On the Impossibility of Structure-Preserving Deterministic Primitives

Complex cryptographic protocols are often constructed in a modular way from primitives such as signatures, commitments, and encryption schemes, verifiable random functions, etc. together with zero-knowledge proofs ensuring that these primitives are properly orchestrated by the protocol participants. Over the past decades a whole framework of discrete logarithm based primitives has evolved. This framework, together with so-called generalized Schnorr proofs, gave rise to the construction of many efficient cryptographic protocols.

[1]  Serge Fehr,et al.  On Notions of Security for Deterministic Encryption, and Efficient Constructions without Random Oracles , 2008, CRYPTO.

[2]  Yael Tauman Kalai,et al.  On the (In)security of the Fiat-Shamir paradigm , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[3]  Vitaly Shmatikov,et al.  Handcuffing Big Brother: an Abuse-Resilient Transaction Escrow Scheme , 2004, EUROCRYPT.

[4]  Aggelos Kiayias,et al.  Group Signatures with Efficient Concurrent Join , 2005, EUROCRYPT.

[5]  Jan Camenisch,et al.  Oblivious transfer with access control , 2009, IACR Cryptol. ePrint Arch..

[6]  Mihir Bellare,et al.  The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols , 2004, CRYPTO.

[7]  Mihir Bellare,et al.  Foundations of Group Signatures: Formal Definitions, Simplified Requirements, and a Construction Based on General Assumptions , 2003, EUROCRYPT.

[8]  Silvio Micali,et al.  Verifiable random functions , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[9]  Silvio Micali,et al.  Soundness in the Public-Key Model , 2001, CRYPTO.

[10]  Silvio Micali,et al.  How to construct random functions , 1986, JACM.

[11]  Silvio Micali,et al.  Micropayments Revisited , 2002, CT-RSA.

[12]  Jan Camenisch,et al.  Signature Schemes and Anonymous Credentials from Bilinear Maps , 2004, CRYPTO.

[13]  Ryo Nishimaki,et al.  Constant-Size Structure-Preserving Signatures: Generic Constructions and Simple Assumptions , 2012, Journal of Cryptology.

[14]  Brent Waters,et al.  Short and Stateless Signatures from the RSA Assumption , 2009, CRYPTO.

[15]  Ran Canetti,et al.  Universally composable security: a new paradigm for cryptographic protocols , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[16]  Amit Sahai,et al.  Efficient Noninteractive Proof Systems for Bilinear Groups , 2008, SIAM J. Comput..

[17]  Amit Sahai,et al.  Efficient Non-interactive Proof Systems for Bilinear Groups , 2008, EUROCRYPT.

[18]  Melissa Chase,et al.  Simulatable VRFs with Applications to Multi-theorem NIZK , 2007, CRYPTO.

[19]  Jan Camenisch,et al.  Oblivious Transfer with Hidden Access Control Policies , 2011, Public Key Cryptography.

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

[21]  Vincent Naessens,et al.  Structure Preserving CCA Secure Encryption and Applications , 2011, ASIACRYPT.

[22]  Ronald Cramer,et al.  Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack , 2003, SIAM J. Comput..

[23]  Yevgeniy Dodis,et al.  Efficient Construction of (Distributed) Verifiable Random Functions , 2003, Public Key Cryptography.

[24]  Masayuki Abe,et al.  Group to Group Commitments Do Not Shrink , 2012, EUROCRYPT.

[25]  Xiaomin Liu,et al.  Efficient Oblivious Pseudorandom Function with Applications to Adaptive OT and Secure Computation of Set Intersection , 2009, TCC.

[26]  Mihir Bellare,et al.  Deterministic and Efficiently Searchable Encryption , 2007, CRYPTO.

[27]  Moses D. Liskov.  Updatable Zero-Knowledge Databases , 2005, ASIACRYPT.

[28]  Rafail Ostrovsky,et al.  Invariant Signatures and Non-Interactive Zero-Knowledge Proofs are Equivalent (Extended Abstract) , 1992, CRYPTO.

[29]  Jan Camenisch,et al.  Compact E-Cash , 2005, EUROCRYPT.

[30]  Yehuda Lindell,et al.  Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries , 2008, Journal of Cryptology.

[31]  Jan Camenisch,et al.  An Efficient System for Non-transferable Anonymous Credentials with Optional Anonymity Revocation , 2001, IACR Cryptol. ePrint Arch..

[32]  Jan Camenisch,et al.  Practical Verifiable Encryption and Decryption of Discrete Logarithms , 2003, CRYPTO.

[33]  Taher ElGamal,et al.  A public key cyryptosystem and signature scheme based on discrete logarithms , 1985 .

[34]  Torben P. Pedersen.  Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing , 1991, CRYPTO.

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

[36]  Tibor Jager,et al.  Tightly secure signatures and public-key encryption , 2012, Designs, Codes and Cryptography.

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

[38]  Jens Groth,et al.  Optimal Structure-Preserving Signatures in Asymmetric Bilinear Groups , 2011, CRYPTO.

[39]  Abhi Shelat,et al.  Simulatable Adaptive Oblivious Transfer , 2007, EUROCRYPT.

[40]  Dario Fiore,et al.  Verifiable Random Functions from Identity-Based Key Encapsulation , 2009, EUROCRYPT.

[41]  Aggelos Kiayias,et al.  On the Portability of Generalized Schnorr Proofs , 2009, EUROCRYPT.

[42]  Claus-Peter Schnorr,et al.  Efficient signature generation by smart cards , 2004, Journal of Cryptology.

[43]  Jan Camenisch,et al.  A Signature Scheme with Efficient Protocols , 2002, SCN.

[44]  Jan Camenisch,et al.  Efficient Structure-Preserving Signature Scheme from Standard Assumptions , 2012, SCN.

[45]  Yevgeniy Dodis,et al.  A Verifiable Random Function with Short Proofs and Keys , 2005, Public Key Cryptography.

[46]  Benny Pinkas,et al.  Keyword Search and Oblivious Pseudorandom Functions , 2005, TCC.

[47]  Georg Fuchsbauer,et al.  Structure-Preserving Signatures and Commitments to Group Elements , 2010, CRYPTO.

[48]  Markulf Kohlweiss,et al.  Compact E-Cash and Simulatable VRFs Revisited , 2009, Pairing.

[49]  Kenneth G. Paterson,et al.  Pairings for Cryptographers , 2008, IACR Cryptol. ePrint Arch..

[50]  Silvio Micali,et al.  How to Construct Random Functions (Extended Abstract) , 1984, FOCS.

[51]  Markulf Kohlweiss,et al.  P-signatures and Noninteractive Anonymous Credentials , 2008, TCC.

[52]  Markulf Kohlweiss,et al.  Non-Interactive Anonymous Credentials , 2007, IACR Cryptol. ePrint Arch..

[53]  Anna Lysyanskaya,et al.  Unique Signatures and Verifiable Random Functions from the DH-DDH Separation , 2002, CRYPTO.

[54]  Jens Groth,et al.  Fine-Tuning Groth-Sahai Proofs , 2014, IACR Cryptol. ePrint Arch..

[55]  Adam O'Neill,et al.  Deterministic Encryption: Definitional Equivalences and Constructions without Random Oracles , 2008, CRYPTO.

[56]  Brent Waters,et al.  Constructing Verifiable Random Functions with Large Input Spaces , 2010, EUROCRYPT.