On Diophantine Complexity and Statistical Zero-Knowledge Arguments
نویسنده
چکیده
We show how to construct laconic honest-verifier statistical zeroknowledge Diophantine arguments of knowledge (HVSZK AoK) that a committed tuple of integers belongs to S for all languages in bounded arithmetic. While doing this, we propose a new algorithm for computing the Lagrange representation of nonnegative integers and a new efficient representing polynomial for the exponential relation. As applications, we construct the most efficient known HVSZK AoK for nonnegativity, the first constant-round laconic HVSZK AoK for exponential relation, and propose communication-efficient versions of the Damgård-Jurik multi-candidate voting scheme and of the Lipmaa-Asokan-Niemi (b+ 1)st-price auction scheme.
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