Extractable Witness Encryption for KZG Commitments and Efficient Laconic OT

Nils Fleischhacker; Mathias Hall-Andersen; Mark Simkin

Paper 2024/264

Extractable Witness Encryption for KZG Commitments and Efficient Laconic OT

Nils Fleischhacker

, Ruhr University Bochum

Mathias Hall-Andersen

, Aarhus University

Mark Simkin

, Ethereum Foundation

Abstract

We present a concretely efficient and simple extractable witness encryption scheme for KZG polynomial commitments. It allows to encrypt a message towards a triple $(\mathsf{com}, \alpha, \beta)$, where $\mathsf{com}$ is a KZG commitment for some polynomial $f$. Anyone with an opening for the commitment attesting $f(\alpha) = \beta$ can decrypt, but without knowledge of a valid opening the message is computationally hidden. Our construction is simple and highly efficient. The ciphertext is only a single group element. Encryption and decryption both require a single pairing evaluation and a constant number of group operations. Using our witness encryption scheme, we construct a simple and highly efficient laconic OT protocol, which significantly outperforms the state of the art in most important metrics.

Note: This revision fixes a flaw in the proof of Claim 5.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Extractable Witness Encryption KZG Commitments Laconic OT AGM
Contact author(s): mail @ nilsfleischhacker de
ma @ cs au dk
mark simkin @ ethereum org
History: 2024-03-13: last of 2 revisions; 2024-02-16: received; See all versions
Short URL: https://ia.cr/2024/264
License: CC BY

BibTeX

@misc{cryptoeprint:2024/264,
      author = {Nils Fleischhacker and Mathias Hall-Andersen and Mark Simkin},
      title = {Extractable Witness Encryption for KZG Commitments and Efficient Laconic OT},
      howpublished = {Cryptology ePrint Archive, Paper 2024/264},
      year = {2024},
      note = {\url{https://eprint.iacr.org/2024/264}},
      url = {https://eprint.iacr.org/2024/264}
}