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See detailAdvancing the Meet-in-the-Filter Technique: Applications to CHAM and KATAN
Biryukov, Alexei UL; Teh, Je Sen UL; Udovenko, Aleksei UL

in Smith, Benjamin; Wu, Huapeng (Eds.) Selected Areas in Cryptography (in press)

Recently, Biryukov et al. presented a new technique for key recovery in differential cryptanalysis, called meet-in-the-filter (MiF). In this work, we develop theoretical and practical aspects of the ... [more ▼]

Recently, Biryukov et al. presented a new technique for key recovery in differential cryptanalysis, called meet-in-the-filter (MiF). In this work, we develop theoretical and practical aspects of the technique, which helps understanding and simplifies application. In particular, we show bounds on MiF complexity and conditions when the MiF-enhanced attack may reach them. We present a method based on trail counting which allows to estimate filtering strength of involved rounds and perform consequent complexity analysis with pen and paper, compared to the computer-aided approach of the original work. Furthermore, we show how MiF can be combined with plaintext structures for linear key schedules, allowing to increase the number of attacked rounds or to reduce the data complexity. We illustrate our methods on block cipher families CHAM and KATAN and show best-to-date single-key differential attacks for these ciphers. [less ▲]

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See detailAn overview of the Eight International Olympiad in Cryptography "Non-Stop University CRYPTO"
Gorodilova, Anastasiya; Tokareva, Natalia; Agievich, Sergey et al

E-print/Working paper (2022)

Non-Stop University CRYPTO is the International Olympiad in Cryptography that was held for the eight time in 2021. Hundreds of university and school students, professionals from 33 countries worked on ... [more ▼]

Non-Stop University CRYPTO is the International Olympiad in Cryptography that was held for the eight time in 2021. Hundreds of university and school students, professionals from 33 countries worked on mathematical problems in cryptography during a week. The aim of the Olympiad is to attract attention to curious and even open scientific problems of modern cryptography. In this paper, problems and their solutions of the Olympiad’2021 are presented. We consider 19 problems of varying difficulty and topics: ciphers, online machines, passwords, binary strings, permutations, quantum circuits, historical ciphers, elliptic curves, masking, implementation on a chip, etc. We discuss several open problems on quantum error correction, finding special permutations and s-Boolean sharing of a function, obtaining new bounds on the distance to affine vectorial functions. [less ▲]

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See detailMeet-in-the-Filter and Dynamic Counting with Applications to Speck
Biryukov, Alexei UL; Cardoso Dos Santos, Luan UL; Teh, Je Sen UL et al

E-print/Working paper (2022)

We propose a new cryptanalytic tool for differential cryptanalysis, called meet-in-the-filter (MiF). It is suitable for ciphers with a slow or incomplete diffusion layer such as the ones based on Addition ... [more ▼]

We propose a new cryptanalytic tool for differential cryptanalysis, called meet-in-the-filter (MiF). It is suitable for ciphers with a slow or incomplete diffusion layer such as the ones based on Addition-Rotation-XOR (ARX). The main idea of the MiF technique is to stop the difference propagation earlier in the cipher, allowing to use differentials with higher probability. This comes at the expense of a deeper analysis phase in the bottom rounds possible due to the slow diffusion of the target cipher. The MiF technique uses a meet-in-the-middle matching to construct differential trails connecting the differential’s output and the ciphertext difference. The proposed trails are used in the key recovery procedure, reducing time complexity and allowing flexible time-data trade-offs. In addition, we show how to combine MiF with a dynamic counting technique for key recovery. We illustrate MiF in practice by reporting improved attacks on the ARXbased family of block ciphers Speck. We improve the time complexities of the best known attacks up to 15 rounds of Speck32 and 20 rounds of Speck64/128. Notably, our new attack on 11 rounds of Speck32 has practical analysis and data complexities of 224.66 and 226.70 respectively, and was experimentally verified, recovering the master key in a matter of seconds. It significantly improves the previous deep learning-based attack by Gohr from CRYPTO 2019, which has time complexity 238. As an important milestone, our conventional cryptanalysis method sets a new high benchmark to beat for cryptanalysis relying on machine learning. [less ▲]

