Page 125 - Towards Trustworthy Elections New Directions in Electronic Voting by Ed Gerck (auth.), David Chaum, Markus Jakobsson, Ronald L. Rivest, Peter Y. A. Ryan, Josh Benaloh, Miroslaw Kutylowski, Ben Adida ( (z-lib.org (1)

Unconditionally Secure Electronic Voting
117
3. Integrity:
be two public verifieres with private information
Let Verifier k 1
and Verifier k 2
respectively. Given all information on the Bulletin Board {E ij }
and Z k 2
Z k 1
and given the outputs of all tallying authorities {S j }, for every choice of
outputs the different final
k 1 ,k 2 , the probability that Verifier k 1 and Verifier k 2
tally islessthan . That is, for every k 1 , k 2 ∈{1,...,L},there exists > 0
such that

Pr [S = S ; S ← Verifier k 1 ({E ij }, {S j }),S ←Verifier k 2 ({E ij }, {S j })] ≤ ,
as final tally. Note
where S and S are outputs of Verifier k 1 and Verifier k 2
that S ,S ∈ Z ∪{⊥}.

Further, if there exists a Verifier k who output a final tally S, then there
exists a list of voters V = {i 1 ,i 2,...,i M }⊆ {1,...,M} whose casted votes
are valid and hence counted, and then S satisfies the following relation:

S = s i
i∈V
where s i is the value of Voter i ’s vote.
For the privacy property of electronic voting schemes, one may notice that the
collusion of voters is not consdered in the definition. This is mainly because,
in the extreme case, it is trivial that every voter except for a targeted voter is
corrupted, then the content of the targeted voter’s vote is revealed from the final
tally and the choice of corrupted voters’ votes. In the other words, the level of
privacy highly depends on the number of honest voters. Thus, we excluded the
corruption of voters from the privacy definition. The construction proposed later
in this paper is actually robust against the corruption of fairly large portion of
voters only if there exists enough number of honest voters.

4.2 Parameters
In the following, we will use the parameters listed below.
L : number of public verifiers
M : number of eligible voters
m : number of participating voters (m ≤ M)
N : number of authorities
T : maximum number of malicious verifiers
t : maximum number of malicious authorities
4.3 Construction

A construction of electronic voting scheme based on bulletin board model [8,2] is
given in the information theoretic model. Our construction is based on US-OPE
and US-PVSS described in the previous section. The construction is separated 4
phases: (1) description of private keys, (2) Voting Phase, (3) Verification Phase,
(4) Tallying Phase.