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PKC
2010
Springer
234views Cryptology» more  PKC 2010»
15 years 1 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...
134
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IMA
2005
Springer
162views Cryptology» more  IMA 2005»
15 years 5 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»
15 years 3 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
80
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SACRYPT
2005
Springer
112views Cryptology» more  SACRYPT 2005»
15 years 5 months 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»
15 years 6 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...