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See detailMathematical Aspects of Division Property
Hebborn, Phil; Leander, Gregor; Udovenko, Aleksei UL

E-print/Working paper (2022)

This work surveys mathematical aspects of division property, which is a state of the art technique in cryptanalysis of symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ... [more ▼]

This work surveys mathematical aspects of division property, which is a state of the art technique in cryptanalysis of symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ciphers. It aims to find integral distinguishers and cube attacks, which exploit weakness in the algebraic normal forms of the output coordinates of the involved vectorial Boolean functions. Division property can also be used to provide arguments for security of primitives against these attacks. The focus of this work is a formal presentation of the theory behind the division property, including rigorous proofs, which were often omitted in the existing literature. This survey covers the two major variants of division property, namely conventional and perfect division property. In addition, we explore relationships of the technique with classic degree bounds [less ▲]

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See detailMILP modeling of Boolean functions by minimum number of inequalities
Udovenko, Aleksei UL

E-print/Working paper (2021)

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See detailCryptanalysis of a Dynamic Universal Accumulator over Bilinear Groups
Biryukov, Alexei UL; Udovenko, Aleksei UL; Vitto, Giuseppe UL

in Topics in Cryptology – CT-RSA 2021 (2021)

In this paper we cryptanalyse the two accumulator variants proposed by Au et al., which we call the alpha-based construction and the common reference string-based (CRS-based) construction. We show that if ... [more ▼]

In this paper we cryptanalyse the two accumulator variants proposed by Au et al., which we call the alpha-based construction and the common reference string-based (CRS-based) construction. We show that if non-membership witnesses are issued according to the alpha-based construction, an attacker that has access to multiple witnesses is able to efficiently recover the secret accumulator parameter alpha and completely break its security. More precisely, if p is the order of the underlying bilinear group, the knowledge of O(log p log log p) non-membership witnesses permits to successfully recover alpha. Further optimizations and different attack scenarios allow to reduce the number of required witnesses to O(log p), together with practical attack complexity. Moreover, we show that accumulator's collision resistance can be broken if just one of these non-membership witnesses is known to the attacker. We then show how all these attacks for the alpha-based construction can be easily prevented by using instead a corrected expression for witnesses. Although outside the original security model assumed by Au \etal but motivated by some possible concrete application of the scheme where the Manager must have exclusive rights for issuing witnesses (e.g. white/black list based authentication mechanisms), we show that if non-membership witnesses are issued using the CRS-based construction and the CRS is kept secret by the Manager, an attacker accessing multiple witnesses can reconstruct the CRS and compute witnesses for arbitrary new elements. In particular, if the accumulator is initialized by adding m secret elements, the knowledge of m non-membership witnesses allows to succeed in such attack. [less ▲]

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See detailConvexity of Division Property Transitions: Theory, Algorithms and Compact Models
Udovenko, Aleksei UL

in Wang, Huaxiong; Tibouchi, Mehdi (Eds.) Advances in Cryptology -- ASIACRYPT 2021 (2021)

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See detailThe Seventh International Olympiad in Cryptography NSUCRYPTO: problems and solutions
Gorodilova, Anastasiya; Tokareva, Natalia N.; Agievich, Sergey et al

E-print/Working paper (2021)

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See detailBreaking the $IKEp182 Challenge
Udovenko, Aleksei UL; Vitto, Giuseppe UL

E-print/Working paper (2021)

We report a break of the \$IKEp182 challenge using a meet-in-the-middle attack strategy improved with multiple SIKE-specific optimizations. The attack was executed on the HPC cluster of the University of ... [more ▼]

We report a break of the \$IKEp182 challenge using a meet-in-the-middle attack strategy improved with multiple SIKE-specific optimizations. The attack was executed on the HPC cluster of the University of Luxembourg and required less than 10 core-years and 256TiB of high-performance network storage (GPFS). Different trade-offs allow execution of the attack with similar time complexity and reduced storage requirements of only about 70TiB. [less ▲]

