Modified self-shrinking generator

Abstract

The self-shrinking generator SSG, an elegant keystream generator proposed by Meier and Staffelbach, is built up from a single n-stage primitive linear feedback shift register (LFSR) to produce a keystream of period P ⩾ 2 n 2 , and linear complexity greater than half its period. In this article, we propose a new variant of the self-shrinking generator called the modified self-shrinking generator MSSG. This new generator is based on a primitive n-stage LFSR and uses an extended selection rule based on the XORed value of a pair of bits. We prove that the keystreams of the MSSG are balanced, and have period greater than or equal to 2 n 3 , linear complexity greater than half the period, and possess good statistical properties. We investigate the security of the generator against various powerful cryptanalytic attacks. We show that the MSSG is more secure than the SSG against most of these attacks. Moreover, experiments show that for odd values of n, 3 < n < 20 , the period of the keystreams generated by the MSSG attains its maximum value 2 n - 1 , and the linear complexity of these keystreams is very close to its upper bound. The NIST statistical test suite is applied to several thousands keystreams of the MSSG to demonstrate their good randomness properties. The obtained results show that keystreams of the MSSG have better randomness properties than those of the SSG.