Programmable Hash Functions and Their Applications

We introduce a new information-theoretic primitive called programmable hash functions(PHFs). PHFs can be used to programthe output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of standard modelrealizations of PHFs (with different parameters). The programmability of PHFs make them a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps.

[1]  L. Dworsky.  An Introduction to Probability , 2008 .

[2]  Jörg Schwenk,et al.  A CDH-Based Ring Signature Scheme with Short Signatures and Public Keys , 2010, Financial Cryptography.

[3]  Dan Boneh,et al.  Secure Identity Based Encryption Without Random Oracles , 2004, CRYPTO.

[4]  Craig Gentry,et al.  Practical Identity-Based Encryption Without Random Oracles , 2006, EUROCRYPT.

[5]  Brent Waters,et al.  Efficient Identity-Based Encryption Without Random Oracles , 2005, EUROCRYPT.

[6]  Eike Kiltz,et al.  Secure Hybrid Encryption from Weakened Key Encapsulation , 2007, CRYPTO.

[7]  Dan Boneh,et al.  Efficient Selective-ID Secure Identity Based Encryption Without Random Oracles , 2004, IACR Cryptol. ePrint Arch..

[8]  Nigel P. Smart,et al.  Identity-Based Encryption Gone Wild , 2006, ICALP.

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

[10]  Birgit Pfitzmann,et al.  Collision-Free Accumulators and Fail-Stop Signature Schemes Without Trees , 1997, EUROCRYPT.

[11]  Amos Fiat,et al.  Zero-knowledge proofs of identity , 1987, Journal of Cryptology.

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

[13]  Yevgeniy Vahlis,et al.  CCA2 Secure IBE: Standard Model Efficiency through Authenticated Symmetric Encryption , 2008, CT-RSA.

[14]  David Chaum,et al.  Cryptographically Strong Undeniable Signatures, Unconditionally Secure for the Signer , 1991, CRYPTO.

[15]  Victor Shoup,et al.  A computational introduction to number theory and algebra , 2005 .

[16]  Eike Kiltz,et al.  Chosen-Ciphertext Security from Tag-Based Encryption , 2006, TCC.

[17]  Dan Boneh,et al.  Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups , 2008, Journal of Cryptology.

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

[19]  Brent Waters,et al.  Dual System Encryption: Realizing Fully Secure IBE and HIBE under Simple Assumptions , 2009, IACR Cryptol. ePrint Arch..

[20]  Yevgeniy Dodis,et al.  On the Generic Insecurity of the Full Domain Hash , 2005, CRYPTO.

[21]  Xavier Boyen,et al.  General Ad Hoc Encryption from Exponent Inversion IBE , 2007, EUROCRYPT.

[22]  Silvio Micali,et al.  A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks , 1988, SIAM J. Comput..

[23]  Qixiang Mei,et al.  Direct chosen ciphertext security from identity-based techniques , 2005, CCS '05.

[24]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[25]  Mihir Bellare,et al.  The Exact Security of Digital Signatures - HOw to Sign with RSA and Rabin , 1996, EUROCRYPT.

[26]  Jens Groth,et al.  Cryptography in Subgroups of Zn , 2005, TCC.

[27]  Mihir Bellare,et al.  Incremental Cryptography: The Case of Hashing and Signing , 1994, CRYPTO.

[28]  P. M. Lee,et al.  Random Walks and Random Environments: Volume 1: Random Walks , 1995 .

[29]  Huafei Zhu.  A Formal Proof of Zhu's Signature Scheme , 2003, IACR Cryptol. ePrint Arch..

[30]  Marc Fischlin.  The Cramer-Shoup Strong-RSASignature Scheme Revisited , 2003, Public Key Cryptography.

[31]  A. Miyaji,et al.  New Explicit Conditions of Elliptic Curve Traces for FR-Reduction , 2001 .

[32]  Shai Halevi,et al.  Secure Hash-and-Sign Signatures Without the Random Oracle , 1999, EUROCRYPT.

[33]  Hideki Imai,et al.  An Efficient Group Signature Scheme from Bilinear Maps , 2005, ACISP.

[34]  Stefan A. Brands,et al.  An Efficient Off-line Electronic Cash System Based On The Representation Problem. , 1993 .

[35]  Eike Kiltz,et al.  Direct chosen-ciphertext secure identity-based key encapsulation without random oracles , 2009, Theor. Comput. Sci..

[36]  David Chaum,et al.  An Improved Protocol for Demonstrating Possession of Discrete Logarithms and Some Generalizations , 1987, EUROCRYPT.

[37]  Tatsuaki Okamoto,et al.  Efficient Blind and Partially Blind Signatures Without Random Oracles , 2006, IACR Cryptol. ePrint Arch..

[38]  Jean-Sébastien Coron,et al.  On the Exact Security of Full Domain Hash , 2000, CRYPTO.

[39]  Mihir Bellare,et al.  Simulation without the Artificial Abort: Simplified Proof and Improved Concrete Security for Waters' IBE Scheme , 2009, EUROCRYPT.

[40]  Jacques Stern,et al.  Twin signatures: an alternative to the hash-and-sign paradigm , 2001, CCS '01.

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

[42]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[43]  D. Boneh,et al.  Short Signatures from the Weil Pairing , 2001, Journal of Cryptology.

[44]  Eike Kiltz,et al.  Practical Chosen Ciphertext Secure Encryption from Factoring , 2009, EUROCRYPT.

[45]  Craig Gentry,et al.  Trapdoors for hard lattices and new cryptographic constructions , 2008, IACR Cryptol. ePrint Arch..

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

[47]  Ronald Cramer,et al.  Signature schemes based on the strong RSA assumption , 2000, TSEC.

[48]  Marc Joye,et al.  A Practical and Tightly Secure Signature Scheme Without Hash Function , 2007, CT-RSA.

[49]  Matthew K. Franklin,et al.  Identity-Based Encryption from the Weil Pairing , 2001, CRYPTO.

[50]  Jung Hee Cheon,et al.  Security Analysis of the Strong Diffie-Hellman Problem , 2006, EUROCRYPT.

[51]  Ivan Damgård,et al.  Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups , 2002, EUROCRYPT.

[52]  Jean-Jacques Quisquater,et al.  A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory , 1988, EUROCRYPT.

[53]  Brent Waters,et al.  Lossy trapdoor functions and their applications , 2008, SIAM J. Comput..

[54]  Dan Boneh,et al.  Short Signatures Without Random Oracles , 2004, EUROCRYPT.

[55]  Tatsuaki Okamoto,et al.  Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations , 1997, CRYPTO.

[56]  Qiong Huang,et al.  New Constructions of Convertible Undeniable Signature Schemes without Random Oracles , 2009, IACR Cryptol. ePrint Arch..