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See detailDummy Shuffling Against Algebraic Attacks in White-Box Implementations
Biryukov, Alexei UL; Udovenko, Aleksei UL

in Canteaut, Anne; Standaert, Francois-Xavier (Eds.) Advances in Cryptology -- EUROCRYPT 2021 (2021)

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See detailLightweight AEAD and Hashing using the Sparkle Permutation Family
Beierle, Christof UL; Biryukov, Alex UL; Cardoso Dos Santos, Luan UL et al

in IACR Transactions on Symmetric Cryptology (2020), 2020(S1), 208-261

We introduce the Sparkle family of permutations operating on 256, 384 and 512 bits. These are combined with the Beetle mode to construct a family of authenticated ciphers, Schwaemm, with security levels ... [more ▼]

We introduce the Sparkle family of permutations operating on 256, 384 and 512 bits. These are combined with the Beetle mode to construct a family of authenticated ciphers, Schwaemm, with security levels ranging from 120 to 250 bits. We also use them to build new sponge-based hash functions, Esch256 and Esch384. Our permutations are among those with the lowest footprint in software, without sacrificing throughput. These properties are allowed by our use of an ARX component (the Alzette S-box) as well as a carefully chosen number of rounds. The corresponding analysis is enabled by the long trail strategy which gives us the tools we need to efficiently bound the probability of all the differential and linear trails for an arbitrary number of rounds. We also present a new application of this approach where the only trails considered are those mapping the rate to the outer part of the internal state, such trails being the only relevant trails for instance in a differential collision attack. To further decrease the number of rounds without compromising security, we modify the message injection in the classical sponge construction to break the alignment between the rate and our S-box layer. [less ▲]

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See detailOptimized Collision Search for STARK-Friendly Hash Challenge Candidates
Udovenko, Aleksei UL

E-print/Working paper (2020)

In this note, we report several solutions to the STARK-Friendly Hash Challenge: a competition with the goal of finding collisions for several hash functions designed specifically for zero-knowledge proofs ... [more ▼]

In this note, we report several solutions to the STARK-Friendly Hash Challenge: a competition with the goal of finding collisions for several hash functions designed specifically for zero-knowledge proofs (ZKP) and multiparty computations (MPC). We managed to find collisions for 3 instances of 91-bit hash functions. The method used is the classic parallel collision search with distinguished points from van Oorshot and Wiener (1994). As this is a general attack on hash functions, it does not exhibit any particular weakness of the chosen hash functions. The crucial part is to optimize the implementations to make the attack cost realistic, and we describe several arithmetic tricks. [less ▲]

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See detailOn the Sixth International Olympiad in Cryptography NSUCRYPTO
Gorodilova, Anastasiya; Tokareva, Natalia N.; Agievich, Sergey et al

E-print/Working paper (2020)

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See detailCryptanalysis of the Legendre PRF and generalizations
Beullens, Ward; Beyne, Tim; Udovenko, Aleksei UL et al

in IACR Transactions on Symmetric Cryptology (2020), 2020(1),

The Legendre PRF relies on the conjectured pseudorandomness properties of the Legendre symbol with a hidden shift. Originally proposed as a PRG by Damgård at CRYPTO 1988, it was recently suggested as an ... [more ▼]

The Legendre PRF relies on the conjectured pseudorandomness properties of the Legendre symbol with a hidden shift. Originally proposed as a PRG by Damgård at CRYPTO 1988, it was recently suggested as an efficient PRF for multiparty computation purposes by Grassi et al. at CCS 2016. Moreover, the Legendre PRF is being considered for usage in the Ethereum 2.0 blockchain. This paper improves previous attacks on the Legendre PRF and its higher-degree variant due to Khovratovich by reducing the time complexity from O(plogp/M) to O(plog^2p/M2) Legendre symbol evaluations when M≤p√4 queries are available. The practical relevance of our improved attack is demonstrated by breaking two concrete instances of the PRF proposed by the Ethereum foundation. Furthermore, we generalize our attack in a nontrivial way to the higher-degree variant of the Legendre PRF and we point out a large class of weak keys for this construction. Lastly, we provide the first security analysis of two additional generalizations of the Legendre PRF originally proposed by Damgård in the PRG setting, namely the Jacobi PRF and the power residue PRF. [less ▲]

