- [scholar]Noninteractive zero-knowledge proof of knowledge and chosen ciphertext attack (Rackoff, Simon, Crypto 91)
- On defining proofs of knowledge (Mihir Bellare, Oded Goldreich, CRYPTO 1992)
- Proving computational ability (Mihir Bellare, Oded Goldreich, 1992)
- Communication-Efficient Non-Interactive Proofs of Knowledge with Online Extractors, Marc Fischlin, Crypto 2005 (05.06.05)
- Black-Box Knowledge Extraction Revisited: Universal Approach with Precise Bounds (Emilia Käsper and Sven Laur and Helger Lipmaaa, eprint 2006/356)
- [scholar]Quantum Proofs of Knowledge (Dominique Unruh, Eurocrypt 2012)
20.05.2012
- Zaps and Their Applications (Cynthia Dwork, Moni Naor, FOCS 2002)
- List-Decoding of Linear Functions and Analysis of a Two-Round Zero-Knowledge Argument (Cynthia Dwork, Ronen Shaltiel, Adam Smith, Luca Trevisan, TCC 2004)
- How to Prove That a Committed Number is Prime (T. Le, Khan Nguyen, Vijay Varadharajan, 2000)
- Proof Systems for General Statements about Discrete Logarithms (Jan Camenisch, Markus Stadler, 1997)
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Proofs that n=pq and related
- An Efficient Non-Interactive Statistical Zero-Knowledge Proof System for Quasi-Safe Prime Products (Rosario Gennaro, Daniele Micciancio, Tal Rabin, 1998)
- Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes (Jan Camenisch, Markus Michels, EUROCRYPT 1999)
- Short Proofs of Knowledge for Factoring (Guillaume Poupard, Jacques Stern, 2000)
- Fast Monte-Carlo Primality Evidence Shown in the Dark (Wenbo Mao, 2000)
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Proofs that the committed numbers belongs to an interval (Range proof)
- [scholar]Easy come - easy go divisible cash (Chan, Frankel, Tsiounis, EUROCRYPT 1998)
- [scholar]Efficient Proofs that a Committed Number Lies in an Interval (Fabrice Boudot, EUROCRYPT 2000)
- A Generalisation, a Simplification and some Applications of Paillier's Probabilistic Public-Key Cryptosystem (Ivan Damgaard, Mads Jurik, PKC 2001)
- Secure Vickrey Auctions without Threshold Trust (Helger Lipmaa, N. Asokan and Valtteri Niemi, FC 2002)
- Statistical Zero-Knowledge Proofs from Diophantine Equations (Helger Lipmaa, eprint 2001/086)
- Efficient Protocols for Set Membership and Range Proofs (Jan Camenisch, Rafik Chaabouni, Abhi Shelat, Asiacrypt 2008)
- [scholar]Efficient Non-interactive Range Proof (Tsz Hon Yuen, Qiong Huang, Yi Mu, Willy Susilo, Duncan S. Wong, Guomin Yang, COCOON 2009)
- Additive Combinatorics and Discrete Logarithm Based Range Protocols (Rafik Chaabouni, Helger Lipmaa, Abhi Shelat, eprint 2009/469)
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Background cryptography
- Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations
(Fujisaki, Okamoto, 1999) - An Integer Commitment Scheme based on Groups with Hidden Order
(Ivan Damgard and Eiichiro Fujisaki, eprint 2001/064)
- Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations
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Applications
- RSA Key Generation with Verifiable Randomness
(Ari Juels, Jorge Guajardo, PKC 2002) - Electronic Jury Voting Protocols
(Alejandro Hevia, Marcos Kiwi, 2001) - A Signature Scheme with Efficient Protocols
(Jan Camenisch, Anna Lysyanskaya, 2002) - Timed Release of Standard Digital Signatures
( Juan A. Garay, Markus Jakobsson) - Adaptive Security in the Threshold Setting: From Cryptosystems to Signature Schemes
( Anna Lysyanskaya, Chris Peikert) - Adaptive Security in the Threshold Setting: From Cryptosystems to Signatures
(Christopher Jason Peikert, 2001) - An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation
( Jan Camenisch, Anna Lysyanskaya, 2001) - Confirmer Signature Schemes Secure against Adaptive Adversaries
( Jan Camenisch, Markus Michels, 2000) - Distribution Chain Security
( Glenn Durfee, Matt Franklin, 2000) - Fair Encryption of RSA Keys
( Guillaume Poupard, Jacques Stern, 2000)
- RSA Key Generation with Verifiable Randomness
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Problems related to discrete logarithms
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Proof of knowledge of a discrete logarithm
- [scholar]Demonstrating possession of a discrete logarithm without revealing it
(D. Chaum, J.-H. Evertse, J. van de Graaf, R. Peralta, CRYPTO 86) - Efficient signature generation for smart cards
(Schnorr, J. of Cryptology, 1991) - Efficient Proofs of Knowledge of Discrete Logarithms and Representations in Groups with Hidden Order
(Endre Bangerter, Jan Camenisch, and Ueli Maurer, PKC 2005)
- [scholar]Demonstrating possession of a discrete logarithm without revealing it
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Proof of knowledge of a dl-representation
- [scholar]An improved protocol for demonstrating possession of discrete logarithms and some generalizations
