Vector Commitments With Proofs of Smallness: Short Range Proofs and More

Benoit Libert

Paper 2023/800

Vector Commitments With Proofs of Smallness: Short Range Proofs and More

Benoit Libert, Zama

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 commitments range proofs ring LWE ciphertexts
Contact author(s): benoit libert @ zama ai
History: 2023-10-20: last of 4 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 Proofs of Smallness: Short Range Proofs and More},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/800},
      year = {2023},
      url = {https://eprint.iacr.org/2023/800}
}