Efficient Protocols based on Probabilistic Encryption using Composite Degree Residue Classes

Resumé

We study various applications and variants of Paillier's
probabilistic encryption scheme. First, we propose a threshold variant of the
scheme, and also zero-knowledge protocols for proving that a given
ciphertext encodes a given plaintext, and for verifying multiplication of
encrypted values.
We then show how these building blocks can be used for applying the
scheme to efficient electronic voting. This reduces dramatically the work
needed to compute the final result of an election, compared to the previously
best known schemes. We show how the basic scheme for a yes/no
vote can be easily adapted to casting a vote for up to t out of L
candidates. The same basic building blocks can also be adapted to
provide receipt-free elections, under appropriate physical assumptions. The
scheme for 1 out of L elections can be optimised such that for a certain
range of parameter values, a ballot has size only O(log L) bits.
Finally, we propose a variant of the encryption scheme, that allows
reducing the expansion factor of Paillier's scheme from 2 to almost 1.