephones to a fixed telecommunications network over a short range. The cryptographic algorithms used in DECT are not publicly available. In this paper we reveal one of the two algorithms used by DECT, the DECT Standard Authentication Algorithm (DSAA). We give a very detailed security analysis of the DSAA including some very effective attacks on the building blocks used for DSAA as well as a common implementation error that can practically lead to a total break of DECT security. We also present a low cost attack on the DECT protocol, which allows an attacker to impersonate a base station and therefore listen to and reroute all phone calls made by a handset.

Many attacks on iterated block ciphers rely on statistical considerations using plaintext/ciphertext pairs to distinguish some part of the cipher from a random permutation. We provide here a simple formula for estimating the amount of plaintext/ciphertext pairs which is needed for such distinguishers and which applies to a lot of different scenarios (linear cryptanalysis, differential-linear cryptanalysis, differential/truncated differential/impossible differential cryptanalysis). The asymptotic data complexities of all these attacks are then derived. Moreover, we give an efficient algorithm for computing the data complexity accurately.

We provide a stronger definition of anonymity in the context of shared symmetric key primitives, and show that existing schemes do not provide this level of anonymity. A new scheme is presented to share symmetric key operations amongst a set of participants according to a $(t,n)$-threshold access structure. We quantify the amount of information the output of the shared operation provides about the group of participants which collaborated to produce it.

In this paper we study the probability of differentials and characteristics over 2 rounds of the AES with the objective to understand how the components of the AES round transformation interact. We extend and correct the analysis of the differential properties of the multiplicative inverse in GF($2^n$). We show that AES has characteristics with a fixed-key probability that is many times larger than the EDP. For instance, in the case of 2-round AES, we measured factors up to $2^{100}$. We study the number of characteristics with EDP $>0$ whose probability adds up to the probability of a differential and derive formulas that allow to produce a close estimate of this number for any differential. We show how the properties discovered in our study can be used to explain the values of the differentials with the largest EDP values and to construct new distinguishers using truncated differentials.

We provide the first proof of security for Tandem-DM one of the oldest and most well-known constructions for turning a blockcipher with n-bit blocklength and 2n-bit keylength into a 2n-bit cryptographic hash function. We prove, that when Tandem-DM is instantiated with AES-256, i.e. blocklength 128 bits and keylength 256 bits, any adversary that asks less than 2^{120.4} queries cannot find a collision with success probability greater than 1/2. We also prove a bound for preimage resistance of Tandem-DM. Interestingly, as there is only one practical construction known (FSE'06, Hirose) turning such an (n,2n)-bit blockcipher into a 2n-bit compression function that has provably birthday-type collision resistance, Tandem-DM is one out of two structures that possess this desirable feature.

Let $X^{(1)},X^{(2)},\ldots,X^{(n)}$ be independent and uniformly distributed over the non-negative integers $\{0,1,\ldots,2^i-1\}$; $S^{(n)}=X^{(1)}+X^{(2)}+\cdots+X^{(n)}$ and $L^{(n)}=X^{(1)}\oplus X^{(2)}\oplus \cdots\oplus X^{(n)}$. Denote the $i$-th bits of $S^{(n)}$ and $L^{(n)}$ by $S^{(n)}_i$ and $L^{(n)}_i$ respectively. We show that as $i\rightarrow \infty$, $\pr[S^{(n)}_i=L^{(n)}_i]\rightarrow \gamma^{(n)}= \frac{1}{2}+\frac{2^{n+1}(2^{n+1}-1)}{2(n+1)}\times\frac{b_{n+1}}{n!}$, where $b_n$ is the $n$-th Bernoulli number. As a consequence, $\gamma^{(2r)}=1/2$ for every $r$; and we show that $\gamma^{(2r+1)}\rightarrow 1/2$ as $r\rightarrow \infty$. For small values of $r$, $\gamma^{(2r+1)}$ is significantly different from $1/2$; for example $\gamma^{(3)}=1/3$ and $\gamma^{(5)}=17/30$. The behaviour of $\gamma^{(n)}$ for even and odd values of $n$ was earlier shown by Staffelbach and Meier without actually obtaining the formula mentioned above. For every fixed $n\geq 2$, we give a simple method for computing $\pr[S^{(n)}_i=L^{(n)}_i]$ for each $i\geq 0$. The expression involving Bernoulli numbers is arrived at via the Eulerian number triangle which in turn arises in relation to the stationary distribution of a Markov chain formed by the carry values.

Pixels in an image are essentially constituted of two properties, position and colour. Pixel Property Separation, a radically different approach for Symmetric-key image encryption, separates these properties to disturb the semantics of the image. The scheme operates in two orthogonal stages each requiring an encryption key. The first stage creates the Position Vector, an ordered set of Pixel Position Information controlled by a set of plaintext dependent Random Permutations. A bitmap flagging the presence of all the 24 bit colours is generated. The second stage randomly positions the image width and height within the ciphertext and finally applies a byte transposition on the ciphertext bytes. The complete set of image properties including width, height and pixel position-colour correlation are obscured, resulting in a practically unbreakable encryption. The orthogonality of the stages acts as an anti-catalyst for cryptanalysis. The information retrieved from compromising a stage is totally independent and cannot be used to derive the other. Classical cryptanalytic techniques demand huge number of attempts, most failing to generate valid encryption information. Plaintext attacks are rendered ineffective due to the dependency of the Random Permutations on the plaintext. Linear and Differential cryptanalysis are highly inefficient due to high Diffusion and Confusion. Although the paper describes the algorithm as applied to images, its applicability is not limited to images only. The cryptographic strength and the efficiency of operation is independent of the nature of the plaintext.

Serpent is a 128-bit block cipher designed by Ross Anderson, Eli Biham and Lars Knudsen as a candidate for the Advanced Encryption Standard (AES). It was a finalist in the AES competition. The winner, Rijndael, got 86 votes at the last AES conference while Serpent got 59 votes [1]. The designers of Serpent claim that Serpent is more secure than Rijndael.In this paper we have observed that the nonlinear order of all output bits of serpent S-boxes are not 3 as it is claimed by the designers.

In this paper, we present several new attacks on multiple encryption block ciphers based on the meet-in-the-middle attack. In the first attack (GDD-MTM), we guess a certain number of secret key bits and apply the meet-in-the-middle attack on multiple ciphertexts. The second attack (TMTO-MTM) is derived from applying the time-memory trade-off attack to the meet-in-the-middle attack on a single ciphertext. We may also use rainbow chains in the table construction to get the Rainbow-MTM attack. The fourth attack (BS-MTM) is defined by combining the time-memory-data trade-off attack proposed by Biryukov and Shamir to the meet-in-the-middle attack on multiple ciphertexts. Lastly, for the final attack (TMD-MTM), we apply the TMTO-Data curve, which demonstrates the general methodology for multiple data trade-offs, to the meet-in-the-middle attack. GDD-MTM requires no pre-processing, but the attack complexity is high while memory requirement is low. In the last four attacks, pre-processing is required but we can achieve lower (faster) online attack complexity at the expense of more memory in comparison with the GDD-MTM attack. To illustrate how the attacks may be used, we applied them in the cryptanalysis of triple DES. In particular, for the BS-MTM attack, we managed to achieve pre-computation and data complexity which are much lower while maintaining almost the same memory and online attack complexity, as compared to a time-memory-data trade-off attack by Biryukov et al. at SAC 2005. In all, our new methodologies offer viable alternatives and provide more flexibility in achieving time-memory-data trade-offs.

