Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algebraic and Slide Attacks on KeeLoq
Fast Software Encryption
Practical Algebraic Attacks on the Hitag2 Stream Cipher
ISC '09 Proceedings of the 12th International Conference on Information Security
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Algebraic cryptanalysis of the data encryption standard
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
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In an algebraic attack on a cipher, one expresses the encryption function as a system (usually overdefined) of multivariate polynomial equations in the bits of the plaintext, the ciphertext and the key, and subsequently solves the system for the unknown key bits from the knowledge of one or more plaintext/ciphertext pairs. The standard eXtended Linearization algorithm (XL) expands the initial system of equations by monomial multiplications. The expanded system is treated as a linear system in the monomials. For most block ciphers (like the Advanced Encryption Standard (AES)), the size of the linearized system turns out to be very large, and consequently, the complexity to solve the system often exceeds the complexity of brute-force search. In this paper, we propose a heuristic strategy XL SGE to reduce the number of linearized equations. This reduction is achieved by applying structured Gaussian elimination before each stage of monomial multiplication. Experimentation on small random systems indicates that XL SGE has the potential to improve the performance of the XL algorithm in terms of the size of the final solvable system. This performance gain is exhibited by our heuristic also in the case of a toy version of AES.