Efficient Protocols based on Probabilistic Encryption using Composite Degree Residue Classes

Abstract

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