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Efficient Maximal Privacy in Boardroom Voting and Anonymous Broadcast

Efficient Maximal Privacy in Boardroom Voting and Anonymous Broadcast. Jens Groth BRICS, University of Aarhus Cryptomathic A/S. Election Privacy. V 1. V 2. V 3. Ballot box. Result. Vote1 = Result – Vote2 – Vote3. Properties.

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Efficient Maximal Privacy in Boardroom Voting and Anonymous Broadcast

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  1. Efficient Maximal Privacy in Boardroom Voting and Anonymous Broadcast Jens Groth BRICS, University of Aarhus Cryptomathic A/S

  2. Election Privacy V1 V2 V3 Ballot box Result Vote1 = Result – Vote2 – Vote3

  3. Properties • Perfect ballot secrecycoalition information = own votes and result • Self-tallyingresult reveals itself • Dispute-freenessdishonest behavior detectable

  4. A V1 V2 V3 BBS Assumptions • Bulletin board system • Semi-synchronousadversary: phases and activations • Static corruption • Group <g> order q, decision diffie-hellman • Random oracle model,NIZK arguments

  5. Protocol • Public keys: h1 gx1,..., hn gxn private keys: x1,..., xn • Votes: V1: (u,v)  (gr1,(h2···hn)r1gv1)V2: (u,v)  (ugr2,vu-x2(h3···hn)r2gv2) = (gr1+r2,(h3···hn)r1+r2gv1+v2)..Vn: (u,v)  (ugrn,vu-xngvn) = (gr1+...+rn,gv1+...+Vn) • Result: v1+...+vn

  6. Complexity • Key generation: O(1) exposverification of proofs: O(n) expos • Voting: O(log c) exposverification of proofs: O(n log c) expos Previous protocols: • Key generation: O(n) exposverification of proofs: O(n2) expos • Voting: O(log c) exposverification of proofs: O(n log c) expos c = number of candidates

  7. Security A S s s V1 V2 V3 V1 V2 V3 cont cont (u,v) (u,v) (u,v) (u,v) (u,v) (u,v) result v2w2 v1 v3 result Partial result: v1+v3Reveal:last honest vote

  8. Anonymous Broadcast • Public keys: h1 gx1,..., hn gxn private keys: x1,..., xn • Messages: P1: (u1,v1)  (gr1,(h2···hn)r1m1)P2: (u2,v2)  (gr2,(h2···hn)r2m2) shuffle (u1,v1), (u2,v2) (u1,v1)  (u1,v1u1-x2) (u2,v2)  (u2,v2u2-x2) ...

  9. Anonymous Broadcast • Pn: (un,vn)  (grn,hnrnmn) shuffle (u1,v1),...,(un,vn) (u1,v1)  (u1,v1u1-xn) . . . (un,vn)  (un,vnun-xn) • {v1,...,vn} = {m1,...,mn} Output: m1,...,mn

  10. Complexity • Key generation: O(1) exposverification of proofs: O(n) expos • Message submission: O(n) exposverification of proofs: O(n2) expos

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