In this paper, we first present a new distinguisher on the CBC-MAC based on a block cipher in Cipher Block Chaining (CBC) mode. It can also be used to distinguish other CBC-like MACs from random functions. The main results of this paper are on the second-preimage attack on CBC-MAC and CBC-like MACs include TMAC, OMAC, CMAC, PC-MAC and MACs based on three-key encipher CBC mode. Instead of exhaustive search, this attack can be performed with the birthday attack complexity.

We consider symmetric key predistribution in grid-based wireless sensor networks. Networks consisting of wireless sensor nodes arranged in a grid pattern have many useful applications, including environmental monitoring and agribusiness. The structured physical distribution of nodes in such networks facilitates efficient distribution of keys to the nodes prior to deployment. It has been shown that combinatorial objects known as distinct-difference configurations (DDCs) can be used to construct effective key predistribution schemes (KPSs) for grid-based networks. In this paper we observe that the regular topology of a grid-based network enables an efficient trade-off between the connectivity, resilience and storage requirements of a KPS, and we discuss the balancing of these properties to suit application requirements. We then show how recent results on the construction of DDCs can be used to produce KPSs that achieve the desired balance, and we provide explicit algorithms for the instantiation of these schemes.

Consider the permutation $S$ in RC4. Roos pointed out in 1995 that after the Key Scheduling Algorithm (KSA) of RC4, each of the initial bytes of the permutation, i.e., $S[y]$ for small values of $y$, is biased towards some linear combination of the secret key bytes. In this paper, for the first time we show that the bias can be observed in $S[S[y]]$ too. Based on this new form of permutation bias after the KSA and other related results, a complete framework is presented to show that many keystream output bytes of RC4 are significantly biased towards several linear combinations of the secret key bytes. The results do not assume any condition on the secret key. We find new biases in the initial as well as in the 256-th and 257-th keystream output bytes. For the first time biases at such later stages are discovered without any knowledge of the secret key bytes. We also identify that these biases propagate further, once the information for the index $j$ is revealed.

A theoretical analysis of the RC4 Key Scheduling Algorithm (KSA) is presented in this paper, where the nonlinear operation is swapping among the permutation bytes. Explicit formulae are provided for the probabilities with which the permutation bytes at any stage of the KSA are biased to the secret key. Theoretical proofs of these formulae have been left open since Roos' work (1995). Next, a generalization of the RC4 KSA is analyzed corresponding to a class of update functions of the indices involved in the swaps. This reveals an inherent weakness of shuffle-exchange kind of key scheduling. We additionally show that each byte of $S_N$ actually reveals secret key information. Looking at all the elements of the final permutation $S_N$ and its inverse $S^{-1}_N$, the value of the hidden index $j$ in each round of the KSA can be estimated from a ``pair of values" in $0, \ldots, N-1$ with a constant probability of success $\pi = \frac{N-2}{N}\cdot(\frac{N-1}{N})^{N-1} + \frac{2}{N}$ (we get $\pi \approx 0.37$, for $N = 256$), which is significantly higher than the random association. Using the values of two consecutive $j$'s, we estimate the $y$-th key byte from at most a ``quadruple of values" in $0, \ldots, N-1$ with a probability $> 0.12$. As a secret key of $l$ bytes is repeated at least $\lfloor \frac{N}{l}\rfloor$ times in RC4, these many quadruples can be accumulated to get each byte of the secret key with very high probability (e.g., 0.8 to close to 1) from a small set of values. Based on our analysis of the key scheduling, we show that the secret key of RC4 can be recovered from the state information in a time much less than the exhaustive search with good probability.

In this paper we present a multicollision and multipreimage attack on the hash function Blender-n [1] for all output sizes n = 224, 256, 384 and 512. The complexity and memory requirements for finding 2^{2n} multipreimages (multicollisions) of Blender-n is roughly 10 times more than finding a collision for n/2-bit random hash function. All previous attacks were based on the trick by Joux [2] using many messages. Our attacks are based on one message with several fixpoints. The state register has eight words. By properly choosing message words we force half of the register to go to the original state. Then we will find a collision in the rest with complexity 2^{n/4}. The collision creates a fix point in the sequence of states of the state register. We use 10 such fix points. Previously known attacks [4, 5] on Blender-n have the complexity at least 2^{n/2}. Our 2^{2n}-multicollision and multipreimage attacks have a complexity 10*2^{n/4}.

In this paper, the impossible differential cryptanalysis is extended to MAC algorithms \textsc{Pelican}, MT-MAC and PC-MAC based on AES and 4-round AES. First, we collect message pairs that produce the inner near-collision with some specific differences by the birthday attack. Then the impossible differential attack on 4-round AES is implemented using a 3-round impossible differential property. For \textsc{Pelican}, our attack can recover the internal state, which is an equivalent subkey. For MT-MAC-AES, the attack turns out to be a subkey recovery attack directly. The data complexity of the two attacks is $2^{85.5}$ chosen messages, and the time complexity is about $2^{85.5}$ queries. For PC-MAC-AES, we can recover the 256-bit key with $2^{85.5}$ chosen messages and $2^{128}$ queries.

In this paper we apply impossible differential attacks to reduced round AES. Using various techniques, including the early abort approach and key schedule considerations, we significantly improve previously known attacks due to Bahrak-Aref and Phan. The improvement of these attacks leads to the best known impossible differential attacks on 7-round AES-128 and AES-192, as well as to the best known impossible differential attacks on 8-round AES-256.

We give a method that appears to be able to find colliding messages for the Waterfall hash function with approximately $O(2^{70})$ work for all hash sizes. If correct, this would show that the Waterfall hash function does not meet the required collision resistance.

In this paper, we present new distinguishers of the MAC construction \textsc{Alred} and its specific instance \textsc{Alpha}-MAC based on AES, which is proposed by Daemen and Rijmen in 2005. For the \textsc{Alred} construction, we describe a general distinguishing attack which leads to a forgery attack directly. The complexity is $2^{64.5}$ chosen messages and $2^{64.5}$ queries with success probability 0.63. We also use a two-round collision differential path for \textsc{Alpha}-MAC, to construct a new distinguisher with about $2^{65.5}$ queries. The most important is that the new distinguisher can be used to recover the internal state, which is an equivalent secret subkey, and leads to a second preimage attack. Moreover, the distinguisher on \textsc{Alred} construction is also applicable to the MACs based on CBC and CFB encryption mode.

We state the design flaws of the 1-round block cipher SHA\-MATA-BC, designed by Fleishmann and Gorski by using the building blocks of SHAMATA hash function. We fix the flaws and then show that the amended version of SHAMATA-BC is much weaker. We believe that there is no connection between security level of SHAMATA as a hash function and that of SHAMATA-BC as a block cipher.

In this note we discuss some observation of the SHA-3 candidate SHAMATA. We observe that its internal block cipher is very weak, which could possibly lead to an attack on the hash function.

Side-channel attacks are a very powerful cryptanalytic technique. Li and Gu [ProvSec'07] proposed an approach against side-channel attacks, which states that a symmetric encryption scheme is IND-secure in side-channel model, if it is IND-secure in black-box model and there is no adversary who can recover the whole key of the scheme computationally in side-channel model, i.e. WKR-SCA ^ IND -> IND-SCA. Our researches show that it is not the case. We analyze notions of security against key recovery attacks and security against distinguishing attacks, and then construct a scheme which is WKR-SCA-secure and IND-secure, but not IND-SCA-secure in the same side-channel environment. Furthermore, even if the scheme is secure again partial key recovery attacks in side-channel model, this approach still does not hold true.

