Key agreement protocol (KAP) using Burau braid groups representation and matrix power function (MPF) is analyzed. MPF arguments are Burau representation matrices defined over finite field or ring. It is shown that KAP security relies on the solution of matrix multivariate quadratic system of equations over the ring with additional commutation constraints for matrices to be found. We are making a conjecture that proposed KAP is a candidate one-way function since its inversion is related with the solution of known multivariate quadratic problem which is NP-complete over any field. The one of advantages of proposed KAP is its possible effective realization even in restricted computational environments by avoiding arithmetic operations with big integers.
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