QUAD: Overview and Recent Developments

Abstract

We give an outline of the specification and provable security
features of the QUAD stream cipher proposed at Eurocrypt 2006.
The cipher relies on the iteration of a multivariate system of quadratic
equations over a finite field, typically GF(2) or a small extension. In the
binary case, the security of the keystream generation can be related, in
the concrete security model, to the conjectured intractability of the MQ
problem of solving a random system of m equations in n unknowns. We
show that this security reduction can be extended to incorporate the key
and IV setup and provide a security argument related to the whole stream
cipher.We also briefly address software and hardware performance issues
and show that if one is willing to pseudorandomly generate the systems
of quadratic polynomials underlying the cipher, this leads to suprisingly
inexpensive hardware implementations of QUAD.