Finite fields
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
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
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields
Journal of Cryptology
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
On the relationship between squared pairings and plain pairings
Information Processing Letters
A pairing SW implementation for Smart-Cards
Journal of Systems and Software
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
A Schnorr-Like Lightweight Identity-Based Signature Scheme
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
On the relationship between squared pairings and plain pairings
Information Processing Letters
Ramanujan's class invariants and their use in elliptic curve cryptography
Computers & Mathematics with Applications
Pairing-friendly elliptic curves with small security loss by Cheon's algorithm
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
On prime-order elliptic curves with embedding degrees k = 3, 4, and 6
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
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
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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
On constructing families of pairing-friendly elliptic curves with variable discriminant
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Algebraic curves and cryptography
Finite Fields and Their Applications
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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In their seminal paper, Miyaji et al. [13] describe a simple method for the creation of elliptic curves of prime order with embedding degree 3, 4, or 6. Such curves are important for the realisation of pairing-based cryptosystems on ordinary (non-supersingular) elliptic curves. We provide an alternative derivation of their results, and extend them to allow for the generation of many more suitable curves.