Paper 2024/208

Asymmetric Cryptography from Number Theoretic Transformations

Abstract

In this work, we introduce a family of asymmetric cryptographic functions based on dynamic number theoretic transformations with multiple rounds of modular arithmetic to enhance diffusion and difficulty of inversion. This function acts as a basic cryptographic building block for a novel communication-efficient zero-knowledge crypto-system. The system as defined exhibits partial homomorphism and behaves as an additive positive accumulator. By using a novel technique to constructively embed lattice problems in a nested fashion, the dimensionality and overall complexity of the lattice structure is increased. This linked lattice framework obscures internal structure and mitigates cryptanalysis by applying a novel ’noisy roots’ technique. By relaxing the need for specifically correct nth ω roots in a given field, we apply offset values to create a framework of consisting of a set of uniquely transforming but arithmetically compatible NTTs. We provide specific parameters for conjectured NIST level V security. Communication costs are extremely low at 288-bytes per public key and 144-bytes per cipher-text or digital signature. Example protocols for key agreement, secure data exchange, additive accumulation, and digital signatures are provided. Peer review is in preliminary stages at time of dissemination. Claims within have not undergone rigorous validation and likely contain inaccuracies, errors, flaws or incomplete analysis. Contents may see significant modification through later iterations.

Note: Revised algorithms for clarity and linked reference implementation of core functions.