An Oblivious Pseudo-Random Function (OPRF) is a two-party protocol for jointly evaluating a Pseudo-Random Function (PRF). OPRFs are a prime tool for building secure authentication and key exchange from passwords, private set intersection, private information retrieval, and many other privacy-preserving systems. While classical OPRFs run as fast as a TLS Handshake, current quantum-safe OPRF candidates with malicious security are still practically inefficient. In this paper, we propose a framework for constructing OPRFs from secure two-party computation. The framework captures a family of so-called 2Hash PRFs, which sandwich a function evaluation between two hashes. The core of our framework is a compiler that yields an OPRF from a secure evaluation of any function that is key-collision resistant and one-more unpredictable. We instantiate this compiler by providing such functions built from Legendre symbols or from a block cipher. We then give a case-tailored protocol for securely evaluating our Legendre-based function, built from Oblivious Transfer (OT) and Zero-Knowledge Proofs (ZKP). Instantiated with lattice-based OT and proofs based on Vector Oblivious Linear Evaluation (VOLE), we obtain the first somewhat practically efficient quantum-safe OPRF with malicious and composable security guarantees. A preliminary implementation shows that an execution of our OPRF protocol, instantiated for 128 bits of security, runs in only \(185 \text { ms}\) if both parties are running in separate threads on the same machine, with a total communication cost of approximately \(748 \text { KB}\) .

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The 2Hash OPRF Framework and Efficient Post-quantum Instantiations

  • Ward Beullens,
  • Lucas Dodgson,
  • Sebastian Faller,
  • Julia Hesse

摘要

An Oblivious Pseudo-Random Function (OPRF) is a two-party protocol for jointly evaluating a Pseudo-Random Function (PRF). OPRFs are a prime tool for building secure authentication and key exchange from passwords, private set intersection, private information retrieval, and many other privacy-preserving systems. While classical OPRFs run as fast as a TLS Handshake, current quantum-safe OPRF candidates with malicious security are still practically inefficient. In this paper, we propose a framework for constructing OPRFs from secure two-party computation. The framework captures a family of so-called 2Hash PRFs, which sandwich a function evaluation between two hashes. The core of our framework is a compiler that yields an OPRF from a secure evaluation of any function that is key-collision resistant and one-more unpredictable. We instantiate this compiler by providing such functions built from Legendre symbols or from a block cipher. We then give a case-tailored protocol for securely evaluating our Legendre-based function, built from Oblivious Transfer (OT) and Zero-Knowledge Proofs (ZKP). Instantiated with lattice-based OT and proofs based on Vector Oblivious Linear Evaluation (VOLE), we obtain the first somewhat practically efficient quantum-safe OPRF with malicious and composable security guarantees. A preliminary implementation shows that an execution of our OPRF protocol, instantiated for 128 bits of security, runs in only \(185 \text { ms}\) if both parties are running in separate threads on the same machine, with a total communication cost of approximately \(748 \text { KB}\) .