We create variable-length pseudorandom permutations (PRPs) and strong PRPs (SPRPs) accepting any input length chosen from the range of b to 2b bits from fixed-length, b-bit PRPs. We utilize the elastic network that underlies the recently introduced concrete design of elastic block ciphers, exploiting it as a network of PRPs. We prove that three and four-round elastic networks are variable-length PRPs and five-round elastic networks are variable-length SPRPs, accepting any input length that is fixed in the range of b to 2b bits, when the round functions are independently chosen fixed-length PRPs on b bits. We also prove that these are the minimum number of rounds required.

The stream ciphers Py, Py6 designed by Biham and Seberry were promising candidates in the ECRYPT-eSTREAM project because of their impressive speed. Since their publication in April 2005, a number of cryptanalytic weaknesses of the ciphers have been discovered. As a result, a strengthened version Pypy was developed to repair these weaknesses; it was included in the category of `Focus ciphers' of the Phase II of the eSTREAM competition. However, even the new cipher Pypy was not free from flaws, resulting in a second redesign. This led to the generation of three new ciphers TPypy, TPy and TPy6. The designers claimed that TPy would be secure with a key size up to 256 bytes, i.e., 2048 bits. In February 2007, Sekar \emph{et al.\ }published an attack on TPy with $2^{281}$ data and comparable time. This paper shows how to build a distinguisher with $2^{268.6}$ key/IVs and one outputword for each key (i.e., the distinguisher can be constructed within the design specifications); it uses a different set of weak states of the TPy. Our results show that distinguishing attacks with complexity lower than the brute force exist if the key size of TPy is longer than 268 bits. Therefore, for longer keys, our attack constitutes an academic break of the cipher. Furthermore, we discover a large number of similar bias-producing states of TPy and provide a general framework to compute them. The attacks on TPy are also shown to be effective on Py.

The stream ciphers Py, Pypy and Py6 were designed by Biham and Seberry for the ECRYPT-eSTREAM project in 2005. The ciphers were promoted to the `Focus' ciphers of the Phase II of the eSTREAM project. However, due to some cryptanalytic results on the ciphers, strengthened versions of the ciphers, namely TPy, TPypy and TPy6 were built. So far there exists no attacks on TPy6. In this paper, we find hitherto unknown weaknesses in the keystream generation algorithms of the Py6 and of its stronger variant TPy6. Exploiting these weaknesses, a large number of distinguishing attacks are mounted on the ciphers, the best of which works with $2^{224.6}$ data and comparable time. In the second part, we present two new ciphers derived from the TPy6, namely TPy6-A and TPy6-B, whose performances are 2.65 cycles/byte and 4.4 cycles/byte on Pentium III. As a result, to the best of our knowledge, on Pentium platforms TPy6-A becomes the fastest stream cipher in the literature. Based on our security analysis, we conjecture that no attacks better than brute force are possible on the ciphers TPy6-A and TPy6-B.

This paper looks at the possibility of combining a block cipher and a stream cipher to get a strong hybrid cipher. It includes two specific proposals for combining AES-128 and RC4-128 to get a cipher that takes a 256-bit key and is significantly faster than AES-256, and arguably more secure. One is immune to algebraic attacks.

In this paper we present a preimage attack on EnRUPT-512. We exploit the fact that the internal state is only a little bit larger than the critical security level: 1152 bits against 1024 bits. The absence of a message expansion and a fairly simple compression function allow us to fix the values for some state words and thus reduce the size of birthday state space in the meet-in-the-middle attack under 1024 bits. Equations that arise through the analysis are solved using look-up tables. The complexity of the attack is around 2^{480} compression function calls and the memory requirement is around 2^{384}.

We present a very simple probabilistic, passive attack against the protocols HB and HB+. Our attack presents some interesting features: it requires less captured transcripts of protocol executions when com- pared to previous results; It makes possible to trade the amount of required transcripts for computational complexity; the value of noise used in the protocols HB and HB+ need not be known.

We propose a new hash domain extension \textit{a prefix-free-Counter-Masking-MD (pfCM-MD)}. And, among security notions for the hash function, we focus on the indifferentiable security notion by which we can check whether the structure of a given hash function has any weakness or not. Next, we consider the security of HMAC, two new prf constructions, NIST SP 800-56A key derivation function, and the randomized hashing in NIST SP 800-106, where all of them are based on the pfCM-MD. Especially, due to the counter of the pfCM-MD, the pfCM-MD are secure against all of generic second-preimage attacks such as Kelsey-Schneier attack \cite{KeSc05} and Elena {\em et al.}' attck \cite{AnBoFoHoKeShZi08}. Our proof technique and most of notations follow those in \cite{BeDaPeAs08,Bellare06,BeCaKr96a}.

This paper analyzes the Improved Cellular Message Encryption Algorithm (CMEA-I) which is an improved version of the Telecommunication Industry Association's Cellular Message Encryption Algorithm (CMEA). We present a chosen-plaintext attack of CMEA-I which requires less than 850 plaintexts in its adaptive version. This demonstrates that the improvements made over CMEA are ineffective to thwart such attacks and confirms that the security of CMEA and its variants must be reconsidered from the beginning.

In this paper we present two new attacks on round reduced versions of the AES. We present the first application of the related-key boomerang attack on 7 and 9 rounds of AES-192. The 7-round attack requires only 2^{18} chosen plaintexts and ciphertexts and needs 2^{67.5} encryptions. We extend our attack to nine rounds of AES-192. This leaves to a data complexity of 2^{67} chosen plaintexts and ciphertexts using about 2^{143.33} encryptions to break 9 rounds of AES-192.

This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we introduce a system of equations that naturally arises in the AES, and then eliminate all the intermediate variables via normal form reductions. The resulting system in key variables only is solved then. We also consider a possibility to apply our method in the meet-in-the-middle scenario especially with several plaintext/ciphertext pairs. We elaborate on the method further by looking for subsystems which contain fewer variables and are overdetermined, thus facilitating solving the large system.

In this paper, we first show that many independent pseudorandom permutations over $\{0,1\}^n$ can be obtained from a single public random permutation and secret $n$ bits. We next prove that a slightly modified IAPM is secure even if the underlying block cipher $F$ is publicly accessible (as a blackbox). We derive a similar result for OCB mode, too. We finally prove that our security bound is tight within a constant factor.

This paper studies the application of slide attacks to hash functions. Slide attacks have mostly been used for block cipher cryptanalysis. But, as shown in the current paper, they also form a potential threat for hash functions, namely for sponge-function like structures. As it turns out, certain constructions for hash-function-based MACs can be vulnerable to forgery and even to key recovery attacks. In other cases, we can at least distinguish a given hash function from a random oracle. To illustrate our results, we describe attacks against the Grindahl-256 and Grindahl-512 hash functions. To the best of our knowledge, this is the first cryptanalytic result on Grindahl-512. Furthermore, we point out a slide-based distinguisher attack on a slightly modified version of RadioGatun. We finally discuss simple countermeasures as a defense against slide attacks.

