Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
A course in computational algebraic number theory
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CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
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ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
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Trading Inversions for Multiplications in Elliptic Curve Cryptography
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WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
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ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient representations on koblitz curves with resistance to side channel attacks
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Using an RSA accelerator for modular inversion
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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Precomputation is essential for window-based scalar multiplications which are the most important operation of elliptic curve cryptography. This precomputation stage may require a significant amount of time due to the expensive inversions over finite fields of large characteristic. Hence, the existing state-of-the-art precomputation schemes try to reduce the number of inversions as much as possible. However, our analysis show that the performance of precomputation schemes not only depends on the cost of field inversions, but also on the cost ratio of inversion to multiplication (i.e. I/M). In this paper, we present a new scheme to precompute all odd multiples [3]P , …, [2k −1]P , k ≥2 on standard elliptic curves in affine coordinates. Our precomputation scheme strikes a balance between the number of inversions and multiplications. We show that our scheme requiring only 2(k −1) registers, offers the best performance in the case of k ≥8 if the I/M-ratio is around 10.