Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
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
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
Journal of Cryptology
Elliptic Curves: Number Theory and Cryptography, Second Edition
Elliptic Curves: Number Theory and Cryptography, Second Edition
On degrees of polynomial interpolations related to elliptic curve cryptography
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
IEEE Transactions on Information Theory
Closed formulae for the Weil pairing inversion
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
A generalization of Verheul's theorem for some ordinary curves
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
The k-BDH assumption family: bilinear map cryptography from progressively weaker assumptions
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear Diffie---Hellman problem. In contrast to the discrete log (or Diffie---Hellman) problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul (Advances in Cryptology--EUROCRYPT 2001, LNCS 2045, pp. 195---210, 2001) proved that on a certain class of curves, the discrete log and Diffie---Hellman problems are unlikely to be provably equivalent to the same problems in a corresponding finite field unless both Diffie---Hellman problems are easy. In this paper we generalize Verheul's theorem and discuss the implications on the security of pairing based systems.