Voting Cryptography Lecture 4 Chantilly Academy Poorvi Vora

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Voting Cryptography Lecture 4: Chantilly Academy Poorvi Vora Department of Computer Science George Washington

Voting Cryptography Lecture 4: Chantilly Academy Poorvi Vora Department of Computer Science George Washington University

Voting with Crypto: Pret a Voter Ryan and Chaum, Ryan, Schneider The draft should

Voting with Crypto: Pret a Voter Ryan and Chaum, Ryan, Schneider The draft should be reinstalled Carries information about your vote for voting system to use it in tally Yes No X 142 Order is different for different ballots 10/2/2020 Only the right half says nothing about your vote Chantilly Academy Crypto Lecture 2: Spring 07 2

To Vote • Mark you choice • Tear apart the two halves, so that

To Vote • Mark you choice • Tear apart the two halves, so that the choices are separate from your mark • Give your marked half to the polling officer; obtain an exact, signed copy from the polling officer. • Destroy other half in front of polling officer 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 3

Your Receipt X 142 Only the right half says nothing about your vote 10/2/2020

Your Receipt X 142 Only the right half says nothing about your vote 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 4

Check Receipts • All cast ballots are on the board. Check that your receipt

Check Receipts • All cast ballots are on the board. Check that your receipt is there. It will be listed as: Bottom, 142 • If not, there’s a problem 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 5

Tellers • Two tellers will decrypt the votes • The number 142 was generated

Tellers • Two tellers will decrypt the votes • The number 142 was generated using RSA encryption 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 6

Teller 1 • The first teller will decrypt mod 187. – The encrypting key

Teller 1 • The first teller will decrypt mod 187. – The encrypting key was (public) 107 – The decrypting key is 3 – Hence first teller performs encryption with private key to obtain message: 1423 mod 187 = 131 • The first digit, 1, represents what to do to the ballot. It says to “flip” it. The other 2 digits, 31, will be sent with the ballot. 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 7

Teller 1 makes a note • Teller 1 makes a note on the ballot

Teller 1 makes a note • Teller 1 makes a note on the ballot X X 142 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 1, 31 8

Teller 1 modifies ballot • And makes a new ballot to pass on X

Teller 1 modifies ballot • And makes a new ballot to pass on X 31 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 9

Teller 1 shuffles • Teller 1 shuffles all ballots before passing them on to

Teller 1 shuffles • Teller 1 shuffles all ballots before passing them on to Teller 2 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 10

Teller 2 decrypts ballots that were encrypted mod 33, using public key 7; (private

Teller 2 decrypts ballots that were encrypted mod 33, using public key 7; (private key is 3) 313 mod 33 = 25 mod 31 Because this number is odd, the mark is flipped again 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 11

Teller 1 makes a note • Teller 1 makes a note on the ballot

Teller 1 makes a note • Teller 1 makes a note on the ballot X X 31 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 25 12

Teller 1 modifies ballot • And makes a new ballot to pass on, which

Teller 1 modifies ballot • And makes a new ballot to pass on, which is interpreted as though TOP = YES X 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 NO 13

Teller 2 shuffles Votes are shuffled and tallied 10/2/2020 Chantilly Academy Crypto Lecture 2:

Teller 2 shuffles Votes are shuffled and tallied 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 14

Votes maybe audited, though we do not have time for that today 10/2/2020 Chantilly

Votes maybe audited, though we do not have time for that today 10/2/2020 Chantilly Academy Crypto Lecture 2: Spring 07 15

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