Binary trinomials divisible by a fixed primitive polynomial

This paper examines the growth of the degrees of binary trinomials that are divisible by a fixed binary primitive polynomial f(x) of degree n. Our goal is to find a heuristic distribution that depends only on n. Our motivation stems from some suggested correlation attacks on certain stream ciphers. These attacks use binary relations-binary polynomials-as parity checks in order to recover information about the cipher key. Low weight relations perform best but require more sequence because of their large degrees