2026/08/01 by G. P. Wilmot, J. Chappell, D. K. Abbott
Mathematics · #math.RA
arxiv created 2026/08/01 · arxiv updated 2026/08/04
The double lock scenario allows a secret to be transferred from one person to another without having previously exchanged secrets such as private/public keys. This can be realised by rotations of generalised calibrations in Clifford algebra. Calibrations map to Cayley-Dickson algebras and generalising this provides the mathematical structure enabling the enormous code space needed for a cryptosystem. Commuting rotations in large dimensional spaces are used but the complexity comes from the message being embedded in generalised calibrations. This system uses ideals of Clifford algebras and quasi-algebras that are sometimes embedded in Cayley-Dickson algebras making it a candidate for post-quantum cryptography. Understanding whether the new mathematics of generalised calibrations can produce a secure cryptosystem is the challenge presented in this manuscript.