Page 155 - 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)

An Implementation of a Mix-Net Based Network Voting Scheme
2
˙ t i =[3z π(i) + τλ i ]g,
n

3
˙ v =[
j=1 z j + τλ + ρz]g ˙ v i =[3z π(i) + ρs i ]g 147
n
2
˙ w =[
˙ w i =[2z π(i) + σs i ]g, z j + σz]g
j=1

j
j
c i = H(p, q, g, ¯y, ˜g, {˜g j }, (G j ,M j ) j , (G ,M ) j ,

j
˜ g , (˜g ) j ,g ,m ,v,w,t,u, (u j ) j ,
( ˙ t j ) j , ˙v, (˙v j ) j , ˙w, (˙w j ) j ,i) (1)
n

r i = c π −1 r = s j c j + z mod q
(i) + z i,
j=1
n
2

λ = λ j c j + λ mod q
j=1
n

ζ = [c j ]G , η =[x]ζ (2)
j
j=1
(3)
y =[z ]g, η =[z ]ζ

c = H(p, q, g, y, ζ, η, y ,η ) (4)

(5)
r = c x + z mod q

i
The prover send the proof g ,m , ˜g , ˜g ,v,w,t,u,u i , ˙ t i , ˙v i , ˙v, ˙w i , ˙w, r, r i , λ ,η,η ,

y ,r (i =1,... ,n) to the verifier along with (G ,M ) i .

i i
3.2 Verifications of the Proof
The verifier first computes (c i ) i=1,...,n according to Eq.(1). Next, the verifier
compute
n

ζ = [c j ]G j
j=1
and generate c according to Eq.(4). The verifier accepts the proof if all of the

following equations hold.
v, t, w ∈ E
n

[r]g + [r j ]G j = g + ζ
j=1
n n

[r]¯ + [r j ]M j = η + m + [c j ]M j
y
j=1 j=1
n n

[r]˜ + [r j ]˜ j =˜ + [c j ]˜ j

g
g
g
g
j=1 j=1