SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
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
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Efficient Subgroup Exponentiation in Quadratic and Sixth Degree Extensions
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
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
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference 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
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Practical cryptography in high dimensional tori
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
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
IEEE Transactions on Information Theory
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
New software speed records for cryptographic pairings
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
High speed flexible pairing cryptoprocessor on FPGA platform
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
Faster explicit formulas for computing pairings over ordinary curves
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Core based architecture to speed up optimal ate pairing on FPGA platform
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Secure dual-core cryptoprocessor for pairings over Barreto-Naehrig curves on FPGA platform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
NEON implementation of an attribute-based encryption scheme
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Comparing the pairing efficiency over composite-order and prime-order elliptic curves
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of $\mathbb{F}_{q^6}^{\times}$, for $q \equiv 1 \bmod{6}$. Our result arises from considering the Weil restriction of scalars of this group from $\mathbb{F}_{q^6}$ to $\mathbb{F}_{q^2}$, and provides efficiency improvements for both pairing-based and torus-based cryptographic protocols. In particular we argue that such fields are ideally suited for the latter when the field characteristic satisfies $p \equiv 1 \pmod{6}$, and since torus-based techniques can be applied to the former, we present a compelling argument for the adoption of a single approach to efficient field arithmetic for pairing-based cryptography.