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. © International Association for Cryptologic Research 2003.
CITATION STYLE
Lipmaa, H. (2003). On Diophantine complexity and statistical zero-knowledge arguments. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2894, 398–415. https://doi.org/10.1007/978-3-540-40061-5_26
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