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Cryptographic Counters and Applications to Electronic Voting.
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Jonathan Katz, Steven Myers, Rafail Ostrovsky
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Abstract:
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We formalize the notion of a \emph{cryptographic counter}, which allows a group of participants to increment and decrement a cryptographic representation of a (hidden) numerical value privately and robustly. The value of the counter can only be determined b y a trusted authority (or group of authorities, which may include participants themselves), and participants cannot determine any information about the increment/decrement operations performed by other parties.

Previous \emph{efficient} implementations of such counters have relied on fully-homomorphic encryption schemes; this is a relatively strong requirement which not all encryption schemes satisfy. We provide an alternate approach, starting with any encryption scheme homomorphic over the additive group $\integers{2}$ (i.e., 1-bit {\sc xor}). As our main result, we show a general and efficient reduction from any such encryption scheme to a general cryptographic counter. Our main reduction does not use additional assumptions, is efficient, and gives a novel implementation of a general counter. The result can also be viewed as an efficient construction of a general $n$-bit cryptographic counter from any 1-bit counter which has the additional property that counters can be added securely.

As an example of the applicability of our construction, we present a cryptographic counter based on the quadratic residuosity assumption and use it to construct an efficient voting scheme which satisfies universal verifiability, privacy, and robustness.

**comment:**
Appeared
in
Proceedings of Advances in Cryptology, (EUROCRYPT-2001)
Springer-Verlag/IACR Lecture Notes in Computer Science.

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