How to Construct Multicast Cryptosystems Provably Secure Against Adaptive Chosen Ciphertext Attack

In this paper we present a general framework for constructing efficient multicast cryptosystems with provable security and show that a line of previous work on multicast encryption are all special cases of this general approach. We provide new methods for building such cryptosystems with various levels of security (e.g., IND-CPA, IND-CCA2). The results we obtained enable the construction of a whole class of new multicast schemes with guaranteed security using a broader range of common primitives such as OAEP. Moreover, we show that multicast cryptosystems with high level of security (e.g. IND-CCA2) can be based upon public key cryptosystems with weaker (e.g. CPA) security as long as the decryption can be securely and efficiently “shared”. Our constructions feature truly constant-size decryption keys whereas the lengths of both the encryption key and ciphertext are independent of group size.

[1]  Yevgeniy Dodis,et al.  Public Key Trace and Revoke Scheme Secure against Adaptive Chosen Ciphertext Attack , 2003, Public Key Cryptography.

[2]  Ran Canetti,et al.  An Efficient Threshold Public Key Cryptosystem Secure Against Adaptive Chosen Ciphertext Attack , 1999, EUROCRYPT.

[3]  Moni Naor,et al.  Revocation and Tracing Schemes for Stateless Receivers , 2001, CRYPTO.

[4]  Mohamed G. Gouda,et al.  Secure group communications using key graphs , 1998, SIGCOMM '98.

[5]  Walter M. Lioen,et al.  Factorization of RSA-140 Using the Number Field Sieve , 1999, CRYPTO 1999.

[6]  Mihir Bellare,et al.  Optimal Asymmetric Encryption-How to Encrypt with RSA , 1995 .

[7]  Jessica Staddon,et al.  Combinatorial Bounds for Broadcast Encryption , 1998, EUROCRYPT.

[8]  Brent Waters,et al.  Collusion Resistant Broadcast Encryption with Short Ciphertexts and Private Keys , 2005, CRYPTO.

[9]  Victor Shoup.  Advances in Cryptology - CRYPTO 2005: 25th Annual International Cryptology Conference, Santa Barbara, California, USA, August 14-18, 2005, Proceedings , 2005, CRYPTO.

[10]  George Varghese,et al.  Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications , 2001, SIGCOMM 2001.

[11]  Duncan S. Wong,et al.  Resilient Lkh: Secure Multicast Key Distribution Schemes , 2006, Int. J. Found. Comput. Sci..

[12]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[13]  Hugh Harney,et al.  Group Key Management Protocol (GKMP) Architecture , 1997, RFC.

[14]  Sushil Jajodia,et al.  Kronos: a scalable group re-keying approach for secure multicast , 2000, Proceeding 2000 IEEE Symposium on Security and Privacy. S&P 2000.

[15]  Ronald Cramer,et al.  A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack , 1998, CRYPTO.

[16]  Masayuki Abe,et al.  Robust Distributed Multiplicaton with out Interaction , 1999, CRYPTO.

[17]  Pascal Paillier,et al.  Public-Key Cryptosystems Based on Composite Degree Residuosity Classes , 1999, EUROCRYPT.

[18]  Eric J. Harder,et al.  Key Management for Multicast: Issues and Architectures , 1999, RFC.

[19]  Avishai Wool,et al.  Long-Lived Broadcast Encryption , 2000, CRYPTO.

[20]  David Pointcheval,et al.  Threshold Cryptosystems Secure against Chosen-Ciphertext Attacks , 2001, ASIACRYPT.

[21]  Aggelos Kiayias,et al.  Self Protecting Pirates and Black-Box Traitor Tracing , 2001, CRYPTO.

[22]  Chae Hoon Lim,et al.  Another Method for Attaining Security Against Adaptively Chosen Ciphertext Attacks , 1993, CRYPTO.

[23]  Tsutomu Matsumoto,et al.  A Quick Group Key Distribution Scheme with "Entity Revocation" , 1999, ASIACRYPT.

[24]  Jacques Stern,et al.  RSA-OAEP Is Secure under the RSA Assumption , 2001, Journal of Cryptology.

[25]  Pil Joong Lee,et al.  An Efficient Public Key Trace and Revoke Scheme Secure against Adaptive Chosen Ciphertext Attack , 2003, ASIACRYPT.

[26]  Moni Naor,et al.  Public-key cryptosystems provably secure against chosen ciphertext attacks , 1990, STOC '90.

[27]  Wen-Guey Tzeng,et al.  A Public-Key Traitor Tracing Scheme with Revocation Using Dynamic Shares , 2001, Public Key Cryptography.

