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In this paper, we describe an optimised variant of Wikstr\"om's mixnet whichshuffles vectors of ElGamal ciphertexts in parallel. We then show in detailthat this construction is secure. Wikstr\"om's verifiable mixnet as we refer toit here was first presented in "Proofs of Restricted Shuffles" by Terelius andWikstr\"om, building on Wikstr\"om's previous work. Specifically we take theoptimised variant for ElGamal which appears to be in common use; for instance,it is presented in Haenni et al's "Pseudo-Code Algorithms for VerifiableRe-Encryption Mix-Nets". We extend the mixnet to support parallel shuffles.(The possibility of doing this is proven by the Wikstr\"om's result but we wishto show that this particular instance with its optimisations is secure.)

A Description and Proof of a Generalised and Optimised Variant of Wikstr\"om's Mixnet