(Chaum, Evertse, van de Graaf, EUROCRYPT 87) - [scholar]Untraceable off-line cash in wallets with observers
(Stefan Brands, CRYPTO 93)
- [scholar]An improved protocol for demonstrating possession of discrete logarithms and some generalizations
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Proof of equality of two discrete logarithms
- [scholar]Wallet databases with observers
(Chaum, Pedersen, CRYPTO 92)
- [scholar]Wallet databases with observers
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Proof of knowledge of at least one of two discrete logarithms
- Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols
( Ronald Cramer, Ivan Damgård, Berry Schoenmakers, CRYPTO 94) - On Monotone Formula Closure of SZK
(de Santis, di Crescenzo, Persiano, Yung, FOCS 1994)
- Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols
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Range proof in exponents
- A Generalisation, a Simplification and some Applications of Paillier's Probabilistic Public-Key System
(Ivan Damgård and Mads Jurik, PKC 2001) - Statistical Zero-Knowledge Proofs from Diophantine Equations
(Helger Lipmaa, eprint 2001/086) - Secure Vickrey Auctions without Threshold Trust
(Helger Lipmaa, N. Asokan, Valtteri Niemi, FC 2002) - On Diophantine Complexity and Statistical Zero-Knowledge Arguments
(Helger Lipmaa, ASIACRYPT 2003)
- A Generalisation, a Simplification and some Applications of Paillier's Probabilistic Public-Key System
-
Proof of knowledge of a discrete logarithm
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Millionaire's problem: which of the committed numbers is greater
- Efficient private bidding and auctions with an oblivious third party (Christian Cachin, ACM CCS 1999)
- A Cost-Effective Pay-Per-Multiplication Comparison Method for Millionaires (Marc Fischlin, RSA 2001)
- Strong Conditional Oblivious Transfer and Computing on Intervals (Ian F. Blake and Vladimir Kolesnikov, Asiacrypt 2004)
- Practical Two-Party Computation Based on the Conditional Gate (Berry Schoenmakers and Pim Tuyls, Asiacrypt 2004)
- Additive Conditional Disclosure Of Secrets and Applications (Sven Laur, Helger Lipmaa, eprint/2005/378)
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Private equality test (Tierce problem, socialist millionaires'): whether committed numbers are equal
- Comparing Information Without Leaking It (Ron Fagin, Moni Naor and Peter Winkler, 1996)
- Proving without Knowing: On Oblivious, Agnostic and Blindfolded Provers (Markus Jakobsson, Moti Yung, 1996)
- Oblivious transfer and polynomial evaluation (Moni Naor, Benny Pinkas, STOC 1999)
- Mix and Match: Secure Function Evaluation via Ciphertexts (M. Jakobsson and A. Juels, Asiacrypt 2000)
- A Fair and Efficient Solution to the Socialist Millionaires' Problem (Fabrice Boudot, Berry Schoenmakers, and Jacques Traore)
- Bit-Slice Auction Circuit, Kaoru Kurosawa and Wakaha Ogata, 2002 (10.03.05)
- Verifiable Homomorphic Oblivious Transfer and Private Equality Test (Helger Lipmaa, ASIACRYPT 2003)
- Also done in
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Proof that one list is a permuted encryption of another one
- A Cryptographic Solution to a Game Theoretic Problem (Yevgeniy Dodis, Shaih Halevi and Tal Rabin, Crypto 2000)
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Multiplicative relationship: PK(y1=E(m1) and y2=E(m2) and y3=E(m3) and m1*m2=m3)
- Simplified VSS and Fast-track Multiparty Computations with Applications to Threshold Cryptography (Rosario Gennaro, Michael Rabin, and Tal Rabin, ACM PODC '98)
- Efficient Multiparty Computations Secure Against an Adaptive Adversary (Ronald Cramer, Ivan Damgard, Stefan Dziembowski, Martin Hirt, Tal Rabin, 1999)
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Proofs that committed numbers satisfy a polynomial relationship
- Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations (Eiichiro Fujisaki, Tatsuaki Okamoto, CRYPTO 97/IEICE 99)
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Exponential relationship
- Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes (Jan Camenisch, Markus Michels, 1999)
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Proofs of properties of trapdoor permutations
- Certifying Permutations: Noninteractive Zero-Knowledge Based on Any Trapdoor Permutation (Mihir Bellare and Moti Yung, JoC 1996)
- A Low Communication Competitive Interactive Proof System for Promised Quadratic Residuosity (Toshiya Itoh, Masafumi Hoshi, and Shigeo Tsujii, 1993)
- Designated Verifier Proofs and Their Applications ( Markus Jakobsson, Kazue Sako, Russell Impagliazzo, 1996)
- Chameleon Hashing and Signatures (Hugo Krawczyk, Tal Rabin, 1997)
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