Anonymity & Cryptology

Classical and Quantum Voting

MIX net schemes, first introduced by David Chaum, have found applications in scenarios involving anonymity, elections and payments. The development of classical MIX net schemes to achieve in particular privacy initially led to ciphertext whose size was proportional to the number of MIX servers involved in the scheme. This problem was resolved by Park, Itoh and Kurosawa, resulting in ciphertext whose length was independent of the number of MIX servers. Sako and Kilian, produced a general MIX net scheme satisfying verifiability but failing with regard to robustness. The first resilient MIX net scheme was produced by Ogata, Kurosawa, Sako and Takatani.

A MIX net election scheme involves the use of shuffle machine agents referred to as MIX servers, which take as input, a ciphertext vector, these could be for example, encrypted votes, (c1, c2, ... , cn ) submitted by for example voters, (v1, v2, ... , vn ) and produces as output a permuted vector (in which the components are shuffled) of corresponding output (for example, decrypted votes) such that the source of each ciphertext (vote) remains hidden. In a k-MIX scheme the output is then passed to the next shuffle agent, the process is repeated with another permutation, and then passed to the next MIX, until each of the agents has processed the data. The resilience properties of privacy, verifiability and robustness may be presented in terms of t-privacy, t-verifiability and t-robustness, where it is understood that t refers to the number of malicious MIX servers that the scheme can withstand given at most n - 2 malicious sources. A scheme satisfying the above three t-properties is said to be t-resilient.

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