Abstract
An algorithm is proposed for the solution of the NP-hard problem of simultaneous nonsymmetric algebraic Riccati equations over finite fields. The proposed algorithm has an application to the solution of some structured quadratic polynomial equations over finite fields with complexity of O˜2(nℓmax+n+ℓmax) for m⋅n variables and m⋅n equations over F2, where n+ℓmax (ℓmax≤m and m arbitrary) is the dimension of a largest invariant subspace (of some special type) of the m+n×m+n matrix of coefficients of a single Riccati equation. The method can be used to attack or crypt-analyze cryptographic systems that are based on structured multivariable quadratic polynomial equations.
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