On Diophantine Complexity and Statistical Zero-Knowledge Arguments

We show how to construct practical honest-verifier statistical zero-knowledge Diophantine arguments of knowledge (HVSZK AoK) that a committed tuple of integers belongs to an arbitrary language 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. We apply our results by constructing the most efficient known HVSZK AoK for non-negativity and the first constant-round practical HVSZK AoK for exponential relation. Finally, we propose the outsourcing model for cryptographic protocols and design communication-efficient versions of the Damgård-Jurik multi-candidate voting scheme and of the Lipmaa-Asokan-Niemi (b+1)st-price auction scheme that work in this model.