Post-Quantum Cryptography: Riemann Primitives and Chrysalis
This addresses the need for quantum-resistant cryptography, but appears incremental as it builds on existing Learning with Errors concepts with a complex variant.
The paper tackles the problem of post-quantum cryptography by proposing the Chrysalis scheme, which uses Riemann primitives and Holomorphic Learning with Errors, resulting in a security reduction based on the non-commutative Grothendieck problem.
The Chrysalis project is a proposed method for post-quantum cryptography using the Riemann sphere. To this end, Riemann primitives are introduced in addition to a novel implementation of this new method. Chrysalis itself is the first cryptographic scheme to rely on Holomorphic Learning with Errors, which is a complex form of Learning with Errors. The proposed NP-Hard problem for security reduction is the non-commutative Grothendieck problem. The reduction of this problem is achieved by applying bilinear matrices in terms of the holomorphic vector bundle such that coordinate systems are intersected via surjective functions between each holomorphic expression. The result is an arbitrarily selected set of points within constraints of bilinear matrix inequalities approximate to the non-commutative problem. This is achieved by applying the quadratic form of bilinear matrices to a linear matrix inequality.