QRKE: Extensions
This addresses the need for post-quantum cryptography to secure communications against quantum computer attacks, though it appears incremental as it builds on known polynomial properties.
The paper tackles the problem of creating quantum-resistant cryptographic algorithms by proposing a Diffie-Hellman-like key exchange based on permutable Chebyshev polynomials, showing how to compute these polynomial values faster and extend the principle to encryption, authentication, and signature schemes.
Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers are suitable for creating a Diffie-Hellman-like key exchange algorithm that is able to withstand attacks using quantum computers. The algorithm takes advantage of the commutative properties of Chebyshev polynomials of the first kind. We show how T polynomial values can be computed faster and how the underlying principle can further be used to create public key encryption methods, as well as certificate-like authentication-, and signature schemes.