We study ballot independence for election schemes. First, we formally define ballot independence as a cryptographic game and prove that ballot secrecy implies ballot independence. Secondly, we introduce a notion of controlled malleability and prove that it is sufficient for ballot independence. We also prove that non-malleable ballots are sufficient for ballot independence. Thirdly, we prove that ballot independence is sufficient for ballot secrecy in a special case. Our results show that ballot independence is necessary in election schemes satisfying ballot secrecy. Furthermore, our sufficient conditions enable simpler proofs of ballot secrecy.
@techreport{2014-ballot-independence-for-election-schemes,
author = {Ben Smyth and David Bernhard},
title = {{Ballot secrecy and ballot independence: definitions and relations}},
year = {2014},
month = {October},
number = {2013/235},
institution = {Cryptology ePrint Archive}
}