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Paper 2018/773

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

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

Abstract

In this work, we construct a short one-out-of-many proof from (Module-SIS) lattices, allowing one to prove knowledge of a secret associated with one of the public values in a set. The proof system follows 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 adapt the above discrete logarithm proof techniques to the lattice setting. To achieve our result, we introduce 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 lattice-based ring signature scheme. Our scheme offers post-quantum security and practical usability in cryptocurrencies and e-voting systems. Even for a very large ring size such as 1 billion, our ring signature size is only 4.5 MB for 100-bit security level compared to 166 MB in the best existing lattice-based result by Libert et al. (EUROCRYPT '16).

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
lattice-based cryptographyzero-knowledge proofring signature
Contact author(s)
muhammed esgin @ monash edu
History
2019-04-15: revised
2018-08-27: received
See all versions
Short URL
https://ia.cr/2018/773
License
Creative Commons Attribution
CC BY
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