On multivariable encryption schemes based on simultaneous algebraic Riccati equations over finite fields

•The security of the systems is based on provable NP-hard problem.•The systems involve truly random choice of the coefficients of the core equations.•The suggested schemes fit to the age of post quantum cryptography.•The suggested systems fit to the realm of limited-power computing devices.•The suggested schemes are highly parallelizable in parallel software or hardware.

New multivariable asymmetric public-key encryption schemes based on the NP-complete problem of simultaneous algebraic Riccati equations over finite fields are suggested. We also provide a systematic way to describe any set of quadratic equations over any field, as a set of algebraic Riccati equations. This has the benefit of systematic algebraic crypt-analyzing any encryption scheme based on quadratic equations, to any possible vulnerable hidden structure, in view of the fact that the set of all solutions to any given single algebraic Riccati equation is fully described in terms of all the T-invariant subspaces of some restricted dimension, where T is the matrix of coefficients of the related algebraic Riccati equation.