LINE: Public-key encryption

TL;DR

This paper introduces a novel public-key encryption scheme leveraging linear equations with multiple solutions, homomorphic matrix transformations, and factorizable substitutions to enhance security and efficiency.

Contribution

It presents a new cryptosystem based on linear equations and homomorphic matrix transformations, offering high security with low computational overhead.

Findings

Multiple solutions prevent polynomial-time cryptanalysis

Homomorphic matrix transformations enable efficient encryption and decryption

Security relies on the complexity of solving underdetermined linear systems

Abstract

We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent solutions for an underdetermined system of linear equations determines the impossibility of its resolution by a cryptanalyst in polynomial time. The completion of input parameters of the equation system is implemented through secret homomorphic matrix transformation for substitutions factorized over the basis of a vector space of dimension m over the field F2. Encryption is implemented through computation of substitutions that are one-way functions on an elementary abelian 2-group of order 2"m. Decryption is implemented through completion of input parameters of the equation system. Homomorphic transformations are constructed based on matrix computations. Matrix computations enable the implementation of high security and low computational overhead for homomorphic transformations.