Powers of Subfield Polynomials, Cyclic Codes and Algebraic Attacks with Applications to the WG Stream Ciphers

Abstract : In this paper we investigate univariate algebraic attacks on filter generators over extension fields F_q = F_{2^n} with focus on the Welch-Gong (WG) family of stream ciphers. Our main contribution is to break WG-5,WG-7,WG-8 and WG-16 by combining results on the so-called spectral immunity (minimum distance of certain cyclic codes) with properties of the WG type stream cipher construction.The spectral immunity is the univariate analog of algebraic immunity and instead of measuring degree of multiples of a multivariate polynomial, it measures the minimum number of nonzero coecients of a multiple of a univariate polynomial. Based on the structure of the general WG-construction, we deduce better bounds for the spectral immunity and the univariate analog of algebraic attacks.