Cryptanalysis based on 2-adic rational approximation

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.