Conference paper
Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives
Microsoft USA1
Graz University of Technology2
Princeton University3
Aarhus University4
Department of Applied Mathematics and Computer Science, Technical University of Denmark5
Cyber Security, Department of Applied Mathematics and Computer Science, Technical University of Denmark6
Austrian Institute of Technology7
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-protocol for statements over general circuits. We improve this X-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 LowMC (EUROCRYPT'15).
Language: | English |
---|---|
Publisher: | Association for Computing Machinery |
Year: | 2017 |
Pages: | 1825-1842 |
Proceedings: | 2017 ACM SIGSAC Conference on Computer and Communications Security |
Series: | Proceedings of the Acm Conference on Computer and Communications Security |
ISBN: | 1450349463 and 9781450349468 |
ISSN: | 15437221 |
Types: | Conference paper |
DOI: | 10.1145/3133956.3133997 |
Block Cipher Computational complexity and cryptography Cryptographic primitives Cryptography Digital signatures Fiat-Shamir Implementation Post-quantum cryptography Public key (asymmetric) techniques Security and privacy Signatures Theory of computation Unruh Zero-Knowledge block cipher block cipher, post-quantum cryptography, signatures, zero-knowledge implementation post-quantum cryptography signatures zero-knowledge