Commitment Schemes and Diophantine Equations

TL;DR

This paper explores the design of cryptographic commitment schemes based on diophantine equations that are computationally hard to solve but have easily countable solutions, aiming to enhance cryptographic security.

Contribution

It introduces a novel approach linking diophantine equations to cryptographic commitments, focusing on equations that are hard to solve yet easy to count solutions.

Findings

Identified classes of diophantine equations suitable for cryptographic commitments.

Demonstrated the feasibility of constructing commitment schemes with these equations.

Provided theoretical analysis of security based on computational hardness.

Abstract

Motivated by questions in cryptography, we look for diophantine equations that are hard to solve but for which determining the number of solutions is easy.