Binary trinomials divisible by a fixed primitive polynomial

摘要

This paper examines the growth of the degrees of binary trinomialsthat are divisible by a fixed binary primitive polynomial f(x) of degreen. Our goal is to find a heuristic distribution that depends only on n.Our motivation stems from some suggested correlation attacks on certainstream ciphers. These attacks use binary relations-binary polynomials-asparity checks in order to recover information about the cipher key. Lowweight relations perform best but require more sequence because of theirlarge degrees