Identity-based cryptosystems and signature schemes
Proceedings of CRYPTO 84 on Advances in cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
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CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
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EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
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ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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SS'08 Proceedings of the 17th conference on Security symposium
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Proceedings of the forty-first annual ACM symposium on Theory of computing
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
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EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
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FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
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We revisit the notion of additively homomorphic encryption with a double decryption mechanism (DD-PKE), which allows for additions in the encrypted domain while having a master decryption procedure that can decrypt all properly formed ciphertexts by using a special master secret. This type of encryption is generally considered as a practical way to enforce access control in hierachical organisations where some form of malleability properties are required. Up to now, only two additively homomorphic DD-PKE schemes have been proposed: CS-Lite by Cramer and Shoup (Eurocrypt 2002), and a variant called BCP by Bresson, Catalano and Pointcheval (Asiacrypt 2003). In this work, we argue that the two existing schemes only provide partial solutions for hierarchical organisations. Essentially, this is due to the fact that the master authority, being in possession of the master secret, has no control on the validity of given ciphertexts. We say that the master is unable to "detect invalid ciphertexts", which limits the employment of such schemes in practice. Therefore, we propose the first additively homomorphic DD-PKE scheme which allows the master to detect invalid ciphertexts. In fact, our scheme has the additional property that the master decryption is independent of the users' public keys. Our solution is based on elliptic curves over rings and we prove it to be semantically secure under a DDH-related assumption. Moreover, we give experimental results on the choice of elliptic curves and their effect on the efficiency of our scheme's setup.