Welcome to the resource topic for 2019/732
Title:
Fully Homomorphic NIZK and NIWI Proofs
Authors: Prabhanjan Ananth, Apoorvaa Deshpande, Yael Tauman Kalai, Anna Lysyanskaya
Abstract:In this work, we define and construct fully homomorphic non-interactive zero knowledge (FH-NIZK) and non-interactive witness-indistinguishable (FH-NIWI) proof systems. We focus on the NP complete language L, where, for a boolean circuit C and a bit b, the pair (C,b) \in L if there exists an input w such that C(w)=b. For this language, we call a non-interactive proof system ‘fully homomorphic’ if, given instances (C_i,b_i) \in L along with their proofs \Pi_i, for i \in \{1,\ldots,k\}, and given any circuit D:\{0,1\}^k \rightarrow \{0,1\}, one can efficiently compute a proof \Pi for (C^*,b) \in L, where C^*(w^{(1)}, \ldots,w^{(k)})=D(C_1(w^{(1)}),\ldots,C_k(w^{(k)})) and D(b_1,\ldots,b_k)=b. The key security property is ‘unlinkability’: the resulting proof \Pi is indistinguishable from a fresh proof of the same statement. Our first result, under the Decision Linear Assumption (DLIN), is an FH-NIZK proof system for L in the common random string model. Our more surprising second result (under a new decisional assumption on groups with bilinear maps) is an FH-NIWI proof system that requires no setup.
ePrint: https://eprint.iacr.org/2019/732
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