International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Michael Clear

Publications

Year
Venue
Title
2019
PKC
Additively Homomorphic IBE from Higher Residuosity
Michael Clear Ciaran McGoldrick
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.
2015
CRYPTO
2014
EPRINT

Coauthors

Ciaran McGoldrick (3)