Elliptic curves in cryptography
Elliptic curves in cryptography
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
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
A new method of building more non-supersingular elliptic curves
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Generating Pairing-Friendly Curves with the CM Equation of Degree 1
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
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
Fast Hashing to G2 on Pairing-Friendly Curves
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
Elliptic curves with a pre-determined embedding degree
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Constructing pairing-friendly elliptic curves using Gröbner basis reduction
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
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
Delaying mismatched field multiplications in pairing computations
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Efficient multiplication in finite field extensions of degree 5
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
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
SAC'11 Proceedings of the 18th 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
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Simple and exact formula for minimum loop length in Atei pairing based on Brezing---Weng curves
Designs, Codes and Cryptography
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We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham [6]. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k 12.