Handbook of Applied Cryptography
Handbook of Applied Cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Implementation of cryptosystems based on Tate pairing
Journal of Computer Science and Technology
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Integer Variable Χ---Based Ate Pairing
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
New software speed records for cryptographic pairings
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Efficient implementation of pairing on BREW mobile phones
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Designing a code generator for pairing based cryptographic functions
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
High speed flexible pairing cryptoprocessor on FPGA platform
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
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
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Security of prime field pairing cryptoprocessor against differential power attack
InfoSecHiComNet'11 Proceedings of the First international conference on Security aspects in information technology
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Faster pairing computations on curves with high-degree twists
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
An improved twisted ate pairing over KSS curves with k=18
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Core based architecture to speed up optimal ate pairing on FPGA platform
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Implementing pairings at the 192-bit security level
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Secure dual-core cryptoprocessor for pairings over Barreto-Naehrig curves on FPGA platform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Inverting the final exponentiation of tate pairings on ordinary elliptic curves using faults
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of "truncated loop" pairings like the R-ate pairing [18]), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing-friendly elliptic curves to reduce to a minimum the computation required for the final exponentiation.