Abstract. In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSR-based stream ciphers. An algorithm is described which permits to compute the algebraic immu-operations necessary in all previous algorithms. Our algorithm is based on multivariate polynomial interpolation. For assessing the vulnerability of arbitrary Boolean functions with respect to fast algebraic attacks, an efficient generic algorithm is presented that is not based on interpolation. This algorithm is demonstrated to be particularly efficient for symmetric Boolean functions. As an application it is shown that large classes of symmetric functions are very vulnerable to fast algebraic attacks despite their proven resistance against conventional algebraic attacks.
Abstract. Klimov and Shamir proposed a new class of simple cryptographic primitives named T-functions. For two concrete proposals based on the squaring operation, a single word T-function and a previously unbroken multi-word T-function with a 256-bit state, we describe an efficient distinguishing attack having a 2 32 data complexity. Furthermore, Hong et al. recently proposed two fully specified stream ciphers, consisting of multi-word T-functions with 128-bit states and filtering functions. We describe distinguishing attacks having a 2 22 and a 2 34 data complexity, respectively. The attacks have been implemented.
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