Abstract: We present a mathematical construct which provides a cryptographic protocol to (verifiably shuffle) a sequence of (k) modular integers, and discuss its application to secure, universally verifiable, multi-authority election schemes. The output of the shuffle operation is another sequence of (k) modular integers, each of which is the same secret power of a corresponding input element, but the order of elements in the output is kept secret. Though it is a trivial matter for the “shuffler” (who chooses the permutation of the elements to be applied) to compute the output from the input, the construction is important because it provides a linear size proof of correctness for the output sequence (i.e. a proof that it is of the form claimed) that can be checked by one or more arbitrary verifiers. The protocol is shown to be honest-verifier zeroknowledge in a special case, and is computational zeroknowledge in general.