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The exact multiplicative complexity of counting votes.

The exact multiplicative complexity of counting votes. Ren é Peralta Yale University 2004. Thanks to: Michael Fischer Joan Boyar Ivan Damgaard…. Basic voting protocol (referendum mode). registration authority emits unforgeable and untraceable ballots.

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The exact multiplicative complexity of counting votes.

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  1. The exact multiplicative complexity of counting votes. René Peralta Yale University 2004 Thanks to: Michael Fischer Joan Boyar Ivan Damgaard…

  2. Basic voting protocol (referendum mode). • registration authority emits unforgeable and untraceable ballots. • voters cast sealed votes into public bulletin board. • counting program decides, announces, and proves outcome.

  3. VOTES

  4. OUTCOME? • exact count. • whether motion passes. • something in between …

  5. It may be desirable to reveal no other information. • coercion. • vote buying and selling.

  6. Circuit computing a function of votes Encrypted votes

  7. x4 x1 x1 x3 x3 x4 x5 Å Å Å Å x2 x1 x4 x5 Å Å x2 x2 Å L L L Motion passes by majority vote

  8. outcome of circuit with encrypted inputs is revealed by a discreet proof (BDP)

  9. The length of a discreet proofis linear in the number of (mod 2) multiplications in the circuit. ADDITIONS are free!

  10. Multiplicative complexity. any Boolean function can be represented by a circuit using only addition and multiplication modulo 2. Multiplicative complexity is the number of multiplications necessary and sufficient.

  11. (Shannon, Lupanov) : almost all Boolean functions on n variables have gate complexity about (BPP 98): Multiplicative complexity over the basis(Å, L, 1)is about 2n n-1 q (2n/2)

  12. NOT MUCH ELSE IS KNOWN!

  13. We focus on concrete multiplicative complexity. For symmetric functions of the votes, computing the Hamming weight is central to this problem.

  14. RESULT (Boyar, Peralta) . The multiplicative complexity of computing the Hamming weight of n bits is exactly n – H(n) e.g. if n = 37 = 100101 then the optimal circuit contains 34 multiplications.

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