Abstract
This paper presents a new algorithm for cryptanalytically attacking stream ciphers. There is an associated measure of security, the 2-adic span. In order for a stream cipher to be secure, its 2-adic span must be large. This attack exposes a weakness of Rueppel and Massey’s summation combiner. The algorithm, based on De Weger and Mahler’s rational approximation theory for 2-adic numbers, synthesizes a shortest feedback with carry shift register that outputs a particular key stream, given a small number of bits of the key stream. It is adaptive in that it does not need to know the number of available bits beforehand.
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Klapper, A., Goresky, M. (1995). Cryptanalysis Based on 2-Adic Rational Approximation. In: Coppersmith, D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44750-4_21
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