[28]  Daniel R. Simon,et al.  Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack , 1991, CRYPTO.

[29]  Alfredo De Santis,et al.  Advances in Cryptology — EUROCRYPT'94 , 1994, Lecture Notes in Computer Science.

[30]  Brad Cain,et al.  Internet Group Management Protocol, Version 3 , 2002, RFC.

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

[32]  Ahmed Obied,et al.  Broadcast Encryption , 2008, Encyclopedia of Multimedia.

[33]  Yvo Desmedt,et al.  Advances in Cryptology — CRYPTO ’94 , 2001, Lecture Notes in Computer Science.

[34]  Adi Shamir,et al.  The LSD Broadcast Encryption Scheme , 2002, CRYPTO.

[35]  Yvo Desmedt,et al.  Threshold Cryptosystems , 1989, CRYPTO.

[36]  Moti Yung,et al.  How to share a function securely , 1994, STOC '94.

[37]  Jacques Stern,et al.  Advances in Cryptology — EUROCRYPT ’99 , 1999, Lecture Notes in Computer Science.

[38]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[39]  Xiaozhou Li,et al.  Reliable group rekeying: a performance analysis , 2001, SIGCOMM '01.

[40]  Xiaozhou Li,et al.  Batch rekeying for secure group communications , 2001, WWW '01.

[41]  Joan Feigenbaum,et al.  Advances in Cryptology-Crypto 91 , 1992 .

[42]  Mihir Bellare,et al.  Optimal Asymmetric Encryption , 1994, EUROCRYPT.

[43]  Chi Sung Laih,et al.  Advances in Cryptology - ASIACRYPT 2003 , 2003 .

[44]  Douglas R. Stinson,et al.  Advances in Cryptology — CRYPTO’ 93 , 2001, Lecture Notes in Computer Science.

[45]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[46]  Matthew K. Franklin,et al.  An Efficient Public Key Traitor Tracing Scheme , 1999, CRYPTO.

[47]  Mihir Bellare.  Advances in Cryptology — CRYPTO 2000 , 2000, Lecture Notes in Computer Science.

[48]  William C. Fenner.  Internet Group Management Protocol, Version 2 , 1997, RFC.

[49]  Masayuki Abe.  Robust distributed multiplication without interaction , 1999 .

[50]  Colin Boyd,et al.  Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[51]  Donggang Liu,et al.  Efficient self-healing group key distribution with revocation capability , 2003, CCS '03.

[52]  Rosario Gennaro,et al.  Securing Threshold Cryptosystems against Chosen Ciphertext Attack , 1998, Journal of Cryptology.

[53]  Dilip D. Kandlur,et al.  Key management for secure lnternet multicast using Boolean function minimization techniques , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[54]  Hugo Krawczyk,et al.  Advances in Cryptology - CRYPTO '98 , 1998 .

[55]  Yvo Desmedt.  Public Key Cryptography — PKC 2003 , 2002, Lecture Notes in Computer Science.

[56]  Moni Naor,et al.  Multicast security: a taxonomy and some efficient constructions , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[57]  Carl Pomerance,et al.  Advances in Cryptology — CRYPTO ’87 , 2000, Lecture Notes in Computer Science.

[58]  Matthew K. Franklin,et al.  Self-healing key distribution with revocation , 2002, Proceedings 2002 IEEE Symposium on Security and Privacy.

[59]  Colin Boyd,et al.  Cryptography and Coding , 1995, Lecture Notes in Computer Science.

[60]  Kaisa Nyberg,et al.  Advances in Cryptology — EUROCRYPT'98 , 1998 .

[61]  Malibu Canyon RdMalibu.  Keystone: a Group Key Management Service , 2000 .

[62]  Hugo Krawczyk,et al.  Robust and Efficient Sharing of RSA Functions , 2000, Journal of Cryptology.

[63]  Neal Koblitz,et al.  Advances in Cryptology — CRYPTO ’96 , 2001, Lecture Notes in Computer Science.

[64]  Yvo Desmedt,et al.  Society and Group Oriented Cryptography: A New Concept , 1987, CRYPTO.

[65]  Victor Shoup,et al.  OAEP Reconsidered , 2001, CRYPTO.

[66]  Amos Fiat,et al.  Tracing traitors , 2000, IEEE Trans. Inf. Theory.

[67]  Stanislaw Jarecki,et al.  Adaptively Secure Threshold Cryptography: Introducing Concurrency, Removing Erasures , 2000, EUROCRYPT.