Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic curves in cryptography
Elliptic curves in cryptography
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
Short Signatures from the Weil Pairing
Journal of Cryptology
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields
Journal of Cryptology
Building cyclic elliptic curves modulo large primes
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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Non-supersingular curves are useful to improve the security of pairing-based cryptosystems. The method proposed by Brezing and Weng is computational inexpensive which can build suitable non-supersingular elliptic curves for pairing-based cryptosystems when the embedding degree is larger than 6. In this paper we propose a new method which extends Brezing and Weng’s method to generate more non-supersingular elliptic curves suitable for pairing-based cryptosystems. Furthermore, we show how our proposed method can be used in the method proposed by Scott and Barreto. Some examples are given to show that new non-supersingular curves can be built.