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
Short Signatures from the Weil Pairing
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Software Implementation of Arithmetic in
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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
IEEE Transactions on Information Theory
Integer Variable Χ---Based Ate Pairing
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Skew Frobenius Map and Efficient Scalar Multiplication for Pairing---Based Cryptography
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
A Schnorr-Like Lightweight Identity-Based Signature Scheme
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
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
Faster $\mathbb{F}_p$-Arithmetic for Cryptographic Pairings on Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Cross twisted Xate pairing with Barreto-Naehrig curve for multi-pairing technique
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
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
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
Constructing tower extensions of finite fields for implementation of pairing-based cryptography
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Network-on-Chip interconnect for pairing-based cryptographic IP cores
Journal of Systems Architecture: the EUROMICRO Journal
Efficient implementation of pairing on BREW mobile phones
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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
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
Non-interactive distributed encryption: a new primitive for revocable privacy
Proceedings of the 10th annual ACM workshop on Privacy in the electronic society
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
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
SMSCrypto: A lightweight cryptographic framework for secure SMS transmission
Journal of Systems and Software
Secure dual-core cryptoprocessor for pairings over Barreto-Naehrig curves on FPGA platform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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In this paper we describe an efficient implementation of the Tate and Ate pairings using Barreto-Naehrig pairing-friendly curves, on both a standard PC and on a 32-bit smartcard. First we introduce a subfamily of such curves with a particularly simple representation. Next we consider the issues that arise in the efficient implemention of field arithmetic in F p12, which is crucial to good performance. Various optimisations are suggested, including a novel approach to the 'final exponentiation', which is faster and requires less memory than the methods previously recommended.