## CryptoDB

### Michael Clear

#### Publications

Year
Venue
Title
2019
PKC
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

#### Coauthors

Ciaran McGoldrick (2)