Page 259 - 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 Introduction to PunchScan
251
The Tables
6.2
We describe the PDR tables using notation from relational algebra, a system
of notation heavily used in databases. It has the notions of relations (tables),
projections (π - SQL SELECT), selection (σ - SQL WHERE) and join ( ).
Arelation R(A, B),A → B means that A implies B (given A, B is uniquely
identified). A is called a key of relation R.
Let P (print) be the following relation:
P(B id ,P 1 ,P 2 ,P 3 ,CP 1 ,CP 2 ),B id → (P 1 ,P 2 ,P 3 ,CP 1 ,CP 2 )
where B id is the ballot id (the serial number of the ballot), P 1 is T p , P 2 is B p ,
P 3 is a projection of B p oT −1 (voter choices), CP 1 is a commitment to P 1 ,and
p
CP 2 is a commitment to P 2 . The commitments are cryptographic commitments
(see Section B.2 for details). P contains 2n records.
Let D (decrypt) be the following relation:
D(D 1 ,D 2 ,D 3,D 4 ,D 5 ,DC),D 1 → (D 2 ,D 3 ,D 4 ,D 5 ,DC)

where D 1 is a foreign key pointing to the B id attribute of P, D 5 is a foreign
key pointingtothe R id attribute of R (see below),D 2 and D 4 are permutations
of S described above, D 3 is P 3 oD 2 ,and DC is a commitment to the tuple
(D 1 ,D 2 ,D 4 ,D 5 ). D contains 2n records.
Let CD (commitments to the columns of D) be the following relation:
CD(CD 1,2 ,CD 3,4)

This relation has only one record. CD 1,2 is a commitment to D 1 and D 2 ; CD 4,5
is a commitments to D 4 and D 5 .
Let R (results) be the following relation:
R(R id ,R 1 ),R id → (R 1 )

where R id is a unique identifier and R 1 is P 3 oD 2 oD 4 . R contains 2n records.
To select all the information for a ballot, we write:
R
(P B id =D 1 D) D 5 =R id

6.3 The Timeline
Before the election the election authority computes P(B id ,P 1 ,P 2 ,CP 1 ,CP 2 ),
D(D 1 ,D 2 ,D 4 ,D 5 ,DC), CD(CD 1,2 ,CD 4,5 ) and makes public P(B id ,CP 1 ,CP 2 ),
D(DC)and CD(CD 1,2 ,CD 4,5 ).
In the preelection audit, the auditor randomly selects half of the records in
D for all the requested records.
P. The election authority reveals P B id =D 1
The auditor can check that B p oT −1 = D 2 oD 4 . and that the commitments CP 1 ,
p
CP 2 ,and DC are valid.
During the election, the voters fill in P 3 .
After the election, the election authority computes D 3 = P 3 oD 2 and R 1 =
D 3 oD 4 and makes D 3 and R 1 public.