Linearities in Cascade Jump Controlled Stream Ciphers
Jansen Cees J.A. · NATO science for peace and security series. D, Information and communication security · 2009
Irregularly clocking of Linear Finite State Machines such as LFSRs is widely employed in stream ciphers. A special form of irregular clocking, known as jumping was introduced in [1,2] and further developed in [3]. Stream ciphers based on jumping appeared as candidates in the eSTREAM competition. One of the identified problems of these ciphers concerns the presence of linear relations of low degree in the key stream of the cipher, the distribution of which appears to be heavily biased. In [4] this issue is addressed leading to an O(n2n) algorithm to determine all linear relations. This paper addresses the problem of finding all linear relations of a given construction efficiently. It is shown that the coefficients of the linear relations are symmetric Boolean functions of the jump control bits, leading to a polynomial time and memory algorithm to determine the number of linear relations and the highest bias value. The results show that it is feasible to determine the linear equivalence bias for LFSMs with characteristic polynomials of degree 100 and higher.