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
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: 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
Efficient Multiplication in GF(pk) for Elliptic Curve Cryptography
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Cryptographic implications of Hess' generalized GHS attack
Applicable Algebra in Engineering, Communication and Computing
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Journal of Symbolic Computation
On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
IEEE Transactions on Information Theory
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
Compact hardware for computing the tate pairing over 128-bit-security supersingular curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
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
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
On the efficient implementation of pairing-based protocols
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Efficient pairing computation on ordinary elliptic curves of embedding degree 1 and 2
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
IEEE Transactions on Information Theory
On the minimal embedding field
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller's algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals's supersingular curves over composite extension fields in parallel implementation.