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Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives

Authors:

Steven Goldfeder,

Claudio Orlandi,

Sebastian Ramacher,

Christian Rechberger,

Daniel Slamanig,

Greg ZaveruchaAuthors Info & Claims

CCS '17: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security

Pages 1825 - 1842

https://doi.org/10.1145/3133956.3133997

Published: 30 October 2017 Publication History

Abstract

We propose a new class of post-quantum digital signature schemes that: (a) derive their security entirely from the security of symmetric-key primitives, believed to be quantum-secure, and (b) have extremely small keypairs, and, (c) are highly parameterizable.

In our signature constructions, the public key is an image y=f(x) of a one-way function f and secret key x. A signature is a non-interactive zero-knowledge proof of x, that incorporates a message to be signed. For this proof, we leverage recent progress of Giacomelli et al. (USENIX'16) in constructing an efficient Σ-protocol for statements over general circuits. We improve this Σ-protocol to reduce proof sizes by a factor of two, at no additional computational cost. While this is of independent interest as it yields more compact proofs for any circuit, it also decreases our signature sizes.

We consider two possibilities to make the proof non-interactive: the Fiat-Shamir transform and Unruh's transform (EUROCRYPT'12, '15,'16). The former has smaller signatures, while the latter has a security analysis in the quantum-accessible random oracle model. By customizing Unruh's transform to our application, the overhead is reduced to 1.6x when compared to the Fiat-Shamir transform, which does not have a rigorous post-quantum security analysis.

We implement and benchmark both approaches and explore the possible choice of f, taking advantage of the recent trend to strive for practical symmetric ciphers with a particularly low number of multiplications and end up using Low MC (EUROCRYPT'15).

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https://doi.org/10.3390/technologies12120241
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Index Terms

Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives
1. Security and privacy
  1. Cryptography
    1. Public key (asymmetric) techniques
      1. Digital signatures
2. Theory of computation
  1. Computational complexity and cryptography
    1. Cryptographic primitives

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cover image ACM Conferences

CCS '17: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security

October 2017

2682 pages

ISBN:9781450349468

DOI:10.1145/3133956

General Chair:
Bhavani Thuraisingham
The University of Texas at Dallas, USA
,
Program Chairs:
David Evans
University of Virginia
,
Tal Malkin
Columbia University
,
Dongyan Xu
Purdue University

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Published: 30 October 2017

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Overall Acceptance Rate 1,261 of 6,999 submissions, 18%

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Cherkaoui Dekkaki KTasic ICano M(2024)Exploring Post-Quantum Cryptography: Review and Directions for the Transition ProcessTechnologies10.3390/technologies1212024112:12(241)Online publication date: 23-Nov-2024
https://doi.org/10.3390/technologies12120241
Wang CLiu ZMambo M(2024)On the Proof of Ownership of Digital WalletsCryptography10.3390/cryptography80400578:4(57)Online publication date: 18-Dec-2024
https://doi.org/10.3390/cryptography8040057
Liu FZheng ZGong ZTian KZhang YHu ZLi JXu Q(2024)A survey on lattice-based digital signatureCybersecurity10.1186/s42400-023-00198-17:1Online publication date: 1-Apr-2024
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