### Additive-Homomorphic Functional Commitments and Applications to Homomorphic Signatures

##### Abstract

Functional Commitments (FC) allow one to reveal functions of committed data in a succinct and verifiable way. In this paper we put forward the notion of additive-homomorphic FC and show two efficient, pairing-based, realizations of this primitive supporting multivariate polynomials of constant degree and monotone span programs, respectively. We also show applications of the new primitive in the contexts of homomorphic signatures: we show that additive-homomorphic FCs can be used to realize homomorphic signatures (supporting the same class of functionalities as the underlying FC) in a simple and elegant way. Using our new FCs as underlying building blocks, this leads to the (seemingly) first expressive realizations of multi-input homomorphic signatures not relying on lattices or multilinear maps.

Available format(s)
Category
Cryptographic protocols
Publication info
A major revision of an IACR publication in ASIACRYPT 2022
Keywords
functional commitments vector commitments homomorphic signatures
Contact author(s)
catalano @ dmi unict it
dario fiore @ imdea org
idatucker91 @ gmail com
History
2022-10-10: approved
See all versions
Short URL
https://ia.cr/2022/1331

CC BY

BibTeX

@misc{cryptoeprint:2022/1331,
author = {Dario Catalano and Dario Fiore and Ida Tucker},
title = {Additive-Homomorphic Functional Commitments and Applications to Homomorphic Signatures},
howpublished = {Cryptology ePrint Archive, Paper 2022/1331},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1331}},
url = {https://eprint.iacr.org/2022/1331}
}

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