LINEture: novel signature cryptosystem

TL;DR

LINEture is a new digital signature system based on matrix transformations and brute-force security principles, avoiding traditional hard problems, with mechanisms for secret sharing, message association, and zero-knowledge verification.

Contribution

It introduces a signature cryptosystem leveraging homomorphic matrix transformations and brute-force security, with a novel secret-sharing theory and zero-knowledge proof integration.

Findings

Security relies on brute-force problem complexity.

Signature generation and verification are computationally efficient.

High security achieved through matrix transformation parameters.

Abstract

We propose a novel digital signature cryptosystem that exploits the concept of the brute-force problem. To ensure the security of the cryptosystem, we employed several mechanisms: sharing a common secret for factorable permutations, associating permutations with the message being signed, and confirming knowledge of the shared secret using a zero-knowledge proof. We developed a secret-sharing theory based on homomorphic matrix transformations for factorized permutations. The inverse matrix transformation for computing the shared secret is determined by secret parameters, which results in incompletely defined functionality and gives rise to a brute-force cryptanalysis problem. Randomization of session keys using a message hash and random parameters guarantees the uniqueness of each signature, even for identical messages. We employed a zero-knowledge authentication protocol to confirm knowledge of the shared secret, thereby protecting the verifier against unauthorized signature imposition. The LINEture cryptosystem is built on linear matrix algebra and does not rely on a computationally hard problem. High security is achieved through the appropriate selection of matrix transformation dimensions. Matrix computations potentially offer low operational costs for signature generation and verification.