Cayley hashing technique uses matrix products for secure data hashing
CHAMP: Cayley HAshing with Matrix Products
Cryptography and Security
Summary
Hashing turns information into short codes to check data integrity and security. The authors study a type of hashing called Cayley hashing, which treats message bits as elements that multiply together in a special way. They introduce CHAMP, a new hash function that uses small matrices over finite fields to compute these products. The paper looks at how secure and efficient this method is and how it can be implemented in practice.
What this means in practice
- •For cryptographic engineers: Build hash functions for secure message verification that use matrix multiplication to enable useful algebraic operations on hashed data.
- •For security software developers: Implement efficient and secure hashing algorithms based on 2x2 matrix products suitable for software needing homomorphic hashing.
Authors
Alexander Demin, Alexey Ovchinnikov, Vladimir Shpilrain
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.