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PKC
2010
Springer
234views Cryptology» more  PKC 2010»
13 years 9 months ago
Solving a 676-Bit Discrete Logarithm Problem in GF(36n)
Abstract. Pairings on elliptic curves over finite fields are crucial for constructing various cryptographic schemes. The T pairing on supersingular curves over GF(3n ) is particula...
Takuya Hayashi, Naoyuki Shinohara, Lihua Wang, Shi...
IMA
2005
Springer
162views Cryptology» more  IMA 2005»
14 years 1 months ago
Pairing-Based Cryptography at High Security Levels
In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. A notable success in this area was the elegant solutio...
Neal Koblitz, Alfred Menezes
PKC
2010
Springer
162views Cryptology» more  PKC 2010»
13 years 11 months ago
Faster Pairing Computations on Curves with High-Degree Twists
Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restric...
Craig Costello, Tanja Lange, Michael Naehrig
SACRYPT
2005
Springer
112views Cryptology» more  SACRYPT 2005»
14 years 29 days ago
Pairing-Friendly Elliptic Curves of Prime Order
Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree k 6. More general methods produce curves over Fp wh...
Paulo S. L. M. Barreto, Michael Naehrig
PAIRING
2009
Springer
124views Cryptology» more  PAIRING 2009»
14 years 2 months ago
Fast Hashing to G2 on Pairing-Friendly Curves
When using pairing-friendly ordinary elliptic curves over prime fields to implement identity-based protocols, there is often a need to hash identities to points on one or both of ...
Michael Scott, Naomi Benger, Manuel Charlemagne, L...