QRKE: Resistance to Attacks using the Inverse of the Cosine Representation of Chebyshev Polynomials

Abstract

We've been able to show recently that Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers can be used to create a Diffie-Hellman-like key exchange algorithm and certificates. The cryptosystem was theoretically proven to withstand attacks using quantum computers. We additionally prove that attacks based on the inverse of the cosine representation of T polynomials fail.