Introduction to finite fields and their applications
Introduction to finite fields and their applications
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
Identity-based confirmer signatures from pairings over elliptic curves
Proceedings of the 4th ACM conference on Electronic commerce
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Untraceable RFID tags via insubvertible encryption
Proceedings of the 12th ACM conference on Computer and communications security
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Implementation of cryptosystems based on Tate pairing
Journal of Computer Science and Technology
Provably secure non-interactive key distribution based on pairings
Discrete Applied Mathematics - Special issue: Coding and cryptography
Special polynomial families for generating more suitable pairing-friendly elliptic curves
EHAC'06 Proceedings of the 5th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications
A pairing SW implementation for Smart-Cards
Journal of Systems and Software
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
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
International Journal of Information and Coding Theory
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Provably secure non-interactive key distribution based on pairings
Discrete Applied Mathematics - Special issue: Coding and cryptography
Constructing pairing-friendly elliptic curves using Gröbner basis reduction
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Constructing tower extensions of finite fields for implementation of pairing-based cryptography
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
Cryptographic pairings based on elliptic nets
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
Deniable authenticated key establishment for internet protocols
Proceedings of the 11th international conference on Security Protocols
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
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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
Hardware acceleration of the tate pairing in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
On the efficient implementation of pairing-based protocols
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On constructing families of pairing-friendly elliptic curves with variable discriminant
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Attractive subfamilies of BLS curves for implementing high-security pairings
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
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Indifferentiable hashing to barreto---naehrig curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Implementing pairings at the 192-bit security level
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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Pairing-based cryptosystems depend on the existence of groups where the Decision Diffie-Hellman problem is easy to solve, but the Computational Diffie-Hellman problem is hard. Such is the case of elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. However, the embedding degree for most elliptic curves is enormous, and the few previously known suitable elliptic curves have embedding degree k ≤ 6. In this paper, we examine criteria for curves with larger k that generalize prior work by Miyaji et al. based on the properties of cyclotomic polynomials, and propose efficient representations for the underlying algebraic structures.