Practical Group Signatures without Random Oracles

We provide a construction for a group signature scheme that is provably secure in a universally composable framework, within the standard model with trusted parameters. Our proposed scheme is fairly simple and its efficiency falls within small factors of the most efficient group signature schemes with provable security in any model (including random oracles). Security of our constructions require new cryptographic assumptions, namely the Strong LRSW, EDH, and Strong SXDH assumptions. Evidence for any assumption we introduce is provided by proving hardness in the generic group model. Our second contribution is the first definition of security for group signatures based on the simulatability of real protocol executions in an ideal setting that captures the basic properties of unforgeability, anonymity, unlinkability, and exculpability for group signature schemes.

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

[2]  David Chaum,et al.  Group Signatures , 1991, EUROCRYPT.

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

[4]  V. Nechaev.  Complexity of a determinate algorithm for the discrete logarithm , 1994 .

[5]  Ran Canetti,et al.  Studies in secure multiparty computation and applications , 1995 .

[6]  Victor Shoup,et al.  Lower Bounds for Discrete Logarithms and Related Problems , 1997, EUROCRYPT.

[7]  Amit Sahai,et al.  Pseudonym Systems , 1999, Selected Areas in Cryptography.

[8]  Gene Tsudik,et al.  Some Open Issues and New Directions in Group Signatures , 1999, Financial Cryptography.

[9]  Birgit Pfitzmann,et al.  Composition and integrity preservation of secure reactive systems , 2000, CCS.

[10]  Marc Joye,et al.  A Practical and Provably Secure Coalition-Resistant Group Signature Scheme , 2000, CRYPTO.

[11]  Ivan Damgård,et al.  Efficient Concurrent Zero-Knowledge in the Auxiliary String Model , 2000, EUROCRYPT.

[12]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

[13]  Steven D. Galbraith,et al.  Supersingular Curves in Cryptography , 2001, ASIACRYPT.

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

[15]  Birgit Pfitzmann,et al.  A model for asynchronous reactive systems and its application to secure message transmission , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[16]  Mike Scott,et al.  Authenticated ID-based Key Exchange and remote log-in with simple token and PIN number , 2002, IACR Cryptol. ePrint Arch..

[17]  Mihir Bellare,et al.  GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks , 2002, CRYPTO.

[18]  Tal Rabin,et al.  On the Security of Joint Signature and Encryption , 2002, EUROCRYPT.

[19]  Alexander W. Dent,et al.  Adapting the Weaknesses of the Random Oracle Model to the Generic Group Model , 2002, ASIACRYPT.

[20]  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..

[21]  Moni Naor,et al.  On Cryptographic Assumptions and Challenges , 2003, CRYPTO.

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

[23]  Hovav Shacham,et al.  Short Signatures from the Weil Pairing , 2001, J. Cryptol..

[24]  Ernest F. Brickell,et al.  Direct anonymous attestation , 2004, CCS '04.

[25]  Hovav Shacham,et al.  Group signatures with verifier-local revocation , 2004, CCS '04.

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

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

[28]  Hovav Shacham,et al.  Short Group Signatures , 2004, CRYPTO.

[29]  Aggelos Kiayias,et al.  Group Signatures: Provable Security, Efficient Constructions and Anonymity from Trapdoor-Holders , 2004, IACR Cryptol. ePrint Arch..

[30]  Donald Beaver,et al.  Secure multiparty protocols and zero-knowledge proof systems tolerating a faulty minority , 2004, Journal of Cryptology.

[31]  Steven D. Galbraith,et al.  Easy decision-Diffie-Hellman groups , 2004, IACR Cryptol. ePrint Arch..

[32]  Mihir Bellare,et al.  Foundations of Group Signatures: The Case of Dynamic Groups , 2005, CT-RSA.

[33]  Aggelos Kiayias,et al.  Traceable Signatures , 2004, EUROCRYPT.

[34]  Eric R. Verheul,et al.  Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems , 2004, Journal of Cryptology.

[35]  John C. Mitchell,et al.  Games and the Impossibility of Realizable Ideal Functionality , 2006, TCC.

[36]  Paulo S. L. M. Barreto,et al.  A New Two-Party Identity-Based Authenticated Key Agreement , 2005, CT-RSA.

[37]  Marc Fischlin,et al.  Communication-Efficient Non-interactive Proofs of Knowledge with Online Extractors , 2005, CRYPTO.

[38]  Paulo S. L. M. Barreto,et al.  Pairing-Friendly Elliptic Curves of Prime Order , 2005, Selected Areas in Cryptography.

[39]  Rafail Ostrovsky,et al.  Perfect Non-Interactive Zero Knowledge for NP , 2006, IACR Cryptol. ePrint Arch..

[40]  R. Rivest,et al.  Ad-Hoc-Group Signatures from Hijacked Keypairs , 2005 .

[41]  Jan Camenisch,et al.  Untraceable RFID tags via insubvertible encryption , 2005, CCS '05.

[42]  Anupam Datta,et al.  The Impossibility of Realizable Ideal Functionality , 2005 .

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

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

[45]  Brent Waters,et al.  Compact Group Signatures Without Random Oracles , 2006, EUROCRYPT.