We show that the binary expansions of algebraic numbers do not form secure pseudorandom sequences; given sufficiently many initial bits of an algebraic number, its minimal polynomial can be ...

A C implementation of Niederreiter's algorithm for factoring polynomials over F 2 is described. The most time-consuming part of this algorithm, which consists of setting up and solving a certain ...

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials: \(6{x^5} - 3{x^2} + 7\) is a polynomial ...

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work. My recent story for Quanta explained a newly proved ...