Threshold public key encryption scheme resilient against continual leakage without random oracles

Abstract

Threshold public key encryption allows a set of servers to decrypt a ciphertext if a given threshold of authorized servers cooperate. In the setting of threshold public key encryption, we consider the question of how to correctly decrypt a ciphertext where all servers continually leak information about their secret keys to an external attacker. Dodis et al. and Akavia et al. show two concrete schemes on how to store secrets on continually leaky servers. However, their constructions are only interactive between two servers. To achieve continual leakage security among more than two servers, we give the first threshold public key encryption scheme against adaptively chosen ciphertext attack in the continual leakage model under three static assumptions. In our model, the servers update their keys individually and asynchronously, without any communication between two servers. Moreover, the update procedure is re-randomized and the randomness can leak as well.

Keywords

leakage-resilient / continual leakage / Threshold Public Key Encryption / adaptive chosen ciphertext security / standard model

References

[1] Boneh D, Boyen X, Halevi S. Chosen ciphertext secure public key threshold encryption without random oracles. In: Proceedings of the 2006 RSA Conference on Topics in Cryptology. 2006, 226-243

[2] Canetti R, Goldwasser S. An efficient threshold public key cryptosystem secure against adaptive chosen ciphertext attack. In: Proceedings of the 1999 International Conference on the Theory and Application of Cryptographic Techniques. 1999, 90-106

[3] Desmedt Y, Frankel Y. Threshold cryptosystems. Lecture Notes in Computer Science, 1989, 435: 307-315

[4] Libert B, Yung M. Adaptively secure non-interactive threshold cryptosystems. In: Proceedings of the 38th International Conference on Automata, Languages and Programming. 2011, 588-600

[5] Dodis Y, Lewko A, Waters B, Wichs D. Storing secrets on continually leaky devices. In: Proceedings of the 52nd IEEE Annual Symposium on Foundations of Computer Science. 2011, 688-697

[6] Akavia A, Goldwasser S, Hazay C. Distributed public key schemes secure against continual leakage. In: Proceedings of the 2012 ACM Symposium on Principles of Distributed Computing. 2012, 155-164

[7] Kocher P C. Timing attacks on implementations of diffie-hellman, rsa, dss, and other systems. In: Proceedings of the 16th Annual International Cryptology Conference. 1996, 104-113

[8] Kocher P, Jaffe J, Jun B. Differential power analysis. In: Proceedings of the 19th Annual International Cryptology Conference. 1999, 388-397

[9] Halderman J. Lest we remember: cold-boot attacks on encryption keys. Communications of the ACM, 2009, 52(5): 91-98

[10] Naor M, Segev G. Public-key cryptosystems resilient to key leakage. SIAM Journal on Computing, 2012, 41(4): 772-814

[11] Micali S, Reyzin L. Physically observable cryptography. Lecture Notes in Computer Science, 2004, 278-296

[12] Dziembowski S, Pietrzak K. Leakage-resilient cryptography. In: Proceedings of the 49th Annual IEEE Annual Symposium on Foundations of Computer Science. 2008, 293-302

[13] Akavia A, Goldwasser S, Vaikuntanathan V. Simultaneous hardcore bits and cryptography against memory attacks. In: Proceedings of the 6th Conference on Theory of Cryptography. 2009, 474-495

[14] Alwen J, Dodis Y, Wichs D. Leakage-resilient public-key cryptography in the bounded-retrieval model. In: Proceedings of the 29th Annual International International Cryptology Conference. 2009, 36-54

[15] Brakerski Z, Kalai Y T, Katz J, Vaikuntanathan V. Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage. In: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science. 2010, 501-510

[16] Lewko A, Rouselakis Y, Waters B. Achieving leakage resilience through dual system encryption. In: Proceedings of the 8th Conference on Theory of Cryptography. 2011, 70-88

[17] Dodis Y, Haralambiev K, López-Alt A, Wichs D. Cryptography against continuous memory attacks. In: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science. 2010, 511-520

[18] Lewko A, Lewko M, Waters B. How to leak on key updates. In: Proceedings of the 43rd Annual ACM Symposium on Theory of Computing. 2011, 725-734

[19] Waters B. Dual system encryption: Realizing fully secure ibe and hibe under simple assumptions. In: Proceedings of the 29th Annual International Cryptology Conference. 2009, 619-636

[20] Lewko A, Waters B. New techniques for dual system encryption and fully secure hibe with short ciphertexts. In: Proceedings of the 7th International Conference on Theory of Cryptography. 2010, 455-479

[21] Boneh D, Goh E J, Nissim K. Evaluating 2-DNF formulas on ciphertexts. In: Proceedings of the 2nd International Conference on Theory of Cryptography. 2005, 325-341

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