Abstract
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.
Chapter PDF
Similar content being viewed by others
References
R. Lidl and H. Niederreiter, Finite Fields (Encyclopedia of Mathematics and its Applications), Addison Wesley. Reading, MA. 1983.
R. J. McEliece, Finite Fields For Computer Scientists and Engineers, Kluwer Academic Publishers. Dordrecht. 1987.
T. Jakobsen and L. Knudsen, The Interpolation Attack on Block Ciphers, LNCS 1267, Fast Software Encryption. pp. 28–40. 1997.
T. Jakobsen, Cryptanalysis of Block Ciphers with Probabilistic Non-linearRelations of Low Degree, Proceedings of Crypto’99. LNCS 1462. pp. 213–222. 1999.
V. Rijmen and B. Preneel, A family of trapdoor ciphers, Proceedings of Fast Software Encryption. LNCS 1267. pp. 139–148. 1997.
M. Sudan, Decoding Reed Solomon Codes beyond the error-correction bound, Journal of Complexity. Vol. 13.no 1. pp180–193. March, 1997.
G. Gong and S. W. Golomb, Transform Domain Analysis of DES, IEEE transactions on Information Theory. Vol. 45.no. 6. pp. 2065–2073. September, 1999.
K. Nyberg and L. Knudsen, Provable Security Against a Differential Attack, Journal of Cryptology. Vol. 8.no. 1. 1995.
K. Aoki, Efficient Evaluation of Security against Generalized Interpolation Attack, Sixth Annual Workshop on Selected Areas in cryptography SAC’99. Workshop record. pp. 154–165. 1999.
S.W. Golomb,Shift Register Sequences, Aegean Park Press. Laguna Hills, California. 1982.
R.E. Blahut, Theory and Practice of Error Control Codes, Addison-Wesley. Reading, MA. 1990.
H. Wu, F. Bao, R. Deng and Q. Ye Cryptanalysis of Rijmen-Preneel Trapdoor Ciphers, LNCS 1514, Asiacrypt’98. pp. 126–132. 1998.
G. Gong and A.M. Youssef, Lagrange Interpolation Formula and Discrete Fourier Transform, Technical Report. Center for Applied Cryptographic Research. University ofWaterloo. 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Youssef, A.M., Gong, G. (2001). On the Interpolation Attacks on Block Ciphers. In: Goos, G., Hartmanis, J., van Leeuwen, J., Schneier, B. (eds) Fast Software Encryption. FSE 2000. Lecture Notes in Computer Science, vol 1978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44706-7_8
Download citation
DOI: https://doi.org/10.1007/3-540-44706-7_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41728-6
Online ISBN: 978-3-540-44706-1
eBook Packages: Springer Book Archive