Algorithmica
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in number theory and cryptography
A course in number theory and cryptography
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Handbook of theoretical computer science (vol. A)
Diffie-Hillman is as Strong as Discrete Log for Certain Primes
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive Oblivious Transfer and Spplications
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
The Use of Interaction in Public Cryptosystems (Extended Abstract)
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
On Ordinary Elliptic Curve Cryptosystems
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
An Efficient Off-line Electronic Cash System Based On The Representation Problem.
An Efficient Off-line Electronic Cash System Based On The Representation Problem.
Random self-reducibility and zero knowledge interactive proofs of possession of information
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Security analysis and applications of standard key agreement protocols
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Electronic Commerce Research and Applications
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We investigate the complexity of breaking cryptosystems of which security is based on the discrete logarithm problem. We denote the algorithms of breaking the Diffie-Hellman's key exchange scheme by DH, the Bellare-Micali's non-interactive oblivious transfer scheme by BM, the ElGamal's public-key cryptosystem by EG, the Okamoto's conferencekey sharing scheme by CONF, and the Shamir's 3-pass key-transmission scheme by 3PASS, respectively. We show a relation among these cryptosystems that 3PASS ≤mFP CONF ≤mFP EG ≡mFP BM ≡mFP DH, where ≤mFP denotes the polynomial-time functionally many-teone reducibility, i.e. a function version of the ≤mp -reducibility. We further give some condition in which these algorithms have equivalent difficulty. Namely, 1. If the complete factorization of p - 1 is given, i.e. if the the discrete logarithm problem is a certified one, then these cryptosystems are equivalent w.r.t. expected polynomial-time functionally Turing reducibility. 2. If the underlying group is the Jacobian of an elliptic curve over Zp, with a prime order, then these cryptosystems are equivalent w.r.t. polynomial-time functionally many-to-one reducibility. We also discuss the complexity of several languages related to those computing problems.