Bounds for differential probabilities

Year, pages: 2004, 89 - 99

We explore the ideas of bounding the maximum differential probability in case of various notions of difference. We give tight bounds for these probabilities in abelian groups. This result strengthens bounds given by [P. Hawkes, L. O'Connor: XOR and non-XOR differential probabilities, EUROCRYPT '99 (Prague), Lecture Notes in Comput. Sci., Vol. 1592, Springer-Verlag, Berlin, 1999, pp. 272–285], [P. Hawkes, L. O'Connor: Asymptotic bounds on differential probabilities, Research Report RZ 3018, IBM Research Report, 1998] and by [T. Tyksiński: Foundations of Differential Cryptanalysis in Abelian Groups, Information Security Proceedings, Lecture Notes in Comput. Sci., Vol 2851, Springer-Verlag, Berlin, 2003, pp. 280–294].

Tyksiński, T. 2004. Bounds for differential probabilities. In Tatra Mountains Mathematical Publications, vol. 29, no.3, pp. 89-99. 1210-3195.

Tyksiński, T. (2004). Bounds for differential probabilities. Tatra Mountains Mathematical Publications, 29(3), 89-99. 1210-3195.