From Laconic Zero-Knowledge to Public-Key Cryptography

Since its inception, public-key encryption (\(\mathsf {PKE}\)) has been one of the main cornerstones of cryptography. A central goal in cryptographic research is to understand the foundations of public-key encryption and in particular, base its existence on a natural and generic complexity-theoretic assumption. An intriguing candidate for such an assumption is the existence of a cryptographically hard language Open image in new window .

[1]  Rafail Ostrovsky,et al.  One-way functions, hard on average problems, and statistical zero-knowledge proofs , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[2]  Carmit Hazay,et al.  Leakage-Resilient Cryptography from Minimal Assumptions , 2013, EUROCRYPT.

[3]  Rafail Ostrovsky,et al.  Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data , 2004, SIAM J. Comput..

[4]  Eyal Kushilevitz,et al.  A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm , 1993, Journal of Cryptology.

[5]  Russell Impagliazzo,et al.  One-way functions are essential for complexity based cryptography , 1989, 30th Annual Symposium on Foundations of Computer Science.

[6]  László Babai,et al.  Graph isomorphism in quasipolynomial time [extended abstract] , 2016, STOC.

[7]  Vinod Vaikuntanathan,et al.  On Basing Private Information Retrieval on NP-Hardness , 2016, TCC.

[8]  Avi Wigderson,et al.  On interactive proofs with a laconic prover , 2001, computational complexity.

[9]  Ron Rothblum,et al.  Enhancements of Trapdoor Permutations , 2012, Journal of Cryptology.

[10]  Silvio Micali,et al.  How to play ANY mental game , 1987, STOC.

[11]  Rafail Ostrovsky,et al.  Resettable Statistical Zero Knowledge , 2012, IACR Cryptol. ePrint Arch..

[12]  Brent Waters,et al.  A Framework for Efficient and Composable Oblivious Transfer , 2008, CRYPTO.

[13]  Thomas Holenstein,et al.  On the Randomness of Independent Experiments , 2006, IEEE Transactions on Information Theory.

[14]  Omer Reingold,et al.  Efficiency improvements in constructing pseudorandom generators from one-way functions , 2010, STOC '10.

[15]  Amit Sahai,et al.  Obfuscation-Based Non-black-box Simulation and Four Message Concurrent Zero Knowledge for NP , 2015, TCC.

[16]  Omer Reingold,et al.  Finding Collisions in Interactive Protocols - Tight Lower Bounds on the Round and Communication Complexities of Statistically Hiding Commitments , 2015, SIAM J. Comput..

[17]  Jürg Wullschleger.  Oblivious-transfer amplification , 2007, Ausgezeichnete Informatikdissertationen.

[18]  Michael Alekhnovich.  More on Average Case vs Approximation Complexity , 2011, computational complexity.

[19]  Andrej Bogdanov,et al.  Limits of Provable Security for Homomorphic Encryption , 2013, CRYPTO.

[20]  Silvio Micali,et al.  Probabilistic encryption & how to play mental poker keeping secret all partial information , 1982, STOC '82.

[21]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[22]  Oded Goldreich,et al.  Computational complexity - a conceptual perspective , 2008 .

[23]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[24]  Moni Naor,et al.  Efficient oblivious transfer protocols , 2001, SODA '01.

[25]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

[26]  Oded Goldreich,et al.  Comparing entropies in statistical zero knowledge with applications to the structure of SZK , 1999, Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317).

[27]  Avi Wigderson,et al.  Public-key cryptography from different assumptions , 2010, STOC '10.

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

[29]  Moni Naor,et al.  Does parallel repetition lower the error in computationally sound protocols? , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[30]  Omer Reingold,et al.  Statistically Hiding Commitments and Statistical Zero-Knowledge Arguments from Any One-Way Function , 2009, SIAM J. Comput..

[31]  Mihir Bellare,et al.  Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening , 2009, EUROCRYPT.

[32]  Salil P. Vadhan,et al.  Characterizing pseudoentropy and simplifying pseudorandom generator constructions , 2012, STOC '12.

[33]  Salil P. Vadhan,et al.  Zero knowledge with efficient provers , 2006, STOC '06.

[34]  Krzysztof Pietrzak,et al.  Cryptography from Learning Parity with Noise , 2012, SOFSEM.

[35]  Benny Applebaum,et al.  On the Relationship Between Statistical Zero-Knowledge and Statistical Randomized Encodings , 2018, computational complexity.

[36]  Ron Rothblum,et al.  Homomorphic Encryption: from Private-Key to Public-Key , 2011, Electron. Colloquium Comput. Complex..

[37]  SahaiAmit,et al.  A complete problem for statistical zero knowledge , 2003 .

[38]  Thomas Holenstein,et al.  One-Way Secret-Key Agreement and Applications to Circuit Polarization and Immunization of Public-Key Encryption , 2005, CRYPTO.

[39]  Renato Renner,et al.  Simple and Tight Bounds for Information Reconciliation and Privacy Amplification , 2005, ASIACRYPT.

[40]  Moni Naor,et al.  One-Way Functions and (Im)Perfect Obfuscation , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[41]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[42]  Oded Goldreich,et al.  On the Complexity of Interactive Proofs with Bounded Communication , 1998, Inf. Process. Lett..

[43]  Salil P. Vadhan,et al.  An Equivalence Between Zero Knowledge and Commitments , 2008, TCC.

[44]  Russell Impagliazzo,et al.  Limits on the Provable Consequences of One-way Permutations , 1988, CRYPTO.

[45]  Oded Goldreich,et al.  The Foundations of Cryptography - Volume 2: Basic Applications , 2001 .

[46]  Ronald Cramer,et al.  Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption , 2001, EUROCRYPT.

[47]  Nir Bitansky,et al.  Structure vs. Hardness Through the Obfuscation Lens , 2017, CRYPTO.

[48]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[49]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[50]  Oded Regev,et al.  On lattices, learning with errors, random linear codes, and cryptography , 2005, STOC '05.

[51]  Omer Reingold,et al.  Inaccessible entropy , 2009, STOC '09.

[52]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[53]  Silvio Micali,et al.  A Completeness Theorem for Protocols with Honest Majority , 1987, STOC 1987.

[54]  Oded Goldreich,et al.  A randomized protocol for signing contracts , 1985, CACM.