Witness encryption (WE) (Garg et al., STOC’13) is a powerful cryptographic primitive that is closely related to the notion of indistinguishability obfuscation (Barak et, JACM’12, Garg et al., FOCS’13). For a given \(\textsf{NP}\) -language L, WE for L enables encrypting a message m using an instance x as the public-key, while ensuring that efficient decryption is possible by anyone possessing a witness for \(x \in L\) , and if \(x\not \in L\) , then the encryption is hiding. We show that this seemingly sophisticated primitive is equivalent to a communication-efficient version of one of the most classic cryptographic primitives—namely that of a zero-knowledge argument (Goldwasser et al., SIAM’89, Brassard et al., JCSS’88): for any \(\textsf{NP}\) -language L, the following are equivalent: Our approach is inspired by an elegant (one-sided) connection between (laconic) zero-knowledge arguments and public-key encryption established by Berman et al. (CRYPTO’17) and Cramer-Shoup (EuroCrypt’02), and the equivalence between a notion of so-called “predictable arguments” and witness encryption by Faonio, Nielsen, and Venturi (PKC’17).

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On Witness Encryption and Laconic Zero-Knowledge Arguments

  • Yanyi Liu,
  • Noam Mazor,
  • Rafael Pass

摘要

Witness encryption (WE) (Garg et al., STOC’13) is a powerful cryptographic primitive that is closely related to the notion of indistinguishability obfuscation (Barak et, JACM’12, Garg et al., FOCS’13). For a given \(\textsf{NP}\) -language L, WE for L enables encrypting a message m using an instance x as the public-key, while ensuring that efficient decryption is possible by anyone possessing a witness for \(x \in L\) , and if \(x\not \in L\) , then the encryption is hiding. We show that this seemingly sophisticated primitive is equivalent to a communication-efficient version of one of the most classic cryptographic primitives—namely that of a zero-knowledge argument (Goldwasser et al., SIAM’89, Brassard et al., JCSS’88): for any \(\textsf{NP}\) -language L, the following are equivalent: Our approach is inspired by an elegant (one-sided) connection between (laconic) zero-knowledge arguments and public-key encryption established by Berman et al. (CRYPTO’17) and Cramer-Shoup (EuroCrypt’02), and the equivalence between a notion of so-called “predictable arguments” and witness encryption by Faonio, Nielsen, and Venturi (PKC’17).