Abstract
We study how does the Hamming weight of the difference between two values influence the probability of this difference preservation after modulo addition and subtraction. By the difference between two random variables we mean the operation XOR which is standard for cryptanalysis. We prove that if the most significant bit of the difference is equal to 0 (is equal to 1) then the probability of the difference preservation is equal to 2−h (equal to 2−(h−1)), where h is the Hamming weight of the difference. The theoretical results are confirmed experimentally.
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References
G. P. Agibalov, “Some Theoretical Aspects of Differential Cryptanalysis of Iterated Block Ciphers with an Additive Round Key,” Prikl. Diskretn.Mat. No. 1, 34–42 (2008).
A. I. Pestunov, “Differential Cryptanalysis of Block Cipher CAST-256,” Bezopasnost’ Inform. Tekhnol. No. 4, 57–62 (2009).
A. I. Pestunov, “Differential Cryptanalysis of the Block Cipher MARS,” Prikl. Diskretn. Mat. No. 4, 56–63 (2009).
A. I. Pestunov, “On the Probability of the Propagation of the One-Bit Difference Through Modulo Addition and Subtraction,” Prikl. Diskretn.Mat. No. 4, 53–60 (2012).
E. Biham, A. Biryukov, and A. Shamir, “Cryptanalysis of Skipjack Reduced to 31 Round Using Impossible Differentials,” in Proceedings of Eurocrypt-99 (Springer, Berlin, 1999), pp. 12–23.
E. Bihamand A. Shamir, “Differential Cryptanalysis of DES-Like Cryptosystem,” J. Cryptology, No. 4, 3–72 (1991).
A. Biryukov and E. Kushilevitz, “Improved Cryptanalysis of RC5,” in Proceedings of Eurocrypt-98 (Springer, Berlin, 1998), pp. 85–99.
J. Kelsey, T. Kohno, and B. Schneier, “Amplified Boomerang Attacks against Reduced-Round MARS and Serpent,” in Proceedings of FSE-00 (Springer, Berlin, 2001), pp. 75–93.
X. Lai and J. Massey, “Markov Ciphers and Differential Cryptanalysis,” in Proceedings of Eurocrypt-91 (Berlin, Springer, 1991), pp. 17–38.
K. Nyberg and L. Knudsen, “Provable Security against a Differential Attack,” J. Cryptology, No. 8, 27–37 (1995).
S. Vaudenay, “Decorrelation: A Theory for Block Cipher Security,” J. Cryptology, No. 16, 249–286 (2003).
D. Wagner, “The Boomerang Attack,” in Proceedings of FSE-99 (Springer, Berlin, 1999), pp. 156–170.
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Original Russian Text © A.I. Pestunov, 2013, published in Diskretnyi Analiz i Issledovanie Operatsii, 2013, Vol. 20, No. 5, pp. 58–65.
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Pestunov, A.I. Impact of the Hamming weight of the difference of two random variables on the probability of its preservation after addition and subtraction. J. Appl. Ind. Math. 8, 92–96 (2014). https://doi.org/10.1134/S1990478914010104
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DOI: https://doi.org/10.1134/S1990478914010104