Correlation Attacks Using a New Class of Weak Feedback Polynomials

In 1985 Siegenthaler introduced the concept of correlation attacks on LFSR based stream ciphers. A few years later Meier and Staffelbach demonstrated a special technique, usually referred to as fast correlation attacks, that is very effective if the feedback polynomial has a special form, namely, if its weight is very low. Due to this seminal result, it is a well known fact that one avoids low weight feedback polynomials in the design of LFSR based stream ciphers. This paper identifies a new class of such weak feedback polynomials, polynomials of the form f(x) = g1(x) + g2(x)x M1 + . . . + gt(x)x Mt−1 , where g1, g2, . . . , gt are all polynomials of low degree. For such feedback polynomials, we identify an efficient correlation attack in the form of a distinguishing attack.