CHAMP: Cayley HAshing with Matrix Products

2026-10-03

AI Summary

This study addresses the challenge that existing hash functions struggle to simultaneously achieve security and homomorphic properties. To this end, it proposes CHAMP, a Cayley hash function based on 2×2 matrix multiplication over finite fields. By mapping binary strings to semigroup elements, the proposed method inherently supports multiplicative homomorphism through its matrix product structure. Integrating finite field algebra with Cayley graph theory, CHAMP enhances homomorphic capabilities while optimizing computational efficiency. Furthermore, this work establishes a rigorous security model for CHAMP and validates its favorable implementation performance. Overall, this research provides a novel paradigm for constructing hash functions that combine strong security guarantees with practical homomorphic functionality.

Abstract

Cayley hash functions hash binary strings by representing the bits of the message as elements of a semigroup and multiplying the corresponding elements. This gives Cayley hash functions useful homomorphic properties. Here, we propose CHAMP, a Cayley hash function based on products of 2 by 2 matrices over a finite field, and discuss its security, implementation, and performance.

Problem

• Cayley hash function
• matrix products
• finite field
• homomorphic properties
• security

Innovation

• Cayley hash function
• Matrix products
• Finite field
• Homomorphic properties
• CHAMP