MAKE: a Matrix Action Key Exchange
This addresses the need for quantum-resistant key exchange protocols in cryptography, though it appears incremental as it builds on matrix-based methods.
The authors tackled the problem of secure key exchange by introducing a new protocol based on a semidirect product of cyclic matrix groups over Z_p, which avoids exposing matrix powers or elements to prevent standard and quantum attacks like Shor's algorithm.
We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z_p is ever exposed, so all standard attacks on Diffie-Hellman-like protocols (including Shor's quantum algorithm attack) are not applicable.