In cryptology we commonly face the problem of finding an unknown key K from the output of an easily computable keyed function F(C,K) where the attacker has the power to choose the public variable C. In this work we focus on self-synchronizing stream ciphers. First we show how to model these primitives in the above-mentioned general problem by relating appropriate functions F to the underlying ciphers. Then we apply the recently proposed framework presented at AfricaCrypt’08 by Fischer et. al. for dealing with this kind of problems to the proposed T-function based self-synchronizing stream cipher by Klimov and Shamir at FSE’05 and show how to deduce some non-trivial information about the key. We also open a new window for answering a crucial question raised by Fischer et. al. regarding the problem of finding weak IV bits which is essential for their attack.

Abstract: This paper describes a new method of creating systems of poly-alphabetic, symmetric ciphers with a large set of algorithms. The method uses two translation tables containing the code-text character set, one for encryption and the other for decryption. After each character is encrypted or decrypted, these tables are permuted through a series of pseudo random, pairwise swaps. The implementation of alternative swap formulas leads to systems with large sets of encryption/decryption algorithms. Systems that contain more than a googol (1E100) algorithms have been easily implemented. An algorithm set can be easily sub-setted, producing hierarchical systems where a program may contain a single algorithm or a portion of the full set. The strength of these systems has not been determined. However strength can be inferred through the use of a substantial number of numeric keys , pseudo random number generators, algorithm switching, and other features.

Relay attacks are a major concern for RFID systems: during an authentication process an adversary transparently relays messages between a verifier and a remote legitimate prover. We present an authentication protocol suited for RFID systems. Our solution is the first that prevents relay attacks without degrading the authentication security level: it minimizes the probability that the verifier accepts a fake proof of identity, whether or not a relay attack occurs.

The stream ciphers Salsa20 and Trivium are two of the finalists of the eSTREAM project which are in the final portfolio of new promising stream ciphers. In this paper we show that initialization and key-stream generation of these ciphers is {\em slidable}, i.e. one can find distinct (Key, IV) pairs that produce identical (or closely related) key-streams. There are $2^{256}$ and more then $2^{39}$ such pairs in Salsa20 and Trivium respectively. We write out and solve the non-linear equations which describe such related (Key, IV) pairs. This allows us to sample the space of such related pairs efficiently as well as detect such pairs in large portions of key-stream very efficiently. We show that Salsa20 does not have 256-bit security if one considers general birthday and related key distinguishing and key-recovery attacks.

In \cite{BPW}, Buchmann, Pyshkin and Weinmann have described two families of Feistel and SPN block ciphers called Flurry and Curry respectively. These two families of ciphers are fully parametrizable and have a sound design strategy against basic statistical attacks; i.e. linear and differential attacks. The encryption process can be easily described by a set of algebraic equations. These ciphers are then targets of choices for algebraic attacks. In particular, the key recovery problem has been reduced to changing the order of a Groebner basis \cite{BPW,BPWext}. This attack - although being more efficient than linear and differential attacks - remains quite limited. The purpose of this paper is to overcome this limitation by using a small number of suitably chosen pairs of message/ciphertext for improving algebraic attacks. It turns out that this approach permits to go one step further in the (algebraic) cryptanalysis of Flurry and \textbf{Curry}. To explain the behavior of our attack, we have established an interesting connection between algebraic attacks and high order differential cryptanalysis \cite{Lai}. From extensive experiments, we estimate that our approach, that we can call an ``algebraic-high order differential" cryptanalysis, is polynomial when the Sbox is a power function. As a proof of concept, we have been able to break Flurry -- up to $8$ rounds -- in few hours.

Online ciphers are those ciphers whose ciphertexts can be computed in real time by using a length-preserving encryption algorithm. HCBC1 and HCBC2 are two known examples of Hash Cipher Block Chaining online ciphers. The first construction is secure against chosen plaintext adversary (or called CPA-secure) whereas the latter is secure against chosen ciphertext adversary (or called CCA-secure). In this paper, we have provided simple security analysis of these online ciphers. We have also proposed two new more efficient chosen ciphertext secure online ciphers modified-HCBC (MHCBC) and modified-CBC (MCBC). If one uses a finite field multiplication based universal hash function, the former needs one less key and one less field multiplication compared to HCBC2. The MCBC does not need any universal hash function and it needs only one blockcipher key unlike the other three online ciphers where two independent keys (hash function and blockcipher) are required.

In this paper, we present some new applications of the bounds for the differential probability of a SDS (Substitution-Diffusion-Substitution) structure by Park et al. at FSE 2003. Park et al. have applied their result on the AES cipher which uses the SDS structure based on MDS matrices. We shall apply their result to practical ciphers that use SDS structures based on {0,1}-matrices of size n times n. These structures are useful because they can be efficiently implemented in hardware. We prove a bound on {0,1}-matrices to show that they cannot be MDS and are almost-MDS only when n=2,3 or 4. Thus we have to apply Park's result whenever {0,1}-matrices where $n \geq 5$ are used because previous results only hold for MDS and almost-MDS diffusion matrices. Based on our bound, we also show that the {0,1}-matrix used in E2 is almost-optimal among {0,1}-matrices. Using Park's result, we prove differential bounds for E2 and an MCrypton-like cipher, from which we can deduce their security against boomerang attack and some of its variants. At ICCSA 2006, Khoo and Heng constructed block cipher-based universal hash functions, from which they derived Message Authentication Codes (MACs) which are faster than CBC-MAC. Park's result provides us with the means to obtain a more accurate bound for their universal hash function. With this bound, we can restrict the number of MAC's performed before a change of MAC key is needed.

Broadcast encryption (BE) deals with secure transmission of a message to a group of receivers such that only an authorized subset of receivers can decrypt the message. The transmission cost of a BE system can be reduced considerably if a limited number of free riders can be tolerated in the system. In this paper, we study the problem of how to optimally place a given number of free riders in a subset difference (SD) based BE system, which is currently the most efficient BE scheme in use and has also been incorporated in standards, and we propose a polynomial-time optimal placement algorithm and three more efficient heuristics for this problem. Simulation experiments show that SD-based BE schemes can benefit significantly from the proposed algorithms.

This paper describes a new approach to creation of fast encryption methods with symmetric (shared) key. The result solution is intermediate one between block and stream ciphers. The main advantages of both types of ciphers are realized, while most of disadvantages are eliminated. The new approach combines encryption with built-in calculation of the hash for the data integrity, pseudo-random generator, and option for dual shared keys. These properties are pivotal for secure applications. These new methods may be designed for different size of shared secret key. Both software and hardware implementations of the new methods are fast and simple and may be used in various security applications. Presented cryptanalysis proves basic features and gives an option to design actual provable security methods.

The eStream cipher proposal TRIVIUM outputs an XOR sum of six internal state bits. These in turn are obtained from 18 bits linearly, plus six ANDings of two bits each. We show that 4 of the 18 linear terms cancel between themselves.

This paper describes the Zcipher - a symmetric encryption/decryption cryptographic algorithm, designed to be secure and high-performance with small memory footprint and simple structure.

HENKOS is a synchronous stream cipher posted by Marius Oliver Gheorghita to eprint. In this paper we are going to present some weaknesses in the cipher. We first present a chosen IV attack which is very straight forward attack on the cipher. Second we present a group of weak keys.

It is shown that an improved version of a previously proposed iterative probabilistic algorithm, based on forward and backward probability recursions along a short keystream segment, is capable of reconstructing the RC4 internal states from a relatively small number of known initial permutation entries. Given a modulus $N$, it is argued that about $N/3$ and $N/10$ known entries are sufficient for success, for consecutive and specially generated entries, respectively. The complexities of the corresponding guess-and-determine attacks are analyzed and, e.g., for $N=256$, the data and time complexities are (conservatively) estimated to be around $D \approx 2^{41}$, $C \approx 2^{689}$ and $D \approx 2^{211}$, $C \approx 2^{262}$, for the two types of guessed entries considered, respectively.

