Abstract
Digital Signatures emerge naturally from Public-Key Encryption based on trapdoor permutations, and the “duality” of the two primitives was noted as early as Diffie-Hellman’s seminal work. The present work is centered around the crucial observation that two well known cryptographic primitives whose connection has not been noticed so far in the literature enjoy an analogous “duality.” The primitives are Group Signature Schemes and Public-Key Traitor Tracing. Based on the observed “duality,” we introduce new design methodologies for group signatures that convert a traitor tracing scheme into its “dual” group signature scheme.
Our first methodology applies to generic public-key traitor tracing schemes. We demonstrate its power by applying it to the Boneh-Franklin scheme, and obtaining its “dual” group signature. This scheme is the first provably secure group signature scheme whose signature size is not proportional to the size of the group and is based only on DDH and a random oracle. The existence of such schemes was open. Our second methodology introduces a generic way of turning any group signature scheme with signature size linear in the group size into a group signature scheme with only logarithmic dependency on the group size. To this end it employs the notion of traceability codes (a central component of combinatorial traitor tracing schemes already used in the first such scheme by Chor, Fiat and Naor). We note that our signatures, obtained by generic transformations, are proportional to a bound on the anticipated maximum malicious coalition size. Without the random oracle assumption our schemes give rise to provably secure and efficient Identity Escrow schemes.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Giuseppe Ateniese, Jan Camenisch, Marc Joye and Gene Tsudik, A Practical and Provably Secure Coalition-Resistant Group Signature Scheme, In Mihir Bellare (Ed.): Advances in Cryptology — CRYPTO 2000, 20th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 20–24, 2000, LNCS 1880, Springer 2000, pp. 255–270.
Giuseppe Ateniese and Gene Tsudik, Some Open Issues and New Directions in Group Signatures, In Matthew K. Franklin (Ed.): Financial Cryptography, Third International Conference, Springer LNCS Vol. 1648, pp. 196–211.
Dan Boneh and Matthew Franklin, An Efficient Public Key Traitor Tracing Scheme, In Michael J. Wiener (Ed.): Advances in Cryptology — CRYPTO’ 99, 19th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 15–19, 1999, LNCS 1666, Springer 1999, pp. 338–353.
Jan Camenisch, Efficient and Generalized Group Signatures, In Walter Fumy (Ed.): Advances in Cryptology — EUROCRYPT’ 97, Konstanz, Germany, May 11–15, 1997, LNCS 1233, Springer 1997, pp. 465–479.
Jan Camenisch and Ivan Dåmgard, Verifiable Encryption, Group Encryption and their Applications to Group Signatures, and Signature Sharing Schemes, In Tatsuaki Okamoto (Ed.): Advances in Cryptology — ASIACRYPT 2000, Kyoto, Japan, December 3–7, 2000, LNCS 1976, Springer 2000, pp. 331–345.
Jan Camenisch and Anna Lysyanskaya, An Identity Escrow Scheme with Appointed Verifiers, In Joe Kilian (Ed.): Advances in Cryptology — CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2001, LNCS 2139, Springer 2001, pp. 388–407.
Jan Camenisch and Markus Michels, Separability and Efficiency for Generic Group Signature Schemes, In Michael J. Wiener (Ed.): Advances in Cryptology — CRYPTO’ 99, 19th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 15–19, 1999, LNCS 1666, Springer 1999, pp. 413–430.
Jan Camenisch and Markus Stadler, Efficient Group Signature Schemes for Large Groups (Extended Abstract), In Burton S. Kaliski Jr. (Ed.): Advances in Cryptology — CRYPTO’ 97, 17th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 17–21, 1997, LNCS 1294, Springer 1997, pp. 410–424.
David Chaum and Eugene van Heyst, Group Signatures, In Donald W. Davies (Ed.): Advances in Cryptology — EUROCRYPT’ 91, Brighton, UK, April 8–11, 1991, LNCS 547, Springer 1991, pp. 257–265.
