Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Evaluating logarithms in GF(2n)
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
An efficient group key establishment in location-aided mobile ad hoc networks
PE-WASUN '05 Proceedings of the 2nd ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
Computing pairings using x-coordinates only
Designs, Codes and Cryptography
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
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
An efficient group signature scheme from bilinear maps
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Fast bilinear maps from the tate-lichtenbaum pairing on hyperelliptic curves
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
Verifiable pairing and its applications
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Efficient computation of tate pairing in projective coordinate over general characteristic fields
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Side channel attacks and countermeasures on pairing based cryptosystems over binary fields
CANS'06 Proceedings of the 5th international conference on Cryptology and Network Security
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The Tate pairing hasp lenty of attractive applications, e.g., ID-based cryptosystems, short signatures, etc. Recently several fast implementationsof the Tate pairing hasb een reported, which make it appear that the Tate pairing is capable to be used in practical applications. The computation time of the Tate pairing strongly depends on underlying elliptic curves and definition fields. However these fast implementation are restricted to supersingular curves with small MOV degrees. In this paper we propose several improvements of computing the Tate pairing over general elliptic curveso ver finite fields IFq (q = pm, p 3) -- some of them can be efficiently applied to supersingular curves. The proposed methods can be combined with previous techniques. The proposed algorithm iss pecially effective upon the curvest hat hasa large MOV degree k. We develop several formulas that compute the Tate pairing using the small number of multiplications over IFqk. For k = 6, the proposed algorithm is about 20% faster than previously fastest algorithm.