We give three weaknesses of a recently proposed streamcipher MICKEY. A small class of weak keys is found and we show time-memory-data tradeoff is applicable. We also show that the state update function reduces entropy of the internal state as it is iterated, resulting in keystreams that start out differently but become merged together towards the end.

In this paper, we revisit the variant of the self-shrinking generator(SSG) proposed by Chang et al. at ICISC 2006. This variant, which we call SSG-XOR was claimed to have better cryptographic properties than SSG in a practical setting. But we show that SSG-XOR has no advantage over SSG from the viewpoint of practical cryptanalysis.

In emerging networks consisting of large-scale deployments of mobile devices, efficient security mechanisms are required to facilitate cryptographic authentication. While computation and bandwidth overheads are expensive for mobile devices, the cost of storage resources continue to fall at a rapid rate. We propose a simple novel key predistribution scheme, \textit{key subset and symmetric certificates} (KSSC) which can take good advantage of inexpensive storage resources, and has many compelling advantages over other approaches for facilitating ad hoc establishment of pairwise secrets in mobile computing environments. We argue that a combination of KSSC with a variant of an elegant KDS proposed by Leighton and Micali is an appealing choice for securing large scale deployments of mobile devices.

SMS4 is a Chinese block cipher standard, mandated for use in protecting wireless net- works, and issued in January 2006. The input, output, and key of SMS4 are each 128 bits. The algorithm has 32 rounds, each of which modifies one of the four 32-bit words that make up the block by xoring it with a keyed function of the other three words. Encryption and decryption have the same structure except that the round key schedule for decryption is the reverse of the round key schedule for encryption.

Time-Memory Tradeoff (TMTO) attacks on stream ciphers are a serious security threat and the resistance to this class of attacks is an important criterion in the design of a modern stream cipher. TMTO attacks are especially effective against stream ciphers where a variant of the TMTO attack can make use of multiple data to reduce the off-line and the on-line time complexities of the attack (given a fixed amount of memory). In this paper we present a new approach to TMTO attacks against stream ciphers using a publicly known initial value (IV): We suggest not to treat the IV as part of the secret key material (as done in current attacks), but rather to choose in advance some IVs and apply a TMTO attack to streams produced using these IVs. We show that while the obtained tradeoff curve is identical to the curve obtained by the current approach, the new technique allows to mount the TMTO attack in a larger variety of settings. For example, if both the secret key and the IV are of length n, it is possible to mount an attack with data, time, and memory complexities of 2^{4n/5}, while in the current approach, either the time complexity or the memory complexity is not less than 2^n. We conclude that if the IV length of a stream cipher is less than 1.5 times the key length, there exists an attack on the cipher with data, time, and memory complexities less than the complexity of exhaustive key search.

We present a birthday attack against DES. It is entirely based on the relationship $L_{i+1}=R_{i}$ and the simple key schedule in DES. It requires about $2^{16}$ ciphertexts of the same $R_{16}$, encrypted by the same key $K$. We conjecture it has a computational complexity of $2^{48}$. Since the requirement for the birthday attack is more accessible than that for Differential cryptanalysis, Linear cryptanalysis or Davies' attack, it is of more practical significance.

We study the security of step-reduced but otherwise unmodified SHA-256. We show the first collision attacks on SHA-256 reduced to 23 and 24 steps with complexities $2^{18}$ and $2^{28.5}$, respectively. We give example colliding message pairs for 23-step and 24-step SHA-256. The best previous, recently obtained result was a collision attack for up to 22 steps. We extend our attacks to 23 and 24-step reduced SHA-512 with respective complexities of $2^{44.9}$ and $2^{53.0}$. Additionally, we show non-random behaviour of the SHA-256 compression function in the form of free-start near-collisions for up to 31 steps, which is 6 more steps than the recently obtained non-random behaviour in the form of a free-start near-collision. Even though this represents a step forwards in terms of cryptanalytic techniques, the results do not threaten the security of applications using SHA-256.

SMS4 is a 128-bit block cipher with a 128-bit user key and 32 rounds, which is used in WAPI, the Chinese WLAN national standard. In this paper, we present a linear attack and a differential attack on a 22-round reduced SMS4; our 22-round linear attack has a data complexity of 2^{117} known plaintexts, a memory complexity of 2^{109} bytes and a time complexity of 2^{109.86} 22-round SMS4 encryptions and 2^{120.39} arithmetic operations, while our 22-round differential attack requires 2^{118} chosen plaintexts, 2^{123} memory bytes and 2^{125.71} 22-round SMS4 encryptions. Both of our attacks are better than any previously known cryptanalytic results on SMS4 in terms of the number of attacked rounds. Furthermore, we present a boomerang and a rectangle attacks on a 18-round reduced SMS4. These results are better than previously known rectangle attacks on reduced SMS4. The methods presented to attack SMS4 can be applied to other unbalanced Feistel ciphers with incomplete diffusion.

We study an infinite class of functions which provably achieve an optimum algebraic immunity, an optimum algebraic degree and a good nonlinearity. We checked that it has also a good behavior against fast algebraic attacks.

This paper studies the security of ARIA against impossible differential cryptanalysis. Firstly an algorithm is given to find many new 4-round impossible differentials of ARIA. Followed by such impossible differentials, we improve the previous impossible differential attack on 5/6-round ARIA. We also point out that the existence of such impossible differentials are due to the bad properties of the binary matrix employed in the diffusion layer.

Bellare and Micciancio's MuHASH applies a pre-existing hash function to map indexed message blocks into a secure group. The resulting hash is the product. Bellare and Micciancio proved, in the random oracle model, that MuHASH is collision-resistant if the group's discrete logarithm problem is infeasible. MuHASH, however, relies on a pre-existing hash being collision resistant. In this paper, we remove such a reliance by replacing the pre-existing hash with a block cipher under a fixed key. We adapt Bellare and Micciancio's collision-resistance proof to the ideal cipher model. Preimage resistance requires us to add a further modification.

Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In this paper, by using the relationship between some flats and support of a n variables Boolean function f, we introduce a general method to determine the algebraic immunity of a Boolean function and finally construct some balanced functions with optimum algebraic immunity.

We investigate the security of $n$-bit to $m$-bit vectorial Boolean functions in stream ciphers. Such stream ciphers have higher throughput than those using single-bit output Boolean functions. However, as shown by Zhang and Chan at Crypto 2000, linear approximations based on composing the vector output with any Boolean functions have higher bias than those based on the usual correlation attack. In this paper, we introduce a new approach for analyzing vector Boolean functions called generalized correlation analysis. It is based on approximate equations which are linear in the input $x$ but of free degree in the output $z=F(x)$. The complexity for computing the generalized nonlinearity for this new attack is reduced from $2^{2^m \times n+n}$ to $2^{2n}$. Based on experimental results, we show that the new generalized correlation attack gives linear approximation with much higher bias than the Zhang-Chan and usual correlation attack. We confirm this with a theoretical upper bound for generalized nonlinearity, which is much lower than for the unrestricted nonlinearity (for Zhang-Chan's attack) and {\em a fortiori} for usual nonlinearity. We also prove a lower bound for generalized nonlinearity which allows us to construct vector Boolean functions with high generalized nonlinearity from bent and almost bent functions. We derive the generalized nonlinearity of some known secondary constructions for secure vector Boolean functions. Finally, we prove that if a vector Boolean function has high nonlinearity or even a high unrestricted nonlinearity, it cannot ensure that it will have high generalized nonlinearity.

