### Two-Round Stateless Deterministic Two-Party Schnorr Signatures From Pseudorandom Correlation Functions

##### Abstract

Schnorr signatures are a popular choice due to their simplicity, provable security, and linear structure that enables relatively easy threshold signing protocols. The deterministic variant of Schnorr (where the nonce is derived in a stateless manner using a PRF from the message and a long term secret) is widely used in practice since it mitigates the threats of a faulty or poor randomness generator (which in Schnorr leads to catastrophic breaches of security). Unfortunately, threshold protocols for the deterministic variant of Schnorr have so far been quite inefficient, as they make non black-box use of the PRF involved in the nonce generation. In this paper, we present the first two-party threshold protocol for Schnorr signatures, where signing is stateless and deterministic, and only makes black-box use of the underlying cryptographic algorithms. We present a protocol from general assumptions which achieves covert security, and a protocol that achieves full active security under standard factoring-like assumptions. Our protocols make crucial use of recent advances within the field of pseudorandom correlation functions (PCFs). As an additional benefit, only two-rounds are needed to perform distributed signing in our protocol, connecting our work to a recent line of research on the trade-offs between round complexity and cryptographic assumptions for threshold Schnorr signatures.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint.
Keywords
Threshold CryptographyThreshold SignaturesPseudorandom Correlation FunctionsSchnorr Signatures
Contact author(s)
ykondi @ cs au dk
orlandi @ cs au dk
ldr709 @ gmail com
History
2023-02-20: approved
See all versions
Short URL
https://ia.cr/2023/216

CC BY

BibTeX

@misc{cryptoeprint:2023/216,
author = {Yashvanth Kondi and Claudio Orlandi and Lawrence Roy},
title = {Two-Round Stateless Deterministic Two-Party Schnorr Signatures From Pseudorandom Correlation Functions},
howpublished = {Cryptology ePrint Archive, Paper 2023/216},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/216}},
url = {https://eprint.iacr.org/2023/216}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.