Anonymous Card Shuffling and its Applications to Parallel Mixnets

TL;DR

This paper introduces a buffer shuffling method for card permutation that enhances anonymity in parallel mixnets, analyzing its effectiveness and robustness against adversarial attacks using a novel sum-of-squares metric.

Contribution

It presents a new buffer shuffling technique for secure card permutation, with analysis of its performance and security in adversarial settings, improving anonymity bounds.

Findings

Buffer shuffling significantly improves anonymity in parallel mixnets.

The sum-of-squares metric provides tighter bounds on anonymity measures.

The method is robust against corrupted servers and adversarial message injections.

Abstract

We study the question of how to shuffle $n$ cards when faced with an opponent who knows the initial position of all the cards {\em and} can track every card when permuted, {\em except} when one takes $K< n$ cards at a time and shuffles them in a private buffer "behind your back," which we call {\em buffer shuffling}. The problem arises naturally in the context of parallel mixnet servers as well as other security applications. Our analysis is based on related analyses of load-balancing processes. We include extensions to variations that involve corrupted servers and adversarially injected messages, which correspond to an opponent who can peek at some shuffles in the buffer and who can mark some number of the cards. In addition, our analysis makes novel use of a sum-of-squares metric for anonymity, which leads to improved performance bounds for parallel mixnets and can also be used to bound well-known existing anonymity measures.