A Length-Flexible Threshold Cryptosystem with Applications

We propose a public-key cryptosystem which is derived from the Paillier cryptosystem. The scheme inherits the attractive homomorphic properties of Paillier encryption. In addition, we achieve two new properties: First, all users can use the same modulus when generating key pairs, this allows more efficient proofs of relations between different encryptions. Second, we can construct a threshold decryption protocol for our scheme that is length-flexible, i.e., it can handle efficiently messages of arbitrary length, even though the public key and the secret key shares held by decryption servers are of fixed size. We show how to apply this cryptosystem to build a self-tallying election scheme with perfect ballot secrecy, and to build a length-flexible mix-net which is universally verifiable, where the size of keys and ciphertexts do not depend on the number of mix servers, and is robust against a corrupt minority.