Post-Quantum Cryptography: Riemann Primitives and Chrysalis

TL;DR

This paper introduces Chrysalis, a novel post-quantum cryptographic scheme based on Riemann primitives and Holomorphic Learning with Errors, leveraging complex mathematical problems for security.

Contribution

It presents the first cryptographic scheme utilizing Holomorphic Learning with Errors and proposes a new NP-Hard problem based on the non-commutative Grothendieck problem for security reduction.

Findings

Chrysalis demonstrates post-quantum security assumptions.

The scheme employs Riemann sphere and holomorphic vector bundles.

Security is based on the non-commutative Grothendieck problem.

Abstract

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.