### Short Lattice-based One-out-of-Many Proofs and Applications to Ring Signatures

Muhammed F. Esgin, Ron Steinfeld, Amin Sakzad, Joseph K. Liu, and Dongxi Liu

##### Abstract

In this work, we construct a short one-out-of-many proof from (module) lattices, allowing one to prove knowledge of a secret associated with one of the public values in a set. The proof system builds on a combination of ideas from the efficient proposals in the discrete logarithm setting by Groth and Kohlweiss (EUROCRYPT '15) and Bootle et al. (ESORICS '15), can have logarithmic communication complexity in the set size and does not require a trusted setup. Our work resolves an open problem mentioned by Libert et al. (EUROCRYPT '16) of how to efficiently extend the above discrete logarithm proof techniques to the lattice setting. To achieve our result, we introduce new technical tools for design and analysis of algebraic lattice-based zero-knowledge proofs, which may be of independent interest. Using our proof system as a building block, we design a short ring signature scheme, whose security relies on post-quantum'' lattice assumptions. Even for a very large ring size such as 1 billion, our ring signature size is only 3 MB for 128-bit security level compared to 216 MB in the best existing lattice-based result by Libert et al. (EUROCRYPT '16).

Note: The full version of the paper accepted to ACNS 2019.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MAJOR revision.ACNS 2019
Keywords
lattice-based cryptographyzero-knowledge proofone-out-of-many proofring signature
Contact author(s)
muhammed esgin @ monash edu
History
2019-04-15: revised
See all versions
Short URL
https://ia.cr/2018/773

CC BY

BibTeX

@misc{cryptoeprint:2018/773,
author = {Muhammed F.  Esgin and Ron Steinfeld and Amin Sakzad and Joseph K.  Liu and Dongxi Liu},
title = {Short Lattice-based One-out-of-Many Proofs and Applications to Ring Signatures},
howpublished = {Cryptology ePrint Archive, Paper 2018/773},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/773}},
url = {https://eprint.iacr.org/2018/773}
}

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