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The differential analysis of S-functions. (English) Zbl 1290.94112

Biryukov, Alex (ed.) et al., Selected areas in cryptography. 17th international workshop, SAC 2010, Waterloo, Ontario, Canada, August 12–13, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-19573-0/pbk). Lecture Notes in Computer Science 6544, 36-56 (2011).
Summary: An increasing number of cryptographic primitives use operations such as addition modulo \(2^n\), multiplication by a constant and bitwise Boolean functions as a source of non-linearity. In NIST’s SHA-3 competition, this applies to 6 out of the 14 second-round candidates. In this paper, we generalize such constructions by introducing the concept of S-functions. An S-function is a function that calculates the \(i\)-th output bit using only the inputs of the \(i\)-th bit position and a finite state \(S[i]\). Although S-functions have been analyzed before, this paper is the first to present a fully general and efficient framework to determine their differential properties. A precursor of this framework was used in the cryptanalysis of SHA-1. We show how to calculate the probability that given input differences lead to given output differences, as well as how to count the number of output differences with non-zero probability. Our methods are rooted in graph theory, and the calculations can be efficiently performed using matrix multiplications.
For the entire collection see [Zbl 1208.94008].

MSC:

94A60 Cryptography
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