Algorithm 312: Absolute value and square root of a complex number
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
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
Fast Implementation of Elliptic Curve Arithmetic in GF(pn)
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Implementation of cryptosystems based on Tate pairing
Journal of Computer Science and Technology
An Efficient Square Root Computation in Finite Fields GF(p2d)
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Efficient Algorithms for Tate Pairing
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
Simple and Efficient Group Signature Scheme Assuming Tamperproof Devices
IWSEC '08 Proceedings of the 3rd International Workshop on Security: Advances in Information and Computer Security
On the application of pairing based cryptography to wireless sensor networks
Proceedings of the second ACM conference on Wireless network security
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and Cryptography
High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
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
Attribute-based strong designated-verifier signature scheme
Journal of Systems and Software
Faster pairing coprocessor architecture
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
| Hi-index | 0.00 |
Here we review the state-of-the-art in cryptographic pairing implementation. Starting with a basic Miller algorithm for the Tate pairing we show how to successively apply a series of optimizations and tricks to improve performance. We will concentrate on the case of nonsupersingular prime characteristic elliptic curves, although many of the optimizations equally apply to the cases of supersingular elliptic and hyperelliptic curves. We also discuss optimal implementation of extension field arithmetic.