Elliptic curves in cryptography
Elliptic curves in cryptography
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: 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
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
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
Ate Pairing on Hyperelliptic Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Identification of Multiple Invalid Signatures in Pairing-Based Batched Signatures
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
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
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
Pairing calculation on supersingular genus 2 curves
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Identity-based threshold decryption revisited
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Encapsulated scalar multiplications and line functions in the computation of Tate pairing
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Finding invalid signatures in pairing-based batches
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Identification of multiple invalid pairing-based signatures in constrained batches
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
A correlation power analysis attack against tate pairing on FPGA
ARC'11 Proceedings of the 7th international conference on Reconfigurable computing: architectures, tools and applications
Another elliptic curve model for faster pairing computation
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
A reconfigurable implementation of the tate pairing computation over GF(2m)*
ARC'10 Proceedings of the 6th international conference on Reconfigurable Computing: architectures, Tools and Applications
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
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
General and efficient certificateless public key encryption constructions
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Instruction set extensions for pairing-based cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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The security and performance of pairing based cryptography has provoked a large volume of research, in part because of the exciting new cryptographic schemes that it underpins. We re-examine how one should implement pairings over ordinary elliptic curves for various practical levels of security. We conclude, contrary to prior work, that the Tate pairing is more efficient than the Weil pairing for all such security levels. This is achieved by using efficient exponentiation techniques in the cyclotomic subgroup backed by efficient squaring routines within the same subgroup.