Circular-Secure Encryption from Decision Diffie-Hellman

We describe a public-key encryption system that remains secure even encrypting messages that depend on the secret keys in use. In particular, it remains secure under a "key cycle" usage, where we have a cycle of public/secret key-pairs (pk i ,sk i ) for i= 1,...,n, and we encrypt each sk i under ${\rm pk}_{(i \bmod n)+1}$. Such usage scenarios sometimes arise in key-management systems and in the context of anonymous credential systems. Also, security against key cycles plays a role when relating "axiomatic security" of protocols that use encryption to the "computational security" of concrete instantiations of these protocols. The existence of encryption systems that are secure in the presence of key cycles was wide open until now: on the one hand we had no constructions that provably meet this notion of security (except by relying on the random-oracle heuristic); on the other hand we had no examples of secure encryption systems that become demonstrably insecure in the presence of key-cycles of length greater than one. Here we construct an encryption system that is circular-secure against chosen-plaintext attacks under the Decision Diffie-Hellman assumption (without relying on random oracles). Our proof of security holds even if the adversary obtains an encryption clique, that is, encryptions of sk i under pk j for all 1 ≤ i,j≤ n. We also construct a circular counterexample: a one-way secure encryption scheme that breaks completely if an encryption cycle (of any size) is published.

[1]  A. J. Menezes,et al.  Advances in Cryptology - CRYPTO 2007, 27th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19-23, 2007, Proceedings , 2007, CRYPTO.

[2]  Matthew Franklin,et al.  Advances in Cryptology – CRYPTO 2004 , 2004, Lecture Notes in Computer Science.

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

[4]  Moni Naor,et al.  Nonmalleable Cryptography , 2000, SIAM Rev..

[5]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[6]  John Black,et al.  Encryption-Scheme Security in the Presence of Key-Dependent Messages , 2002, Selected Areas in Cryptography.

[7]  Martín Abadi,et al.  Reconciling Two Views of Cryptography (The Computational Soundness of Formal Encryption) , 2007, Journal of Cryptology.

[8]  Peeter Laud,et al.  Sound Computational Interpretation of Formal Encryption with Composed Keys , 2003, ICISC.

[9]  Marvin Theimer,et al.  Feasibility of a serverless distributed file system deployed on an existing set of desktop PCs , 2000, SIGMETRICS '00.

[10]  Thomas Holenstein,et al.  On the (Im)Possibility of Key Dependent Encryption , 2009, TCC.

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

[12]  Hovav Shacham,et al.  A Cramer-Shoup Encryption Scheme from the Linear Assumption and from Progressively Weaker Linear Variants , 2007, IACR Cryptol. ePrint Arch..

[13]  Moni Naor,et al.  Non-malleable cryptography , 1991, STOC '91.

[14]  Jonathan Katz,et al.  Unforgeable Encryption and Chosen Ciphertext Secure Modes of Operation , 2000, FSE.

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

[16]  Gerhard Goos,et al.  Fast Software Encryption , 2001, Lecture Notes in Computer Science.

[17]  Dennis Hofheinz,et al.  Towards Key-Dependent Message Security in the Standard Model , 2008, EUROCRYPT.

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

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

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

[21]  Chanathip Namprempre,et al.  Authenticated Encryption: Relations among Notions and Analysis of the Generic Composition Paradigm , 2000, Journal of Cryptology.

[22]  Jongin Lim,et al.  Information Security and Cryptology - ICISC 2003 , 2003, Lecture Notes in Computer Science.

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

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

[25]  Birgit Pfitzmann,et al.  Key-dependent Message Security under Active Attacks--BRSIM/UC-Soundness of Symbolic Encryption with Key Cycles , 2007, 20th IEEE Computer Security Foundations Symposium (CSF'07).

[26]  R. RNall.  Probabilistic methods in group theory II , 1976 .

[27]  Aggelos Kiayias,et al.  Polynomial Reconstruction Based Cryptography , 2001, Selected Areas in Cryptography.

[28]  Nigel P. Smart.  Advances in Cryptology - EUROCRYPT 2008, 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Istanbul, Turkey, April 13-17, 2008. Proceedings , 2008, EUROCRYPT.

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

[30]  Tatsuaki Okamoto.  Advances in Cryptology — ASIACRYPT 2000 , 2000, Lecture Notes in Computer Science.

[31]  Dieter Gollmann,et al.  Computer Security - ESORICS 2005, 10th European Symposium on Research in Computer Security, Milan, Italy, September 12-14, 2005, Proceedings , 2005, ESORICS.

[32]  Mihir Bellare,et al.  Encode-Then-Encipher Encryption: How to Exploit Nonces or Redundancy in Plaintexts for Efficient Cryptography , 2000, ASIACRYPT.

[33]  Hugo Krawczyk,et al.  Security under key-dependent inputs , 2007, CCS '07.

[34]  Jonathan Herzog,et al.  Soundness of Formal Encryption in the Presence of Key-Cycles , 2005, ESORICS.

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

[36]  Hugo Krawczyk,et al.  The Order of Encryption and Authentication for Protecting Communications (or: How Secure Is SSL?) , 2001, CRYPTO.