Finite fields
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
Multivariate Public Key Cryptosystems (Advances in Information Security)
Multivariate Public Key Cryptosystems (Advances in Information Security)
On solving sparse algebraic equations over finite fields
Designs, Codes and Cryptography
On the Number of Linearly Independent Equations Generated by XL
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Algebraic Techniques in Differential Cryptanalysis
Fast Software Encryption
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
About the XL algorithm over GF(2)
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Cryptanalysis of variants of UOV
ISC'06 Proceedings of the 9th international conference on Information Security
Algebraic attacks on clock-controlled cascade ciphers
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
An analysis of the XSL algorithm
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Inverting HFE systems is quasi-polynomial for all fields
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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We give exact formulas for the growth of the ideal Aλ for λ a quadratic element of the algebra of Boolean functions over the Galois field GF(2). That is, we calculate $\dim A_k \lambda$ where Ak is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made in the article of Yang, Chen and Courtois [22,23] concerning the efficiency of the XL algorithm.