Alex Biryukov

Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials

In this paper we present a new cryptanalytic technique, based on impossible differentials, and use it to show that Skipjack reduced from 32 to 31 rounds can be broken by an attack which is faster than exhaustive search.

Real Time Cryptanalysis of A5/1 on a PC

A5/1 is the strong version of the encryption algorithm used by about 130 million GSM customers in Europe to protect the over-the-air privacy of their cellular voice and data communication. The best published attacks against it require between 240 and 245 steps. This level of security makes it vulnerable to hardware-based attacks by large organizations, but not to software-based attacks on multiple targets by hackers. In this paper we describe new attacks on A5/1, which are based on subtle flaws in the tap structure of the registers, their noninvertible clocking mechanism, and their frequent resets. After a 248 parallelizable data preparation stage (which has to be carried out only once), the actual attacks can be carried out in real time on a single PC. The first attack requires the output of the A5/1 algorithm during the first two minutes of the conversation, and computes the key in about one second. The second attack requires the output of the A5/1 algorithm during about two seconds of the conversation, and computes the key in several minutes. The two attacks are related, but use different types of time-memory tradeoffs. The attacks were verified with actual implementations, except for the preprocessing stage which was extensively sampled rather than completely executed. REMARK: We based our attack on the version of the algorithm which was derived by reverse engineering an actual GSM telephone and published at http://www.scard.org. We would like to thank the GSM organization for graciously confirming to us the correctness of this unofficial description. In addition, we would like to stress that this paper considers the narrow issue of the cryptographic strength of A5/1, and not the broader issue of the practical security of fielded GSM systems, about which we make no claims.

Cryptanalytic Time/Memory/Data Tradeoffs for Stream Ciphers

In 1980 Hellman introduced a general technique for breaking arbitrary block ciphers with N possible keys in time T and memory M related by the tradeoff curve TM2 = N2 for 1 ≤ T ≤ N. Recently, Babbage and Golic pointed out that a different TM = N tradeoff attack for 1 ≤ T ≤ D is applicable to stream ciphers, where D is the amount of output data available to the attacker. In this paper we show that a combination of the two approaches has an improved time/memory/data tradeoff for stream ciphers of the form TM2D2 = N2 for any D2 ≤ T ≤ N. In addition, we show that stream ciphers with low sampling resistance have tradeoff attacks with fewer table lookups and a wider choice of parameters.

Related-Key Cryptanalysis of the Full AES-192 and AES-256

In this paper we present two related-key attacks on the full AES. For AES-256 we show the first key recovery attack that works for all the keys and has 299.5 time and data complexity, while the recent attack by Biryukov-Khovratovich-Nikolic works for a weak key class and has much higher complexity. The second attack is the first cryptanalysis of the full AES-192. Both our attacks are boomerang attacks, which are based on the recent idea of finding local collisions in block ciphers and enhanced with the boomerang switching techniques to gain free rounds in the middle. The extended version of this paper is available at http://eprint.iacr.org/2009/317.pdf .

Distinguisher and Related-Key Attack on the Full AES-256

In this paper we construct a chosen-key distinguisher and a related-key attack on the full 256-bit key AES. We define a notion of differential q -multicollision and show that for AES-256 q-multicollisions can be constructed in time q·267 and with negligible memory, while we prove that the same task for an ideal cipher of the same block size would require at least

Advanced slide attacks

O(q\cdot 2^{\frac{q-1}{q+1}128})

Miss in the Middle Attacks on IDEA and Khufu

time. Using similar approach and with the same complexity we can also construct q-pseudo collisions for AES-256 in Davies-Meyer mode, a scheme which is provably secure in the ideal-cipher model. We have also computed partial q-multicollisions in time q·237 on a PC to verify our results. These results show that AES-256 can not model an ideal cipher in theoretical constructions. Finally we extend our results to find the first publicly known attack on the full 14-round AES-256: a related-key distinguisher which works for one out of every 235 keys with 2120 data and time complexity and negligible memory. This distinguisher is translated into a key-recovery attack with total complexity of 2131 time and 265 memory.

On Multiple Linear Approximations

Recently a powerful cryptanalytic tool--the slide attack-- was introduced [3]. Slide attacks are very successful in breaking iterative ciphers with a high degree of self-similarity and even more surprisingly are independent of the number of rounds of a cipher. In this paper we extend the applicability of slide attacks to a larger class of ciphers. We find very efficient known- and chosen-text attacks on generic Feistel ciphers with a periodic key-schedule with four independent subkeys, and consequently we are able to break a DES variant proposed in [2] using just 128 chosen texts and negligible time for the analysis (for one out of every 216 keys). We also describe known-plaintext attacks on DESX and Even-Mansour schemes with the same complexity as the best previously known chosen-plaintext attacks on these ciphers. Finally, we provide new insight into the design of GOST by successfully analyzing a 20-round variant (GOST⊕) and demonstrating weak key classes for all 32 rounds.

Key recovery attacks of practical complexity on AES-256 variants with up to 10 rounds

In a recent paper we developed a new cryptanalytic technique based on impossible differentials, and used it to attack the Skipjack encryption algorithm reduced from 32 to 31 rounds. In this paper we describe the application of this technique to the block ciphers IDEA and Khufu. In both cases the new attacks cover more rounds than the best currently known attacks. This demonstrates the power of the new cryptanalytic technique, shows that it is applicable to a larger class of cryptosystems, and develops new technical tools for applying it in new situations.

A toolbox for cryptanalysis: linear and affine equivalence algorithms

In this paper we study the long standing problem of information extraction from multiple linear approximations. We develop a formal statistical framework for block cipher attacks based on this technique and derive explicit and compact gain formulas for generalized versions of Matsui’s Algorithm 1 and Algorithm 2. The theoretical framework allows both approaches to be treated in a unified way, and predicts significantly improved attack complexities compared to current linear attacks using a single approximation. In order to substantiate the theoretical claims, we benchmarked the attacks against reduced-round versions of DES and observed a clear reduction of the data and time complexities, in almost perfect correspondence with the predictions. The complexities are reduced by several orders of magnitude for Algorithm 1, and the significant improvement in the case of Algorithm 2 suggests that this approach may outperform the currently best attacks on the full DES algorithm.