Security of the Fiat-Shamir Transformation in the Quantum Random-Oracle Model

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called \(\Sigma {\text {-protocol}}\), into a non-interactive proof in the random-oracle model. We study this transformation in the setting of a quantum adversary that in particular may query the random oracle in quantum superposition.

[1]  Dominique Unruh,et al.  Non-Interactive Zero-Knowledge Proofs in the Quantum Random Oracle Model , 2015, EUROCRYPT.

[2]  Dominique Unruh,et al.  Computationally Binding Quantum Commitments , 2016, EUROCRYPT.

[3]  Fang Song,et al.  Making Existential-Unforgeable Signatures Strongly Unforgeable in the Quantum Random-Oracle Model , 2015, IACR Cryptol. ePrint Arch..

[4]  Mihir Bellare,et al.  On Defining Proofs of Knowledge , 1992, CRYPTO.

[5]  Serge Fehr,et al.  The Measure-and-Reprogram Technique 2.0: Multi-Round Fiat-Shamir and More , 2020, IACR Cryptol. ePrint Arch..

[6]  Takashi Yamakawa,et al.  Tightly-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model , 2018, IACR Cryptol. ePrint Arch..

[7]  Amos Fiat,et al.  How to Prove Yourself: Practical Solutions to Identification and Signature Problems , 1986, CRYPTO.

[8]  Ran Canetti,et al.  The random oracle methodology, revisited , 2000, JACM.

[9]  Dominique Unruh,et al.  Quantum Proofs of Knowledge , 2012, IACR Cryptol. ePrint Arch..

[10]  Rafail Ostrovsky,et al.  Zero-knowledge from secure multiparty computation , 2007, STOC '07.

[11]  Eike Kiltz,et al.  A Concrete Treatment of Fiat-Shamir Signatures in the Quantum Random-Oracle Model , 2018, IACR Cryptol. ePrint Arch..

[12]  Damien Stehlé,et al.  CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM , 2017, 2018 IEEE European Symposium on Security and Privacy (EuroS&P).

[13]  Serge Fehr Classical Proofs for the Quantum Collapsing Property of Classical Hash Functions , 2018, IACR Cryptol. ePrint Arch..

[14]  Mark Zhandry,et al.  Revisiting Post-Quantum Fiat-Shamir , 2019, IACR Cryptol. ePrint Arch..

[15]  Daniel Slamanig,et al.  Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives , 2017, CCS.

[16]  Mark Zhandry,et al.  Secure Identity-Based Encryption in the Quantum Random Oracle Model , 2012, CRYPTO.

[17]  Mark Zhandry,et al.  Random Oracles in a Quantum World , 2010, ASIACRYPT.

[18]  Dominique Unruh,et al.  Post-quantum Security of Fiat-Shamir , 2017, ASIACRYPT.

[19]  Dominique Unruh,et al.  Quantum Position Verification in the Random Oracle Model , 2014, CRYPTO.

[20]  Vadim Lyubashevsky,et al.  Lattice Signatures Without Trapdoors , 2012, IACR Cryptol. ePrint Arch..

[21]  Vadim Lyubashevsky,et al.  Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures , 2009, ASIACRYPT.

[22]  Tommaso Gagliardoni,et al.  The Fiat-Shamir Transformation in a Quantum World , 2013, IACR Cryptol. ePrint Arch..

[23]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[24]  Markulf Kohlweiss,et al.  On the Non-malleability of the Fiat-Shamir Transform , 2012, INDOCRYPT.

[25]  Mark Zhandry,et al.  How to Record Quantum Queries, and Applications to Quantum Indifferentiability , 2019, IACR Cryptol. ePrint Arch..

[26]  Erdem Alkim,et al.  Revisiting TESLA in the Quantum Random Oracle Model , 2017, PQCrypto.

[27]  Mark Zhandry,et al.  Quantum Lightning Never Strikes the Same State Twice. Or: Quantum Money from Cryptographic Assumptions , 2017, Journal of Cryptology.

[28]  Mark Zhandry,et al.  How to Construct Quantum Random Functions , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[29]  Mehdi Tibouchi,et al.  Tightly Secure Signatures From Lossy Identification Schemes , 2015, Journal of Cryptology.

[30]  Andris Ambainis,et al.  Quantum Attacks on Classical Proof Systems: The Hardness of Quantum Rewinding , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[31]  Jesper Madsen,et al.  ZKBoo: Faster Zero-Knowledge for Boolean Circuits , 2016, USENIX Security Symposium.