A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Verifier-Local revocation group signature schemes with backward unlinkability from bilinear maps
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Information Theory
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
Faster explicit formulas for computing pairings over ordinary curves
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Identity-based key distribution for mobile Ad Hoc networks
Frontiers of Computer Science in China
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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In implementing an efficient pairing calculation, it is saidthat the lower bound of the number of iterations of Miller'salgorithm is log2r/φ(k),where φ(·) is the Euler's function. Ate pairingreduced the number of the loops of Miller's algorithm of Tatepairing from $\lfloor\log_2r\rfloor$ to $\lfloor\log_2(t-1)\rfloor$. Recently, it is known to systematicallyprepare a pairing---friendly elliptic curve whose parameters aregiven by a polynomial of integer variable "Χ". For thecurve, this paper gives integer variable Χ---basedAte pairing that achieves the lower bound byreducing it to $\lfloor\log_2\chi\rfloor$.