Abstract
In this paper, we study a strategy for constructing fast and practically secure round functions that yield suffciently small values of the maximum differential and linear probabilities p; q. We consider mn-bit round functions with 2-round SPN structure for Feistel ciphers. In this strategy, we regard a linear transformation layer as an n× n matrix P over 0,1. We describe the relationship between the matrix representation and the actual construction of the linear transformation layer. We propose a search algorithm for constructing the optimal linear transformation layer by using the matrix representation in order to minimize probabilities p; q as much possible. Furthermore, by this algorithm, we determine the optimal linear transformation layer that provides p≤ p5 s; q≤ q5 s in the case of n = 8, where p s ; q s denote the maximum differential and linear probabilities of s-box.
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References
C. M. Adams, “Simple and Effective Key Scheduling for Symmetric Ciphers,” Workshop on Selected Areas in Cryptology SAC’94, 1994.
K. Aoki, K. Kobayashi, S. Moriai, “Best Differential Characteristic Search of FEAL,” Fourth International Workshop on Fast Software Encryption (FSE4), LNCS 1267, 1997.
K. Aoki, K. Ohta, “Strict Evaluation of the Maximum Average of Differential Probability and the Maximum Average of Linear Probability,” IEICE Transactions Fundamentals of Electronics, Communications and Computer Sciences, Vol. E80-A, No. 1, pp. 2–8, 1997.
E. Biham, “On Matsui’s Linear Cryptanalysis,” Advances in Cryptology-EUROCRYPT’ 94, LNCS 950, 1995.
L. Brown, M. Kwan, J. Pieprzyk, J. Seberry, “Improving Resistance to Differential Cryptanalysis and the Redesign of LOKI”, Advances in Cryptology-ASIACRYPT’ 91, LNCS 739, 1993.
E. Biham, A. Shamir, “Differential Cryptanalysis of DES-like Cryptosystems,” Journal of Cryptology, Vol. 4 No. 1, pp. 3–72, 1991. (The extended abstract appeared at CRYPTO’90)
F. Chabaud, S. Vaudenay, “Links Between Differential and Linear Cryptanalysis,” Advances in Cryptology-EUROCRYPT’94, LNCS 950, 1995.
Data Encryption Standard, FIPS-PUB-46, 1977.
H. M. Heys, S. E. Tavares, “Substitution-Permutation Networks Resistant to Differential and Linear Cryptanalysis,” Journal of Cryptology, Vol. 9 No. 1, pp. 1–19, 1996.
T. Jakobsen, L. R. Knudsen, “The Interpolation Attack on Block Ciphers,” Fourth International Workshop on Fast Software Encryption (FSE4), LNCS 1267, 1997.
L. R. Knudsen, “Practically Secure Feistel Ciphers,” Cambridge SecurityWorkshop on Fast Software Encryption (FSE1), LNCS 809, 1994.
L. R. Knudsen, “Truncated and Higher Order Differentials,” Second International Workshop on Fast Software Encryption (FSE2), LNCS 1008, 1995.
X. Lai, “Higher order derivatives and differential cryptanalysis,” In Proc. of Symposium on Communication, Coding, and Cryptography,” in honor of James L. Massey on the occasion of his 60’th birthday, Feb. 10–13, 1994, Monte-Verita, Ascona, Switzerland, 1994.
X. Lai, J. L. Massey, S. Murphy, “Markov Ciphers and Differential Cryptanalysis,” Advances in Cryptology-EUROCRYPT’91, LNCS 547, 1991.
M. Matsui, “Linear Cryptanalysis Method for DES Cipher,” Advances in Cryptology-EUROCRYPT’93, LNCS 765, 1994.
M. Matsui, “On Correlation Between the Order of S-boxes and the Strength of DES,” Advances in Cryptology-EUROCRYPT’94, LNCS 950, 1995.
M. Matsui, “New Block Encryption Algorithm MISTY,” Fourth International Workshop on Fast Software Encryption (FSE4), LNCS 1267, 1997.
K. Nyberg, “Linear Approximation of Block Ciphers,” Advances in Cryptology-EUROCRYPT’94, LNCS 950, 1995.
K. Nyberg, “Generalized Feistel Networks,” Advances in Cryptology-ASIACRYPT’ 96, LNCS 1163, 1996.
K. Nyberg, L. R. Knudsen, “Provable Security Against a Differential Attack,” Journal of Cryptology, Vol. 8 No. 1, pp. 27–37, 1995. (The extended abstract appeared at CRYPTO’92)
K. Ohta, S. Moriai, K. Aoki, “Improving the Search Algorithm for the Best Linear Expression.,” Advances in Cryptology-CRYPTO’95, LNCS 963, 1995.
V. Rijmen, J. Daemen, B. Preneel, A. Bosselaers, E. DcWin, “The Cipher SHARK,” Third International Workshop on Fast Software Encryption (FSE3), LNCS 1039, 1996.
S. Vaudenay, “On the Need for Multipermutations: Cryptanalysis of MD4 and SAFER,” Second International Workshop on Fast Software Encryption (FSE2), LNCS 1008, 1995.
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© 1999 Springer-Verlag Berlin Heidelberg
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Kanda, M., Takashima, Y., Matsumoto, T., Aoki, K., Ohta, K. (1999). A Strategy for Constructing Fast Round Functions with Practical Security Against Differential and Linear Cryptanalysis. In: Tavares, S., Meijer, H. (eds) Selected Areas in Cryptography. SAC 1998. Lecture Notes in Computer Science, vol 1556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48892-8_21
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DOI: https://doi.org/10.1007/3-540-48892-8_21
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