Recent articles~\cite{kucuk,ckp08,isobe,cryptoeprint:2008:128} introduce the concept of phase shifting equivalent keys in stream ciphers, and exploit this concept in order to mount attacks on some specific ciphers. The idea behind phase shifting equivalent keys is that, for many ciphers, each internal state can be considered as the result of an injection of a key and initialization vector. This enables speeding up the standard exhaustive search algorithm among the $2^n$ possible keys by decreasing the constant factor of $2^n$ in the time complexity of the algorithm. However, this has erroneously been stated in~\cite{isobe,cryptoeprint:2008:128} as decreasing the complexity of the algorithm below $2^n$. In this note, we show why this type of attacks, using phase shifting equivalent keys to improve exhaustive key search, can never reach time complexity below $2^n$, where $2^n$ is the size of the key space.

DECIM v2 is a stream cipher submitted to the ECRYPT stream cipher project (eSTREAM) and ISO/IEC 18033-4. No attack against DECIM v2 has been proposed yet. In this paper, we propose a chosen IV attack against DECIM v2 using a new equivalent key class. Our attack can recover an $80$-bit key with a time complexity of $2^{79.90}$ when all bits of the IV are zero. This result is the best one on DECIM v2.

MiFare Crypto 1 is a lightweight stream cipher used in London's Oyster card, Netherland's OV-Chipcard, US Boston's CharlieCard, and in numerous wireless access control and ticketing systems worldwide. Recently, researchers have been able to recover this algorithm by reverse engineering. We have examined MiFare from the point of view of the so called "algebraic attacks". We can recover the full 48-bit key of MiFare algorithm in 200 seconds on a PC, given 1 known IV (from one single encryption). The security of this cipher is therefore close to zero. This is particularly shocking, given the fact that, according to the Dutch press, 1 billion of MiFare Classic chips are used worldwide, including in many governmental security systems.

We study the standard block cipher modes of operation: CBC, CFB, and OFB and analyse their security. We don't look at ECB other than briefly to note its insecurity, and we have no new results on counter mode. Our results improve over those previously published in that (a) our bounds are better, (b) our proofs are shorter and easier, (c) the proofs correct errors we discovered in previous work, or some combination of these. We provide a new security notion for symmetric encryption which turns out to be rather useful when analysing block cipher modes. Finally, we pay attention to different methods for selecting initialization vectors for the block cipher modes, and prove security for a number of different selection policies. In particular, we introduce the concept of a `generalized counter', and prove that generalized counters suffice for security in (full-width) CFB and OFB modes and that generalized counters encrypted using the block cipher (with the same key) suffice for all three modes.

With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean functions play important role in the construction of a symmetric cryptosystem. In this paper the modifed hill climbing method is considered. The method allows using hill climbing techniques to modify bent functions used to design balanced, highly nonlinear Boolean functions with high algebraic degree and low autocorrelation. The experimental results of constructing the cryptographically strong Boolean functions are presented.

This paper presents an improved impossible differential attack on the new block cipher CLEFIA which is proposed by Sony Corporation at FSE 2007. Combining some observations with new tricks, we can filter out the wrong keys more efficiently, and improve the impossible differential attack on 11-round CLEFIA-192/256, which also firstly works for CLEFIA-128. The complexity is about $2^{103.1}$ encryptions and $2^{103.1}$ chosen plaintexts. By putting more constraint conditions on plaintext pairs, we give the first attack on 12-round CLEFIA for all three key lengths with $2^{119.1}$ encryptions and $2^{119.1}$ chosen plaintexts. For CLEFIA-192/256, our attack is applicable to 13-round variant, of which the time complexity is about $2^{181}$, and the data complexity is $2^{120}$. We also extend our attack to 14-round CLEFIA-256, with about $2^{245.4}$ encryptions and $2^{120.4}$ chosen plaintexts. Moreover, a birthday sieve method is introduced to decrease the complexity of the core precomputation.

KeeLoq remote keyless entry systems are widely used for access control purposes such as garage door openers for car anti-theft systems. We present the first successful differential power analysis attacks on numerous commercially available products employing KeeLoq code hopping. Our new techniques combine side-channel cryptanalysis with specific properties of the KeeLoq algorithm. They allow for efficiently revealing both the secret key of a remote transmitter and the manufacturer key stored in a receiver. As a result, a remote control can be cloned from only ten power traces, allowing for a practical key recovery in few minutes. Once knowing the manufacturer key, we demonstrate how to disclose the secret key of a remote control and replicate it from a distance, just by eavesdropping at most two messages. This key-cloning without physical access to the device has serious real-world security implications. Finally, we mount a denial-of-service attack on a KeeLoq access control system. All the proposed attacks have been verified on several commercial KeeLoq products.

Here we present a new security notion called as pseudo random involution or PRI which are associated with tweakable involution enciphering schemes or TIES (i.e., the encryption and decryption are same algorithm). This new security notion is important in two reasons. Firstly, it is the natural security notion for TIES which are having practical importance. Secondly, we show that there is a generic method to obtain a sprp-secure tweakable enciphering scheme (TES) from pri-secure construction. The generic method costs an extra xor with an extra key. In this paper, we also propose an efficient pri-secure construction Hash-Counter Involution or HCI and based on it we obtain a sprp-secure construction which is real improvement over XCB. We call the new construction as MXCB or Modified-XCB. HCH, XCB and HCTR are some of the popular counter based enciphering schemes, where HCTR is more efficient among them and HCH, XCB guarantee more security compare to HCTR. The new proposal MXCB has efficiency similar to HCTR and guarantees more security similar to HCH and XCB. We consider this new construction to be an important in light of the current activities of the IEEE working group on storage security which is working towards a standard for a wide block TES.

In this paper we present an efficient and secure generic method which can encrypt messages of size at least $n$. This generic encryption algorithm needs a secure encryption algorithm for messages of multiple of $n$. The first generic construction, XLS, has been proposed by Ristenpart and Rogaway in FSE-07. It needs two extra invocations of an independently chosen strong pseudorandom permutation or SPRP defined over $\s^n$ for encryption of an incomplete message block. Whereas our construction needs only one invocation of a weak pseudorandom function and two multiplications over a finite field (equivalently, two invocations of an universal hash function). We prove here that the proposed method preserves (tweakable) SPRP. This new construction is meaningful for two reasons. Firstly, it is based on weak pseudorandom function which is a weaker security notion than SPRP. Thus we are able to achieve stronger security from a weaker one. Secondly, in practice, finite field multiplication is more efficient than an invocation of SPRP. Hence our method can be more efficient than XLS.

McGrew and Fluhrer first proposed hash-counter-hash approach to encrypt arbitrary length messages. By its nature, counter can handle incomplete message blocks as well as complete message blocks in the same manner. HCTR is the till date best (in terms of efficiency) strong pseudo random permutation or SPRP among all known counter based SPRPs. But as of now, a cubic bound for HCTR is known. Moreover, all invocations of underlying block ciphers can not be made in parallel. Our new proposal (we call it HMC or Hash Modified Counter) provides a quadratic security bound and all block cipher invocations are parallel in nature even if we have an incomplete message block. We also present a prp-distinguishing attack on a generic counter based encryption, which makes $q$ non-adaptive encryption queries consisting of $(\ell+1)$ $n$-bit blocks and has success probability roughly $\ell^2q^2/2^n$. Loosely speaking, the success probability matches with the upper bound of distinguishing probability. As a result, we prove that the known quadratic bounds for XCB, HCH and HMC are tight.

