Security
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. The first proof was done over field GF(2) for an old-fashioned stream cipher (where the key is the initial state). It was later extended by Berbain and Gilbert in order to take into account the set-up procedure of a modern cipher (with a setup stage deriving the initial state from the key). The security of the whole cipher as a Pseudo Random Function can be related to the conjectured intractability of the MQ problem. The authors also studied the resistance of the cipher against classical attacks.
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