QUAD: A practical stream cipher with provable security

Abstract

We introduce a practical stream cipher with provable security named QUAD. The cipher relies on the iteration of a multivariate quadratic system of m equations in n < m unknowns over a finite field. The security of the keystream generation of QUAD is provably reducible to the conjectured intractability of the MQ problem, namely solving a multivariate system of quadratic equations. Our recommended version of QUAD uses a 80-bit key, 80-bit IV and an internal state of n = 160 bits. It outputs 160 keystream bits (m = 320) at each iteration until 40 bits of keystream have been produced. © International Association for Cryptologic Research 2006.