Page 124 - 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)

A. Otsuka and H. Imai
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– Integrity
Ensures that any party, including public verifiers, can be convinced that all
valid votes have been included in the final tally.
More formally an information-theoretically secure electronic voting is defined as
follows.
Definition 7. (efficient electronic voting scheme) Suppose we have three kinds
of players, a finite set of voters, Voter i (i =1,... ,M), a finite set of tallying
authority, Authority j (j =1,... ,N), and a finite set of passive public verifiers
, Verifier k (k =1,... ,L). Each player has its own private information X i , Y j ,
Z k respectively. Further, let P be public information and R i (i =1,... ,M)be
internal random coins of each voter. In an efficient electronic voting scheme,
there exists the following three phases:
1. Voting Phase:
Given a private information X i , public information P and internal random
coin R i , a voter Voter i decides his vote s i ∈{0, 1} and computes and writes
information E ij (j =1,... ,N) on a bulletin board.
2. Tallying Phase:
Given a private information Y j , public information P and information on bul-
letin board {E ij } (i =1,... ,M), an tallying authority Authority j outputs S j .
3. Verification Phase:
Given a private information Z k , public information P and information on bul-
letin board {E ij }, a public verifier, Verifier k , outputs accept or reject on every
E ij for i =1,... ,M and j =1,... ,N. Furthermore, given a private infor-
mation Z k , public information P and the outputs of tallying authorities, {S j }
(j =1,... ,N), a public verifier, Verifier k , outputs the final tally S or ⊥.
Definition 8. ( -secure electronic voting) An electronic voting scheme is called
-secure in information theoretical sense if it satisfies the following properties.
1. Eligibility:
There exists a function f which maps E ij , the information on the bulletin
board, to a single voter Voter i such that for all i 1 = i 2 ,where i 1,i 2 ∈
{1,... ,M},and for all j ∈{1,...,N}, the following is satisfied:

f(E i 1 j ) = f(E i 2 j ).
2. Privacy:
Let Y t be the collusion of tallying authorities with t authorities, and let
Z T be the collusion of public verifiers with T verifiers. Let P be the public
information including the information written on the bulletin board, hence
P, {E ij }, {S j } and S. Then, given Y t , Z T , P, for every algorithm A,for
every i, for every choice of t corrupting tallying authorities and for every
choice of T corrupting public verifiers, the success probability of A to guess
the value of the vote s i of Voter i over random guess is less than . That is,

1

Pr [A(Y t , Z T , P)= s i ] − ≤ .
2