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Paper: Additively Homomorphic IBE from Higher Residuosity

Authors:
Michael Clear
Ciaran McGoldrick
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DOI: 10.1007/978-3-030-17253-4_17
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Conference: PKC 2019
Abstract: 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
}