# An identification system based on the explicit isomorphism problem

## TL;DR

This paper introduces a novel identification system leveraging the computational difficulty of finding isomorphisms between central simple algebras, extending prior protocols based on quadratic forms.

## Contribution

It presents a new zero-knowledge protocol based on the isomorphism problem for division algebras, generalizing existing protocols that rely on quadratic form equivalence.

## Key findings

- Protocol is statistically zero-knowledge
- Relies on the hardness of algebraic isomorphism problems
- Extends prior quadratic form-based protocols

## Abstract

We propose a new identification system based on algorithmic problems related to computing isomorphisms between central simple algebras. We design a statistical zero knowledge protocol which relies on the hardness of computing isomorphisms between orders in division algebras which generalizes a protocol by Hartung and Schnorr, which relies on the hardness of integral equivalence of quadratic forms.