Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A key distribution system equivalent to factoring
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Reducing elliptic curve logarithms to logarithms in a finite field
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A course in computational algebraic number theory
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A Family of Jacobians Suitable for Discrete Log Cryptosystems
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On the Randomness of Legendre and Jacobi Sequences
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Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
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SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Non-interactive public-key cryptography
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
CT-RSA '02 Proceedings of the The Cryptographer's Track at the RSA Conference on Topics in Cryptology
Security of Blind Discrete Log Signatures against Interactive Attacks
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
The Hidden Number Problem in Extension Fields and Its Applications
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CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Assumptions Related to Discrete Logarithms: Why Subtleties Make a Real Difference
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Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Two-Pass Authenticated Key Arrangement Protocol with Key Confirmation
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Security of Signed ElGamal Encryption
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Selective Forgery of RSA Signatures with Fixed-Pattern Padding
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
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Is the Notion of Divisible On-Line/Off-Line Signatures Stronger than On-Line/Off-Line Signatures?
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ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptocomputing with rationals
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Quantum Information & Computation
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Finite Fields and Their Applications
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We introduce the notion of a black box field and present several algorithms for manipulating such fields. Black box fields arise naturally in cryptography and our algorithms have several cryptographic implications. First, our results show that any algebraically homomorphic cryptosystem can be broken in sub-exponential time. The existence of such cryptosystems was posed as an open problem in [12]. Second we show that, over elliptic (or hyperelliptic) curves the hardness of computing discrete-log implies the security of the Diffie- Hellman protocol. This provable security of the Diffie-Hellman protocol over elliptic curves demonstrates an additional advantage of elliptic curve cryptosystems over conventional ones. Finally, we prove that manipulating black box fields over the rationals is as hard as factoring integers.