An identification protocol based on the twisted ring-root extraction problem

This paper introduces the twisted ring-root extraction problem, and proposes an identification protocol whose security is tied to the twisted ring-root extraction problem: given an endomorphism ψ of a ring R of N-truncated single-variable polynomials over a finite field of prime order, and given an integer e ≥ 2, and a polynomial y ∈ R; find a polynomial s ∈ R such that y = ψ(s^e) (assuming at least one such s exists). We suggest that this problem is suitably difficult to serve as a cryptographic assumption over the platform ring R. The performance, key space, and other security issues are also discussed.