Paper 2017/398
Post-Quantum Security of Fiat-Shamir
Dominique Unruh
Abstract
The Fiat-Shamir construction (Crypto 1986) is an efficient transformation in the random oracle model for creating non-interactive proof systems and signatures from sigma-protocols. In classical cryptography, Fiat-Shamir is a zero-knowledge proof of knowledge assuming that the underlying sigma-protocol has the zero-knowledge and special soundness properties. Unfortunately, Ambainis, Rosmanis, and Unruh (FOCS 2014) ruled out non-relativizing proofs under those conditions in the quantum setting. In this paper, we show under which strengthened conditions the Fiat-Shamir proof system is still post-quantum secure. Namely, we show that if we require the sigma-protocol to have computational zero-knowledge and statistical soundness, then Fiat-Shamir is a zero-knowledge simulation-sound proof system (but not a proof of knowledge!). Furthermore, we show that Fiat-Shamir leads to a post-quantum secure unforgeable signature scheme when additionally assuming a "dual-mode hard instance generator" for generating key pairs. Finally, we study the extractability (proof of knowledge) property of Fiat-Shamir. While we have no proof of the extractability itself, we show that if we can prove extractability, then other desired properties such as simulation-sound extractability (i.e., non-malleability), and unforgeable signatures follow.
Note: Added an analysis of the concrete security. Various minor changes.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- A major revision of an IACR publication in ASIACRYPT 2017
- Keywords
- quantum cryptographyzero knowledgedigital signatures
- Contact author(s)
- unruh @ ut ee
- History
- 2018-05-16: last of 3 revisions
- 2017-05-09: received
- See all versions
- Short URL
- https://ia.cr/2017/398
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/398,
author = {Dominique Unruh},
title = {Post-Quantum Security of Fiat-Shamir},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/398},
year = {2017},
url = {https://eprint.iacr.org/2017/398}
}
