We introduce a new number-theoretic based protocol for secure electronic voting. Our scheme is much more communication efficient than previous schemes of its type, and has a much lower round complexity than is currently possible using the anonymous-channel/mixer techniques. Preprocessing allows for nearly all of the communication and computation to be performed before any voting takes place. Unlike the mixer-based protocols, anyone can verify that everyone’s vote has been properly counted. Also, our techniques allow for a wide variety of different schemes. Our protocols are based on families of homomorphic encryptions which have a partial compatibility property, generalizing a method of Benaloh and Yung . We use these functions to generate very simple interactive proofs on encrypted shares. We also develop amortization techniques yielding dramatic efficiency improvements over our simple protocols. Our protocols can be realized by current-generation PC’s with access to an electronic bulletin board.