Lidong Chen and Torben P. Pedersen, On the Efficiency of Group Signatures Providing Information-Theoretic Anonymity, In Louis C. Guillou, Jean-Jacques Quisquater (Eds.): Advances in Cryptology — EUROCRYPT’ 95, Saint-Malo, France, May 21–25, 1995, LNCS 921, Springer 1995, pp. 39–49.
Benny Chor, Amos Fiat, and Moni Naor, Tracing Traitors, In Yvo Desmedt (Ed.): Advances in Cryptology — CRYPTO’ 94, 14th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 21–25, 1994, LNCS 839, Springer 1994, pp. 257–270.
Benny Chor, Amos Fiat, Moni Naor, and Benny Pinkas, Tracing Traitors, IEEE Transactions on Information Theory, Vol. 46, no. 3, pp. 893–910, 2000.
Whitfield Diffie and Martin Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory IT-22(6): pp. 644–654, 1976.
Yevgeniy Dodis and Nelly Fazio, Public Key Broadcast Encryption for Stateless Receivers, 2002 ACM Workshop on Security and Privacy in Digital Rights Management, to appear in Springer LNCS, 2003.
Yevgeniy Dodis and Nelly Fazio, Public Key Trace and Revoke Scheme Secure against Adaptive Chosen Ciphertext Attack, In Yvo Desmedt (Ed.): Public Key Cryptography — PKC 2003, 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, FL, USA, January 6–8, 2003, LNCS 2567, Springer 2002, pp. 100–115.
Amos Fiat and Adi Shamir, How to Prove Yourself: Practical Solutions to Identification and Signature Problems, In Andrew M. Odlyzko (Ed.): Advances in Cryptology — CRYPTO’ 86, Santa Barbara, CA, USA, 1986, LNCS 263, Springer 1987, pp. 186–194.
Amos Fiat and T. Tassa, Dynamic Traitor Tracing, In Michael J. Wiener (Ed.): Advances in Cryptology — CRYPTO’ 99, 19th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 15–19, 1999, LNCS 1666, Springer 1999, pp. 354–371.
Eli Gafni, Jessica Staddon and Yiqun Lisa Yin, Efficient Methods for Integrating Traceability and Broadcast Encryption, In Michael J. Wiener (Ed.): Advances in Cryptology — CRYPTO’ 99, 19th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 15–19, 1999, LNCS 1666, Springer 1999, pp. 372–387.
Juan A. Garay, Jessica Staddon, and Avishai Wool, Long-Lived Broadcast Encryption, In Mihir Bellare (Ed.): Advances in Cryptology — CRYPTO 2000, 20th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 20–24, 2000, LNCS 1880, Springer 2000, pp. 333–352.
Aggelos Kiayias and Moti Yung, Self Protecting Pirates and Black-Box Traitor Tracing, In Joe Kilian (Ed.): Advances in Cryptology — CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2001, LNCS 2139 Springer 2001, pp. 63–79.
Aggelos Kiayias and Moti Yung, Traitor Tracing with Constant Transmission Rate, In Lars R. Knudsen (Ed.): Advances in Cryptology — EUROCRYPT 2002, Amsterdam, The Netherlands, April 28–May 2, 2002, LNCS 2332, Springer 2002, pp. 450–465.
Aggelos Kiayias and Moti Yung, Breaking and Repairing Asymmetric Public-Key Traitor Tracing, 2002 ACM Workshop on Digital Rights Management, to appear in Springer LNCS, 2003.
Joe Kilian and Erez Petrank, Identity Escrow, In Hugo Krawczyk (Ed.): Advances in Cryptology — CRYPTO’ 98, 18th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 23–27, 1998, LNCS 1462, Springer 1998, pp. 169–185.
K. Kurosawa and Y. Desmedt, Optimum Traitor Tracing and Asymmetric Schemes, In Kaisa Nyberg (Ed.): Advances in Cryptology — EUROCRYPT’ 98, Espoo, Finland, May 31–June 4, 1998, LNCS 1403, Springer 1998, pp. 145–157.