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See detailOn degree-d zero-sum sets of full rank
Beierle, Christof UL; Biryukov, Alex UL; Udovenko, Aleksei UL

in Cryptography and Communications (2019)

A set 𝑆⊆𝔽𝑛2 is called degree-d zero-sum if the sum ∑𝑠∈𝑆𝑓(𝑠) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean ... [more ▼]

A set 𝑆⊆𝔽𝑛2 is called degree-d zero-sum if the sum ∑𝑠∈𝑆𝑓(𝑠) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of degree at most n − d − 1. We prove some results on the existence of degree-d zero-sum sets of full rank, i.e., those that contain n linearly independent elements, and show relations to degree-1 annihilator spaces of Boolean functions and semi-orthogonal matrices. We are particularly interested in the smallest of such sets and prove bounds on the minimum number of elements in a degree-d zero-sum set of rank n. The motivation for studying those objects comes from the fact that degree-d zero-sum sets of full rank can be used to build linear mappings that preserve special kinds of nonlinear invariants, similar to those obtained from orthogonal matrices and exploited by Todo, Leander and Sasaki for breaking the block ciphers Midori, Scream and iScream. [less ▲]

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See detailAlzette: A 64-bit ARX-box
Beierle, Christof UL; Biryukov, Alex UL; Cardoso Dos Santos, Luan UL et al

E-print/Working paper (2019)

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ... [more ▼]

S-boxes are the only source of non-linearity in many symmetric primitives. While they are often defined as being functions operating on a small space, some recent designs propose the use of much larger ones (e.g., 32 bits). In this context, an S-box is then defined as a subfunction whose cryptographic properties can be estimated precisely. In this paper, we present a 64-bit ARX-based S-box called Alzette, which can be evaluated in constant time using only 12 instructions on modern CPUs. Its parallel application can also leverage vector (SIMD) instructions. One iteration of Alzette has differential and linear properties comparable to those of the AES S-box, while two iterations are at least as secure as the AES super S-box. Since the state size is much larger than the typical 4 or 8 bits, the study of the relevant cryptographic properties of Alzette is not trivial. [less ▲]

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See detailCryptanalysis of SKINNY in the Framework of the SKINNY 2018--2019 Cryptanalysis Competition
Derbez, Patrick UL; Lallemand, Virginie; Udovenko, Aleksei UL

in Patterson, Kenneth G.; Stebila, Douglas (Eds.) Selected Areas in Cryptography -- SAC 2019 (2019)

In April 2018, Beierle et al. launched the 3rd SKINNY cryptanalysis competition, a contest that aimed at motivating the analysis of their recent tweakable block cipher SKINNY . In contrary to the previous ... [more ▼]

In April 2018, Beierle et al. launched the 3rd SKINNY cryptanalysis competition, a contest that aimed at motivating the analysis of their recent tweakable block cipher SKINNY . In contrary to the previous editions, the focus was made on practical attacks: contestants were asked to recover a 128-bit secret key from a given set of 2^20 plaintext blocks. The suggested SKINNY instances are 4- to 20-round reduced variants of SKINNY-64-128 and SKINNY-128-128. In this paper, we explain how to solve the challenges for 10-round SKINNY-128-128 and for 12-round SKINNY-64-128 in time equivalent to roughly 2^52 simple operations. Both techniques benefit from the highly biased sets of messages that are provided and that actually correspond to the encryption of various books in ECB mode. [less ▲]

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See detailOn Degree-d Zero-Sum Sets of Full Rank
Beierle, Christof UL; Biryukov, Alex UL; Udovenko, Aleksei UL

E-print/Working paper (2018)

A set S⊆Fn2 is called degree-d zero-sum if the sum ∑s∈Sf(s) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of ... [more ▼]

