Paper 2023/800
Vector Commitments With Short Proofs of Smallness
Abstract
Vector commitment schemes are compressing commitments to vectors that make it possible to succinctly open a commitment for individual vector positions without revealing anything about other positions. We describe vector commitments enabling constant-size proofs that the committed vector is small (i.e., binary, ternary, or of small norm). As a special case, we obtain range proofs featuring the shortest proof length in the literature with only $3$ group elements per proof. As another application, we obtain short pairing-based NIZK arguments for lattice-related statements. In particular, we obtain short proofs (comprised of $3$ group elements) showing the validity of ring LWE ciphertexts and public keys. Our constructions are proven simulation-extractable in the algebraic group model and the random oracle model.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Vector commitmentsrange proofsring LWE ciphertexts
- Contact author(s)
- benoit libert @ zama ai
- History
- 2023-07-18: last of 2 revisions
- 2023-05-31: received
- See all versions
- Short URL
- https://ia.cr/2023/800
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/800,
author = {Benoit Libert},
title = {Vector Commitments With Short Proofs of Smallness},
howpublished = {Cryptology ePrint Archive, Paper 2023/800},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/800}},
url = {https://eprint.iacr.org/2023/800}
}
