Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and 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 implementation of the pairing on mobilephones using BREW
WISA'07 Proceedings of the 8th international conference on Information security applications
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 software implementation of the optimal ate pairing over Barreto-Naehrig curves
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
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key 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
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
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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We report on relative performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to reduce to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs. In our implementation, this favors using affine coordinates, even for the current 128-bit minimum security level specified by NIST. We use Barreto-Naehrig (BN) curves and report on the performance of an optimal ate pairing for curves covering security levels between 128 and 192 bits. We compare with other reported performance numbers for pairing computation on ARM CPUs.