# Keyed hash function from large girth expander graphs

## TL;DR

This paper introduces a new keyed hash function based on large girth expander graphs, offering flexible output lengths, high efficiency, and strong mixing properties suitable for message authentication.

## Contribution

The paper presents a novel MAC construction using expander graphs with large girth, providing flexible output lengths and efficient implementation.

## Key findings

- Achieves 4 operations per input bit.
- Outputs are indistinguishable from random bits.
- Supports messages of arbitrary length.

## Abstract

In this paper we present an algorithm to compute keyed hash function (message authentication code MAC). Our approach uses a family of expander graphs of large girth denoted $D(n,q)$, where $n$ is a natural number bigger than one and $q$ is a prime power. Expander graphs are known to have excellent expansion properties and thus they also have very good mixing properties. All requirements for a good MAC are satisfied in our method and a discussion about collisions and preimage resistance is also part of this work. The outputs closely approximate the uniform distribution and the results we get are indistinguishable from random sequences of bits. Exact formulas for timing are given in term of number of operations per bit of input. Based on the tests, our method for implementing DMAC shows good efficiency in comparison to other techniques. 4 operations per bit of input can be achieved. The algorithm is very flexible and it works with messages of any length. Many existing algorithms output a fixed length tag, while our constructions allow generation of an arbitrary length output, which is a big advantage.