Finite field for scientists and engineers
Finite field for scientists and engineers
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Shift Register Sequences
Efficient Evaluation of Security against Generalized Interpolation Attack
SAC '99 Proceedings of the 6th Annual International Workshop on Selected Areas in Cryptography
Cryptanalysis of Block Ciphers with Probabilistic Non-linear Relations of Low Degree
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of Rijmen-Preneel Trapdoor Ciphers
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
The Interpolation Attack on Block Ciphers
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
Transform domain analysis of DES
IEEE Transactions on Information Theory
Cryptanalysis of Imai and Matsumoto Scheme B Asymmetric Cryptosystem
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Further Results Related to Generalized Nonlinearity
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Hummingbird: ultra-lightweight cryptography for resource-constrained devices
FC'10 Proceedings of the 14th international conference on Financial cryptograpy and data security
A new method to determine algebraic expression of power mapping based S-boxes
Information Processing Letters
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The complexity of interpolation attacks on block ciphers depends on the degree of the polynomial approximation and/or on the number of terms in the polynomial approximation expression. In some situations, the round function or the S-boxes of the block cipher are expressed explicitly in terms of algebraic function, yet in many other occasions the S-boxes are expressed in terms of their Boolean function representation. In this case, the cryptanalyst has to evaluate the algebraic description of the S-boxes or the round function using the Lagrange interpolation formula. A natural question is what is the effect of the choice of the irreducible polynomial used to construct the finite field on the degree of the resulting polynomial. Another question is whether or not there exists a simple linear transformation on the input or output bits of the S-boxes (or the round function) such that the resulting polynomial has a less degree or smaller number of non-zero coefficients. In this paper we give an answer to these questions. We also present an explicit relation between the Lagrange interpolation formula and the Galois Field Fourier Transform.