Group homomorphic encryption: characterizations, impossibility results, and applications

@article{Armknecht2013GroupHE,
  title={Group homomorphic encryption: characterizations, impossibility results, and applications},
  author={Frederik Armknecht and Stefan Katzenbeisser and Andreas Peter},
  journal={Designs, Codes and Cryptography},
  year={2013},
  volume={67},
  pages={209-232}
}
We give a complete characterization both in terms of security and design of all currently existing group homomorphic encryption schemes, i.e., existing encryption schemes with a group homomorphic decryption function such as ElGamal and Paillier. To this end, we formalize and identify the basic underlying structure of all existing schemes and say that such schemes are of shift-type. Then, we construct an abstract scheme that represents all shift-type schemes (i.e., every scheme occurs as an… 
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