Abstract
The cryptographic strength of an SP network depends crucially on the strength of its substitution boxes (S-boxes). In this paper we use the concept of information leakage to evaluate the strength of S-boxes and SP networks. We define an equivalence class on n × n S-boxes that is invariant in information leakage. Simulation results for a 16 × 16 SP network suggest that after a sufficient number of rounds the distribution of the output XOR in the SP network looks random. We further present simulation results to show that the information leakage for an SP network diminishes more rapidly with the number of rounds when the S-boxes are cryptographically strong.
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N. B. of Standards, “Data Encryption Standard,” No. 46, U.S. Department of Commerce, 1977.
C. E. Shannon, “Communication theory of secrecy systems,” in Bell Systems Technical Journals, vol. 28, pp. 656–715, 1949.
H. Feistel, “Cryptography and Computer privacy,” in Scientific American, vol. 228, pp. 15–23, 1973.
H. Feistel, W. Notz, and J. L. Smith, “Some Cryptographic Techniques for Machine-to-Machine Data Comminications,” in Proc. of the IEEE, vol. 63, pp. 1545–1554, 1975.
A. F. Webster and S. E. Tavares, “On the Design of S-boxes,” in Advances in Cryptology, Proc. of CRYPTO’ 85, pp. 523–534, Springer-Verlag, New York, 1986.
E. F. Brickell, J. H. Moore, and M. R. Purtill, “Structure in the S-boxes of the DES (extended abstract),” in Advances in Cryptology: Proc. of CRYPTO’ 86, pp. 3–8, Springer-Verlag, New York, 1987.
J. Pieprzyk and G. Finkelstein, “Towards effective nonlinear cryptosystem design,” in IEE Proceedings, Part E: Computers and Digital Techniques, vol. 135, pp. 325–335, 1988.
C. A. Adams and S. Tavares, “The structured design of cryptographically good S-boxes,” in Journal of Cryptology, vol. 3, pp. 27–41, 1990.
R. Forré, “Methods and Instruments for designing S-boxes,” in Journal of Cryptology, vol. 2, pp. 115–130, 1990.
M. H. Dawson and S. E. Tavares, “An Expanded Set of S-box Design Criteria Based on Information Theory and its Relation to Differential-Like Attacks,” in Advances in Cryptology, Proc. of EUROCRYPT’ 91, pp. 352–367, Springer-Verlag, New York, 1992.
J. B. Kam and G. I. Davida, “Structured Design of Substitution-Permutation Encryption Networks,” in IEEE Transaction on Computers, C-28, pp. 747–753, 1979.
A. F. Webster, “Plaintext/Ciphertext Bit Dependence in Cryptographic Systems,” Master’s thesis, Queen’s University at Kingston, Canada, 1985.
L. O’Connor, “A Differential-like cryptanalysis of SP-networks,” tech. rep., Department of Computer Science, University of Waterloo, Canada, 1992., (submitted for publication).
A. Shimizu and S. Miyaguchi, “Fast data encryption algorith FEAL,” in Advances in Cryptology, EUROCRYPT’ 87, pp. 267–278, 1988.
L. Brown, J. Pieprzyk, and J. Seberry, “LOKI — cryptographic primitive for authentication and secrecy applications,” in Advances in Cryptology, Proc. of AUSCRYPT’ 90, pp. 229–236, Springer-Verlag, New York, 1990.
E. Biham and A. Shamir, “Differential cryptanalysis of DES-like cryptosystem,” in Journal of Cryptology, vol. 4, pp. 3–72, 1991.
C. A. Adams, “On immunity against Biham and Shamir’s “differential cryptanalysis”,” in Information Processing Letters, vol. 41, pp. 77–80, 1992.
E. Biham, Differential Cryptanalyst of Iterative Cryptosystem. PhD thesis, Weizmann Institute of Science, Rehovolt, Israel, 1992.
X. Lai and J. Massey, “Markov Ciphers and Differential Cryptanalysis,” in Advances in Cryptology, Proc. of EUROCRYPT’ 91, pp. 17–38, Springer-Verlag, New York, 1992.
H. Heys, Department of Electrical Engineering, Queen’s University, Kingston, Canada, (personal communication).
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Sivabalan, M., Tavares, S.E., Peppard, L.E. (1993). On the Design of SP Networks from an Information Theoretic Point of View. In: Brickell, E.F. (eds) Advances in Cryptology — CRYPTO’ 92. CRYPTO 1992. Lecture Notes in Computer Science, vol 740. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48071-4_18
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DOI: https://doi.org/10.1007/3-540-48071-4_18
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