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Fully Homomorphic NIZK and NIWI Proofs

  • Prabhanjan AnanthEmail author
  • Apoorvaa Deshpande
  • Yael Tauman Kalai
  • Anna Lysyanskaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11892)

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 \(\mathbf {w}\) such that \(C(\mathbf {w})=b\). 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 \(\varPi _i\), for \(i\in \{1,\ldots ,k\}\), and given any circuit \(D:\{0,1\}^k\rightarrow \{0,1\}\), one can efficiently compute a proof \(\varPi \) for \((C^*,b)\in L\), where \(C^*(\mathbf {w}^{(1)},\ldots ,\mathbf {w}^{(k)})=D(C_1(\mathbf {w}^{(1)}),\ldots ,C_k(\mathbf {w}^{(k)}))\) and \(D(b_1,\ldots ,b_k)=b\). The key security property is unlinkability: the resulting proof \(\varPi \) 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.

Keywords

Homomorphism Non-interactive zero-knowledge Non-interactive Witness Indistinguishability 

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Prabhanjan Ananth
    • 1
    Email author
  • Apoorvaa Deshpande
    • 2
  • Yael Tauman Kalai
    • 3
  • Anna Lysyanskaya
    • 2
  1. 1.UCSBSanta BarbaraUSA
  2. 2.Brown UniversityProvidenceUSA
  3. 3.MIT and Microsoft ResearchCambridgeUSA

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