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Conversion algorithms and implementations for koblitz curve cryptography

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Conversion algorithms and implementations for koblitz curve cryptography. / Brumley, Billy Bob; Jarvinen, Kimmo U.

In: IEEE Transactions on Computers, Vol. 59, No. 1, 5255226, 04.01.2010, p. 81-92.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Brumley, BB & Jarvinen, KU 2010, 'Conversion algorithms and implementations for koblitz curve cryptography', IEEE Transactions on Computers, vol. 59, no. 1, 5255226, pp. 81-92. https://doi.org/10.1109/TC.2009.132

APA

Brumley, B. B., & Jarvinen, K. U. (2010). Conversion algorithms and implementations for koblitz curve cryptography. IEEE Transactions on Computers, 59(1), 81-92. [5255226]. https://doi.org/10.1109/TC.2009.132

Vancouver

Brumley BB, Jarvinen KU. Conversion algorithms and implementations for koblitz curve cryptography. IEEE Transactions on Computers. 2010 Jan 4;59(1):81-92. 5255226. https://doi.org/10.1109/TC.2009.132

Author

Brumley, Billy Bob ; Jarvinen, Kimmo U. / Conversion algorithms and implementations for koblitz curve cryptography. In: IEEE Transactions on Computers. 2010 ; Vol. 59, No. 1. pp. 81-92.

Bibtex - Download

@article{82d2fe2cc2964aeb976eff66c9de1f86,
title = "Conversion algorithms and implementations for koblitz curve cryptography",
abstract = "In this paper, we discuss conversions between integers and \tau-adic expansions and we provide efficient algorithms and hardware architectures for these conversions. The results have significance in elliptic curve cryptography using Koblitz curves, a family of elliptic curves offering faster computation than general elliptic curves. However, in order to enable these faster computations, scalars need to be reduced and represented using a special base-τ expansion. Hence, efficient conversion algorithms and implementations are necessary. Existing conversion algorithms require several complicated operations, such as multiprecision multiplications and computations with large rationals, resulting in slow and large implementations in hardware and microcontrollers with limited instruction sets. Our algorithms are designed to utilize only simple operations, such as additions and shifts, which are easily implementable on practically all platforms. We demonstrate the practicability of the new algorithms by implementing them on Altera Stratix ∥ FPGAs. The implementations considerably improve both computation speed and required area compared to the existing solutions.",
keywords = "Elliptic curve cryptography, Field-programmable gate arrays, Koblitz curves, Public-key cryptosystems",
author = "Brumley, {Billy Bob} and Jarvinen, {Kimmo U.}",
year = "2010",
month = "1",
day = "4",
doi = "10.1109/TC.2009.132",
language = "English",
volume = "59",
pages = "81--92",
journal = "IEEE Transactions on Computers",
issn = "0018-9340",
publisher = "Institute of Electrical and Electronics Engineers",
number = "1",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Conversion algorithms and implementations for koblitz curve cryptography

AU - Brumley, Billy Bob

AU - Jarvinen, Kimmo U.

PY - 2010/1/4

Y1 - 2010/1/4

N2 - In this paper, we discuss conversions between integers and \tau-adic expansions and we provide efficient algorithms and hardware architectures for these conversions. The results have significance in elliptic curve cryptography using Koblitz curves, a family of elliptic curves offering faster computation than general elliptic curves. However, in order to enable these faster computations, scalars need to be reduced and represented using a special base-τ expansion. Hence, efficient conversion algorithms and implementations are necessary. Existing conversion algorithms require several complicated operations, such as multiprecision multiplications and computations with large rationals, resulting in slow and large implementations in hardware and microcontrollers with limited instruction sets. Our algorithms are designed to utilize only simple operations, such as additions and shifts, which are easily implementable on practically all platforms. We demonstrate the practicability of the new algorithms by implementing them on Altera Stratix ∥ FPGAs. The implementations considerably improve both computation speed and required area compared to the existing solutions.

AB - In this paper, we discuss conversions between integers and \tau-adic expansions and we provide efficient algorithms and hardware architectures for these conversions. The results have significance in elliptic curve cryptography using Koblitz curves, a family of elliptic curves offering faster computation than general elliptic curves. However, in order to enable these faster computations, scalars need to be reduced and represented using a special base-τ expansion. Hence, efficient conversion algorithms and implementations are necessary. Existing conversion algorithms require several complicated operations, such as multiprecision multiplications and computations with large rationals, resulting in slow and large implementations in hardware and microcontrollers with limited instruction sets. Our algorithms are designed to utilize only simple operations, such as additions and shifts, which are easily implementable on practically all platforms. We demonstrate the practicability of the new algorithms by implementing them on Altera Stratix ∥ FPGAs. The implementations considerably improve both computation speed and required area compared to the existing solutions.

KW - Elliptic curve cryptography

KW - Field-programmable gate arrays

KW - Koblitz curves

KW - Public-key cryptosystems

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U2 - 10.1109/TC.2009.132

DO - 10.1109/TC.2009.132

M3 - Article

VL - 59

SP - 81

EP - 92

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 1

M1 - 5255226

ER -