Dalit Naor, Moni Naor and Jeffrey B. Lotspiech Revocation and Tracing Schemes for Stateless Receivers, In Joe Kilian (Ed.): Advances in Cryptology — CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2001, LNCS 2139 Springer 2001, pp. 41–62.
Moni Naor and Benny Pinkas, Threshold Traitor Tracing, In Hugo Krawczyk (Ed.): Advances in Cryptology — CRYPTO’ 98, 18th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 23–27, 1998, LNCS 1462, Springer 1998, pp. 502–517.
Moni Naor and Benny Pinkas, Efficient Trace and Revoke Schemes, In Yair Frankel (Ed.): Financial Cryptography, 4th International Conference, Anguilla, British West Indies, February 20–24, 2000, LNCS 1962, Springer 2001, pp. 1–20.
Holger Petersen, How to Convert any Digital Signature Scheme into a Group Signature Scheme, In Bruce Christianson, Bruno Crispo, T. Mark A. Lomas, Michael Roe (Eds.): Security Protocols, 5th International Workshop, Paris, France, April 7–9, 1997, LNCS 1361, Springer 1998, pp. 177–190.
Birgit Pfitzmann, Trials of Traced Traitors, In Ross J. Anderson (Ed.): Information Hiding, First International Workshop, Cambridge, U.K., May 30–June 1, 1996, LNCS 1174, Springer 1996, pp. 49–64.
Reihaneh Safavi-Naini and Yejing Wang, Sequential Traitor Tracing, In Mihir Bellare (Ed.): Advances in Cryptology — CRYPTO 2000, 20th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 20–24, 2000, LNCS 1880, Springer 2000, pp. 316–332.
Alice Silverberg, Jessica Staddon and Judy L. Walker, Efficient Traitor Tracing Algorithms Using List Decoding, In Colin Boyd (Ed.): Advances in Cryptology — ASIACRYPT 2001, Springer LNCS 2248, pp. 175–192.
Jessica N. Staddon, Douglas R. Stinson and Ruizhong Wei, Combinatorial Properties of Frameproof and Traceability Codes, Cryptology ePrint 2000/004.
Douglas R. Stinson and Ruizhong Wei, Key preassigned traceability schemes for broadcast encryption, In Stafford E. Tavares, Henk Meijer (Eds.): Selected Areas in Cryptography 1998, Springer LNCS Vol. 1556, pp. 144–156.
Douglas R. Stinson and Ruizhong Wei, Combinatorial Properties and Constructions of Traceability Schemes and Frameproof Codes, SIAM J. on Discrete Math, Vol. 11, no. 1, 1998.
Yuji Watanabe, Goichiro Hanaoka and Hideki Imai, Efficient Asymmetric Public-Key Traitor Tracing without Trusted Agents, In David Naccache (Ed.): Topics in Cryptology — CT-RSA 2001 — The Cryptographer’s Track, Springer LNCS Vol. 2020, pp. 392–407.
Adam Young and Moti Yung, Auto-recoverable Cryptosystems with Faster Initialization and the Escrow Hierarchy, In Hideki Imai, Yuliang Zheng (Eds.): Public-Key Cryptography 1999, Springer LNCS Vol. 1560, pp. 306–314.
Adam Young and Moti Yung, A PVSS as Hard as Discrete Log and Shareholder Separability, In Kwangjo Kim (Ed.): Public Key Cryptography 2001, Springer LNCS Vol. 1992, pp. 287–299.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 International Association for Cryptologic Research
About this paper
Cite this paper
Kiayias, A., Yung, M. (2003). Extracting Group Signatures from Traitor Tracing Schemes. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_39
Download citation
DOI: https://doi.org/10.1007/3-540-39200-9_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-14039-9
Online ISBN: 978-3-540-39200-2
eBook Packages: Springer Book Archive