# Information Security and Cryptography Research Group

## Zero-knowledge proofs of knowledge for group homomorphisms

### Ueli Maurer

Designs, Codes and Cryptography, vol. 77, pp. 663–676, 2015.

A simple zero-knowledge proof of knowledge protocol is presented of which many known protocols are instantiations. These include Schnorr's protocol for proving knowledge of a discrete logarithm, the Fiat-Shamir and Guillou-Quisquater protocols for proving knowledge of a modular root, protocols for proving knowledge of representations (like Okamoto's protocol), protocols for proving equality of secret values, a protocol for proving the correctness of a Diffie-Hellman key, protocols for proving the multiplicative relation of three commitments (as required in secure multi-party computation), and protocols used in credential systems. This unifies a substantial body of work and can also lead to instantiations of the protocol for new applications.

## BibTeX Citation

@article{Maurer15,
author       = {Ueli Maurer},
title        = {Zero-knowledge proofs of knowledge for group homomorphisms},
journal      = {Designs, Codes and Cryptography},
pages        = 663--676,
volume       = 77,
year         = 2015,
}