## CryptoDB

### Paper: Additively Homomorphic IBE from Higher Residuosity

Authors: Michael Clear Ciaran McGoldrick DOI: 10.1007/978-3-030-17253-4_17 Search ePrint Search Google PKC 2019 We present an identity-Based encryption (IBE) scheme that is group homomorphic for addition modulo a “large” (i.e. superpolynomial) integer, the first such group homomorphic IBE. Our first result is the construction of an IBE scheme supporting homomorphic addition modulo a poly-sized prime e. Our construction builds upon the IBE scheme of Boneh, LaVigne and Sabin (BLS). BLS relies on a hash function that maps identities to $e^{\text {th}}$ residues. However there is no known way to securely instantiate such a function. Our construction extends BLS so that it can use a hash function that can be securely instantiated. We prove our scheme secure under the (slightly modified) $e^{\text {th}}$ residuosity assumption in the random oracle model and show that it supports a (modular) additive homomorphism. By using multiple instances of the scheme with distinct primes and leveraging the Chinese Remainder Theorem, we can support homomorphic addition modulo a “large” (i.e. superpolynomial) integer. We also show that our scheme for $e > 2$ is anonymous by additionally assuming the hardness of deciding solvability of a special system of multivariate polynomial equations. We provide a justification for this assumption by considering known attacks.
##### BibTeX
@inproceedings{pkc-2019-29291,
title={Additively Homomorphic IBE from Higher Residuosity},
booktitle={Public-Key Cryptography – PKC 2019},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={11442},
pages={496-515},
doi={10.1007/978-3-030-17253-4_17},
author={Michael Clear and Ciaran McGoldrick},
year=2019
}