SAT Attacks on ARX Ciphers with Automated Equations Generation

Andrzejczak, Michał; Dudzic, Wladyslaw

doi:10.36244/icj.2019.4.1

Cited by 3 publications

(3 citation statements)

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“…In our experiments we use a 4-round SPN with n B = 16, m = 4 with variable S-boxes, and a fixed permutation layer given by bit permutation (1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16). As a key schedule, we use either repetition of a 16-bit key (for n K = 16), 5 independent 16-bit subkeys (for n K = 80), or a sequence of low 16-bits from a shifted 32-bit key (for n K = 32).…”

Section: Preliminariesmentioning

confidence: 99%

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A new representation of S-boxes for algebraic diﬀerential cryptanalysis

Bednáriková¹,

Zajac²

2021

Rad Hrvatske akademije znanosti i umjetnosti

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Algebraic cryptanalysis can be used to break (small versions of) block ciphers with small data complexity. If we have access to a large number of P-C pairs, algebraic cryptanalysis can be combined with differential techniques. Differential characteristic produces extra linear equations, which can be used to augment the original algebraic system. In our experiments with algebraic differential cryptanalysis, we have developed a different technique to represent the system. In our new method, we model a single P-C pair based encryption, but we use the differential to restrict the equations that model active S-boxes.An algebraic system created with our new model is smaller, and can theoretically be solved faster. Our experiments show that the advantage depends on the overall number of P-C pairs available and whether the chosen differential characteristic is correctly estimated. One of the advantages of the new method is that it can use partial information from the differential and still determine a correct solution faster than both the standard algebraic attack and the standard algebraic-differential attack.

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Section: Preliminariesmentioning

confidence: 99%

“…In a recent article [2], Andrzejczak and Dudzic attack smaller versions of block ciphers SIMON and SPECK. Instead of modeling the whole cipher, they do not model the key expansion algorithm, and instead, try to find independent subkeys.…”

Section: Introductionmentioning

confidence: 99%

A new representation of S-boxes for algebraic diﬀerential cryptanalysis

Bednáriková¹,

Zajac²

2021

Rad Hrvatske akademije znanosti i umjetnosti

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“…Boolean and SAT encoding, among other mathematical methods of software systems specification and verification [3,4], can be used to solve problems in many fields [5][6][7][8][9][10]. This approach usually consists in transforming the studied problems into the SAT problem, solving it, and then mapping the obtained model to the solution of the source problem.…”

Section: Introductionmentioning

confidence: 99%

Partial mathematical modeling and analysis of the AES system

Stachowiak,

Kurkowski

2023

J. Appl. Math. Comput. Mech.

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Many types of decision problems can be solved using mathematical modeling and analysis. Such techniques are also developed on the border of mathematical logic and computer science. A good example is the translation of the issues examined into the Satisfiability Problem (SAT) of a logical propositional formula. Unfortunately, this method is not always practical, considering the high computational complexity of solving the SAT problem. It often happens that in the studied cases, the encoding formulas contain even hundreds of thousands of clauses and propositional variables. However, even in these cases, modern SAT solvers can sometimes successfully solve these problems. This approach can be used to cryptanalyze some symmetric ciphers or parts/modifications. In this case, the encryption algorithm is first translated into a boolean formula. Then additional formulas are created to encode randomly selected plaintext and the key bits. Using the SAT solver; we can count the values of the ciphertext bits. Then, using the SAT solver again, we proceed to the cryptanalysis of the cipher with the selected plaintext and proper ciphertext, looking for the bits of the encryption key. In this paper, we will present the new results of how SAT techniques behave against representative fragments of the AES cipher, the current standard for symmetric encryption. We also compare the results obtained in this case by several SAT solvers. In addition, we present the results of the SAT-solver CryptoMiniSat obtained during the attack on the 1st round of the AES-128 cipher.

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Algebraic Cryptanalysis with MRHS Equations

Zajac

2023

Cryptography

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In this work, we survey the existing research in the area of algebraic cryptanalysis based on Multiple Right-Hand Sides (MRHS) equations (MRHS cryptanalysis). MRHS equation is a formal inclusion that contains linear combinations of variables on the left-hand side, and a potential set of values for these combinations on the right-hand side. We describe MRHS equation systems in detail, including the evolution of this representation. Then we provide an overview of the methods that can be used to solve MRHS equation systems. Finally, we explore the use of MRHS equation systems in algebraic cryptanalysis and survey existing experimental results.

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SAT Attacks on ARX Ciphers with Automated Equations Generation

Cited by 3 publications

References 0 publications

A new representation of S-boxes for algebraic diﬀerential cryptanalysis

A new representation of S-boxes for algebraic diﬀerential cryptanalysis

Partial mathematical modeling and analysis of the AES system

Algebraic Cryptanalysis with MRHS Equations

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