A set S⊆Fn2 is called degree-d zero-sum if the sum ∑s∈Sf(s) vanishes for all n-bit Boolean functions of algebraic degree at most d. Those sets correspond to the supports of the n-bit Boolean functions of degree at most n−d−1. We prove some results on the existence of degree-d zero-sum sets of full rank, i.e., those that contain n linearly independent elements, and show relations to degree-1 annihilator spaces of Boolean functions and semi-orthogonal matrices. We are particularly interested in the smallest of such sets and prove bounds on the minimum number of elements in a degree-d zero-sum set of rank n. The motivation for studying those objects comes from the fact that degree-d zero-sum sets of full rank can be used to build linear mappings that preserve special kinds of nonlinear invariants, similar to those obtained from orthogonal matrices and exploited by Todo, Leander and Sasaki for breaking the block ciphers Midori, Scream and iScream. [less ▲]

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See detailAttacks and Countermeasures for White-box Designs
Biryukov, Alex UL; Udovenko, Aleksei UL

in Peyrin, Thomas; Galbraith, Steven (Eds.) Advances in Cryptology – ASIACRYPT 2018 (2018, November)

In traditional symmetric cryptography, the adversary has access only to the inputs and outputs of a cryptographic primitive. In the white-box model the adversary is given full access to the implementation ... [more ▼]

In traditional symmetric cryptography, the adversary has access only to the inputs and outputs of a cryptographic primitive. In the white-box model the adversary is given full access to the implementation. He can use both static and dynamic analysis as well as fault analysis in order to break the cryptosystem, e.g. to extract the embedded secret key. Implementations secure in such model have many applications in industry. However, creating such implementations turns out to be a very challenging if not an impossible task. Recently, Bos et al. proposed a generic attack on white-box primitives called differential computation analysis (DCA). This attack was applied to many white-box implementations both from academia and industry. The attack comes from the area of side-channel analysis and the most common method protecting against such attacks is masking, which in turn is a form of secret sharing. In this paper we present multiple generic attacks against masked white-box implementations. We use the term “masking” in a very broad sense. As a result, we deduce new constraints that any secure white-box implementation must satisfy. Based on the new constraints, we develop a general method for protecting white-box implementations. We split the protection into two independent components: value hiding and structure hiding. Value hiding must pro- vide protection against passive DCA-style attacks that rely on analysis of computation traces. Structure hiding must provide protection against circuit analysis attacks. In this paper we focus on developing the value hiding component. It includes protection against the DCA attack by Bos et al. and protection against a new attack called algebraic attack. We present a provably secure first-order protection against the new al- gebraic attack. The protection is based on small gadgets implementing secure masked XOR and AND operations. Furthermore, we give a proof of compositional security allowing to freely combine secure gadgets. We derive concrete security bounds for circuits built using our construction. [less ▲]

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See detailOptimal First-Order Boolean Masking for Embedded IoT Devices
Biryukov, Alex UL; Dinu, Dumitru-Daniel UL; Le Corre, Yann UL et al

in CARDIS 2017: Smart Card Research and Advanced Applications (2018, January 26)

Boolean masking is an effective side-channel countermeasure that consists in splitting each sensitive variable into two or more shares which are carefully manipulated to avoid leakage of the sensitive ... [more ▼]

Boolean masking is an effective side-channel countermeasure that consists in splitting each sensitive variable into two or more shares which are carefully manipulated to avoid leakage of the sensitive variable. The best known expressions for Boolean masking of bitwise operations are relatively compact, but even a small improvement of these expressions can significantly reduce the performance penalty of more complex masked operations such as modular addition on Boolean shares or of masked ciphers. In this paper, we present and evaluate new secure expressions for performing bitwise operations on Boolean shares. To this end, we describe an algorithm for efficient search of expressions that have an optimal cost in number of elementary operations. We show that bitwise AND and OR on Boolean shares can be performed using less instructions than the best known expressions. More importantly, our expressions do no require additional random values as the best known expressions do. We apply our new expressions to the masked addition/subtraction on Boolean shares based on the Kogge-Stone adder and we report an improvement of the execution time between 14% and 19%. Then, we compare the efficiency of first-order masked implementations of three lightweight block ciphers on an ARM Cortex-M3 to determine which design strategies are most suitable for efficient masking. All our masked implementations passed the t-test evaluation and thus are deemed secure against first-order side-channel attacks. [less ▲]

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