July 27, 2021

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Ballot secrecy: Security definition, sufficient conditions, and analysis of Helios, by Ben Smyth

We propose a definition of ballot secrecy as an indistinguishability game in the
computational model of cryptography. Our definition improves upon
earlier definitions to ensure
ballot secrecy is preserved in the presence
of an adversary that controls
ballot collection.
We also propose
a definition
of ballot independence as
an adaptation of an indistinguishability game
for asymmetric
encryption. We prove relations between our definitions. In particular, we prove
ballot independence is sufficient for ballot secrecy in voting systems with
zero-knowledge tallying proofs. Moreover, we prove that building
systems
from non-malleable asymmetric encryption schemes suffices for ballot secrecy,
thereby eliminating
the expense of ballot-secrecy proofs for a class
of encryption-based voting systems. We demonstrate applicability of
our results by analysing the Helios voting system and its mixnet variant.
Our analysis reveals that Helios does not satisfy ballot secrecy in the presence of
an adversary that controls
ballot collection. The
vulnerability cannot be detected by earlier definitions of ballot secrecy, because
they do not consider such adversaries. We adopt non-malleable ballots
as a fix and prove that the fixed system satisfies ballot secrecy.