This paper describes an improved preimage attack on the cryptographic hash function MD2. The attack has complexity equivalent to about $2^{73}$ evaluations of the MD2 compression function. This is to be compared with the previous best known preimage attack, which has complexity about $2^{97}$.

In Eurocrypt 2006, Bellare and Rogaway \cite{BeRo06} gave a proof of the PRP/PRF switching Lemma using their game-based proof technique. In the appendix of the same paper, they also gave an proof without games. In this paper, we give another proof of the switching lemma, which is simple and mathematically-clear and easy to uderstand. Our proof is based on \textit{the strong interpolation theorem}.

In this paper, we investigate the application of an algorithm to find the best linear approximation of a basic Substitution-Permutation Network block cipher. The results imply that, while it is well known that the S-box used for the Advanced Encryption Standard has good nonlinear properties, it is straightforward to randomly select other S-boxes which are able to provide a similar level of security, as indicated by the exact bias of the best linear approximation found by the algorithm, rather than a simple upper bound on the maximum bias.

This paper describes a series of vulnerabilities found on HENKOS algorithm (http://eprint.iacr.org/080) having a description below, regarding to the related key attacks, mounting this type of attack for a particular relation between keys and showing that is a practical attack, having results in real time.

In case of security analysis of hash functions, finding a good collision-inducing differential paths has been only focused on. However, it is not clear how differential paths of a hash function influence the securities of schemes based on the hash function. In this paper, we show that any differential path of a hash function can influence the securities of schemes based on the hash function. We explain this fact with the MD4 hash function. We first show that APOP-MD4 with a nonce of fixed length can be analyzed efficiently with a new differential path. Then we improve the result of the key-recovery attack on NMAC-MD4 described by Fouque {\em et al.} \cite{FoLeNg07} by combining new differential paths. Our results mean that good hash functions should have the following property : \textit{It is computationally infeasible to find differential a path of hash functions with a high probability}.

In this paper, we will present a cryptanalysis of CRUSH hash structure. Surprisingly, our attack could find pre-image for any desired length of internal message. Time complexity of this attack is completely negligible. We will show that the time complexity of finding a pre-image of any length is O(1). In this attack, an adversary could freely find a pre-image with the length of his own choice for any given message digits. We can also find second pre-image, collision, multi-collision in the same complexity with our attack. In this paper, we also introduce a stronger variant of the algorithm, and show that an adversary could still be able to produce collisions for this stronger variant of CRUSH hash structure with a time complexity less than a Birthday attack.

Manual authentication is a recently proposed model of communication motivated by the settings where the only trusted infrastructure is a low bandwidth authenticated channel, possibly realized by the aid of a human, that connects the sender and the receiver who are otherwise connected through an insecure channel and do not have any shared key or public key infrastructure. A good example of such scenarios is pairing of devices in Bluetooth. Manual authentication systems are studied in computational and information theoretic security model and protocols with provable security have been proposed. In this paper we extend the results in information theoretic model in two directions. Firstly, we extend a single receiver scenario to multireceiver case where the sender wants to authenticate the same message to a group of receivers. We show new attacks (compared to single receiver case) that can launched in this model and demonstrate that the single receiver lower bound $2\log(1/\epsilon)+O(1)$ on the bandwidth of manual channel stays valid in the multireceiver scenario. We further propose a protocol that achieves this bound and provides security, in the sense that we define, if up to $c$ receivers are corrupted. The second direction is the study of non-interactive protocols in unconditionally secure model. We prove that unlike computational security framework, without interaction a secure authentication protocol requires the bandwidth of the manual channel to be at least the same as the message size, hence non-trivial protocols do not exist.

\begin{abstract} Let $A$ be a Feistel scheme with $5$ rounds from $2n$ bits to $2n$ bits. In the present paper we show that for most such schemes $A$: \begin{enumerate} \item It is possible to distinguish $A$ from a random permutation from $2n$ bits to $2n$ bits after doing at most ${\cal O}(2^{n})$ computations with ${\cal O}(2^{n})$ non-adaptive {\bf chosen} plaintexts. \item It is possible to distinguish $A$ from a random permutation from $2n$ bits to $2n$ bits after doing at most ${\cal O}(2^{\frac{3n}{2}})$ computations with ${\cal O}(2^{\frac{3n}{2}})$ {\bf random} plaintext/ciphertext pairs. \end{enumerate} Since the complexities are smaller than the number $2^{2n}$ of possible inputs, they show that some generic attacks always exist on Feistel schemes with $5$ rounds. Therefore we recommend in Cryptography to use Feistel schemes with at least $6$ rounds in the design of pseudo-random permutations. We will also show in this paper that it is possible to distinguish most of $6$ round Feistel permutations generator from a truly random permutation generator by using a few (i.e. ${\cal O}(1)$) permutations of the generator and by using a total number of ${\cal O}(2^{2n})$ queries and a total of ${\cal O}(2^{2n})$ computations. This result is not really useful to attack a single $6$ round Feistel permutation, but it shows that when we have to generate several pseudo-random permutations on a small number of bits we recommend to use more than $6$ rounds. We also show that it is also possible to extend these results to any number of rounds, however with an even larger complexity. \end{abstract}

In this paper we don't examine security of Turbo SHA-2 completely; we only show new collision attacks on it, with smaller complexity than it was considered by Turbo SHA-2 authors. In [1] they consider Turbo SHA-224/256-r and Turbo SHA-384/512-r with variable number of rounds r from 1 to 8. The authors of [1] show collision attack on Turbo SHA-256-1 with one round which has the complexity of 2^64. For other r from 2 to 8 they don't find better attack than with the complexity of 2^128. Similarly, for Turbo SHA-512 they find only collision attack on Turbo SHA-512-1 with one round which has the complexity of 2^128. For r from 2 to 8 they don't find better attack than with the complexity of 2^256. In this paper we show collision attack on SHA-256-r for r = 1, 2,..., 8 with the complexity of 2^{16*r}. We also show collision attack on Turbo SHA-512-r for r = 1, 2,..., 8 with the complexity of 2^{32*r}. It follows that the only one remaining candidate from the hash family Turbo SHA is Turbo SHA-256 (and Turbo SHA-512) with 8 rounds. The original security reserve of 6 round has been lost.

This letter proposes a differential fault analysis on the AES key schedule and shows how an entire 128-bit AES key can be retrieved. In the workshop at FDTC 2007, we presented the DFA mechanism on the AES key schedule and proposed general attack rules. Using our proposed rules, we showed an efficient attack that can retrieve 80 bits of the 128-bit key. Recently, we have found a new attack that can obtain an additional 8 bits compared with our previous attack. As a result, we present most efficient attack for retrieving 88 bits of the 128-bit key using approximately two pairs of correct and faulty ciphertexts.

This paper presents a new powerful side-channel cryptanalytic method - algebraic collision attacks - representing an efficient class of power analysis being based on both the power consumption information leakage and specific structure of the attacked cryptographic algorithm. This can result in an extremely low measurement count needed for a key recovery. The algebraic collision attacks are well applicable to AES, if one-byte collisions are detectable. For the recovery of the complete AES key, one needs 3 measurements with a probability of 0.42 and 4.24 PC hours post-processing, 4 measurements with a probability of 0.82 and several seconds of offline computations or 5 measurements with success probability close to 1 and several seconds of post-processing.

In this paper we present a group of statistical tests that explore the random behavior of encryption modes of operations, when used in disk encryption applications. The results of these tests help us to better understand how these modes work. We tested ten modes of operations with the presented statistical tests, five of the narrow-block type and the other five of the wide-block type. Our analysis shows some weakness in some of these modes.

We present a novel instrument of automated cryptanalysis suitable for measuring the number of rounds that can build one PRF round, so that 4 such rounds could be recommended as a Luby-Rackoff cipher secure against adaptive attacks. ASD tests can detect structural flaws in all kinds of cryptographic primitives and their implementations. We present our results for some of the well-known ciphers and hash functions and for some of the eSTREAM candidates. Our tools can distinguish complete Achterbahn, Grain v1 and Grain-128 from random, detect weak keys in the complete IDEA cipher and find fatal structural flaws even in complete ciphers like LILI, KeeLoq or TEA in a matter of seconds. Cryptanalysts can save their valuable time by requiring that all new ciphers must pass not only randomness tests, but also automated cryptanalysis tests like ours before they could be considered interesting for manual cryptanalytic study.

In this paper we study the neighbourhood of $15$-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and $1$-resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.

This article analyses some properties of the \emph{template attack}. Examples come from attacks against an unprotected ASIC implementation of DES. The principal components analysis (PCA) is used to represent the templates in two dimensions. We give a physical interpretation of the templates PCA eigenvalues and eigenvectors. We show that the S-boxes are \emph{not} the target of template attacks. We point out that the efficiency of template attacks on unprotected implementations can be unleashed by using a power model. The most suitable power-model happens to be linked to the key schedule. This casts a new light on key schedule requirements for SCA resistance against a ``template'' attacker. The results are tailored for DES, because this symmetric block cipher is emblematic and is still promised a long life. Its key schedule is also remarkably simple, with cryptanalytic weaknesses,that paradoxically turn out to be a strength against SCA.

Tweakable enciphering schemes are length preserving block cipher modes of operation that provide a strong pseudo-random permutation. It has been suggested that these schemes can be used as the main building blocks for achieving in-place disk encryption. In the past few years there has been an intense research activity towards constructing secure and efficient tweakable enciphering schemes. But, actual experimental performance data of these newly proposed schemes are yet to be reported. Accordingly, in this paper we present optimized FPGA implementations of five tweakable enciphering schemes, namely, HCH, HCTR, XCB, EME and TET, using a 128-bit AES core as the underlying block cipher. We report performance timings of these modes when using both, pipelined and sequential AES structures. The universal polynomial hash function included in the specification of HCH, HCHfp (a variant of HCH), HCTR, XCB and TET, was implemented using a Karatsuba-Ofman multiplier as the main building block. We provide detailed analyses of each of the schemes and their experimental performances achieved in various scenarios. Our experiments show that a sequential AES core is not an attractive option for the design of these modes as it leads to rather poor throughputs. In contrast, by using an encryption/decryption pipelined AES core we get a throughput of 3.67 Gbps for HCTR and by using a encryption only pipeline AES core we get a throughput of 5.71 Gbps for EME. The performance results reported in this paper provide experimental evidence that hardware implementations of tweakable enciphering schemes can actually match and even outperform the data rates achieved by state-of-the-technology disk controllers, thus showing that they might be used for achieving provably secure in-place hard disk encryption.

We show that the LASH-$x$ hash function is vulnerable to attacks that trade time for memory, including collision attacks as fast as $2^{\frac{4}{11}x}$ and preimage attacks as fast as $2^{\frac47x}$. Moreover, we describe heuristic lattice based collision attacks that use small memory but require very long messages. Based upon experiments, the lattice attacks are expected to find collisions much faster than $2^{x/2}$. All of these attacks exploit the designers' choice of an all zero IV. We then consider whether LASH can be patched simply by changing the IV. In this case, we show that LASH is vulnerable to a $2^{\frac78x}$ preimage attack. We also show that LASH is trivially not a PRF when any subset of input bytes is used as a secret key. None of our attacks depend upon the particular contents of the LASH matrix -- we only assume that the distribution of elements is more or less uniform. Additionally, we show a generalized birthday attack on the final compression of LASH which requires $O\left(x2^{\frac{x}{2(1+\frac{107}{105})}}\right) \approx O(x2^{x/4})$ time and memory. Our method extends the Wagner algorithm to truncated sums, as is done in the final transform in LASH.

In this paper, the Ness-Helleseth functions over $F_{p^n}$ defined by the form $f(x)=ux^{\frac{p^n-1}{2}-1}+x^{p^n-2}$ are proven to be a new class of almost perfect nonlinear (APN) functions and they are CCZ-inequivalent with all other known APN functions when $p\geq 7$. The original method of Ness and Helleseth showing the functions are APN for $p=3$ and odd $n\geq 3$ is also suitable for showing their APN property for any prime $p\geq 7$ with $p\equiv 3\,({\rm mod}\,4)$ and odd $n$.

The nonlinearity profile of a Boolean function (i.e. the sequence of its minimum Hamming distances $nl_r(f)$ to all functions of degrees at most $r$, for $r\geq 1$) is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers. It plays also a role in coding theory, since it is related to the covering radii of Reed-Muller codes. We introduce a method for lower bounding its values and we deduce bounds on the second order nonlinearity for several classes of cryptographic Boolean functions, including the Welch and the multiplicative inverse functions (used in the S-boxes of the AES). In the case of this last infinite class of functions, we are able to bound the whole profile, and we do it in an efficient way when the number of variables is not too small. This allows showing the good behavior of this function with respect to this criterion as well.

We prove that a random map drawn from any class ${\frak C}$ of polynomial maps from $F_q^n$ to $F_q^{n+r}$ that is (i) totally random in the affine terms, and (ii) has a negligible chance of being not strongly one-way, provides a secure PRNG (hence a secure stream cipher) for any q. Plausible choices for ${\frak C}$ are semi-sparse (i.e., the affine terms are truly random) systems and other systems that are easy to evaluate from a small (compared to a generic map) number of parameters. To our knowledge, there are no other positive results for provable security of specialized polynomial systems, in particular sparse ones (which are natural candidates to investigate for speed). We can build a family of provably secure stream ciphers a rough implementation of which at the same security level can be more than twice faster than an optimized QUAD (and any other provably secure stream ciphers proposed so far), and uses much less storage. This may also help build faster provably secure hashes. We also examine the effects of recent results on specialization on security, e.g., Aumasson-Meier (ICISC 2007), which precludes Merkle-Damgaard compression using polynomials systems {uniformly very sparse in every degree} from being universally collision-free. We conclude that our ideas are consistent with and complements these new results. We think that we can build secure primitives based on specialized (versus generic) polynomial maps which are more efficient.

This paper studies the security of a recently-proposed chaos-based image encryption scheme, and points out the following problems: 1) there exist a number of invalid keys and weak keys, and some keys are partially equivalent for encryption/decryption; 2) given one chosen plain-image, a subkey $K_{10}$ can be guessed with a smaller computational complexity than that of the simple brute-force attack; 3) given at most 128 chosen plain-images, a chosen-plaintext attack can possibly break the following part of the secret key: $\{K_i\bmod 128\}_{i=4}^{10}$, which works very well when $K_{10}$ is not too large; 4) when $K_{10}$ is relatively small, a known-plaintext attack can be carried out with only one known plain-image to recover some visual information of any other plain-images encrypted by the same key.