Extended NIST prime family for efficient modular reduction

Young In Cho; Nam Su Chang; Chang Han Kim; Seokhie Hong

doi:10.1007/978-94-007-2792-2_10

Extended NIST prime family for efficient modular reduction

Young In Cho, Nam Su Chang, Chang Han Kim, Seokhie Hong

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The FIPS 186-2 standard recommends five prime fields with a modulus so-called NIST primes for elliptic curve cryptosystems. Primes of the special form such as NIST primes have a property yields modular reduction algorithms that are significantly fast. However the number of NIST primes are not large enough. In this paper, we further extend the idea of NIST primes. Then we find more primes can provide fast modular reduction computation that NIST prime family does not support. Our method provides more efficient modular arithmetic than Montgomery algorithm in prime fields that NIST primes does not support.

Original language	English
Title of host publication	Computer Science and Convergence, CSA 2011 and WCC 2011 Proceedings
Pages	105-111
Number of pages	7
DOIs	https://doi.org/10.1007/978-94-007-2792-2_10
Publication status	Published - 2012
Event	3rd International Conference on Computer Science and Its Applications, CSA 2011 and 2011 FTRA World Convergence Conference, WCC 2011 - Jeju, Korea, Republic of Duration: 2011 Dec 12 → 2011 Dec 15

Publication series

Name	Lecture Notes in Electrical Engineering
Volume	114 LNEE
ISSN (Print)	1876-1100
ISSN (Electronic)	1876-1119

Other

Other	3rd International Conference on Computer Science and Its Applications, CSA 2011 and 2011 FTRA World Convergence Conference, WCC 2011
Country/Territory	Korea, Republic of
City	Jeju
Period	11/12/12 → 11/12/15

Keywords

Finite field arithmetic
Modular arithmetic
NIST prime

ASJC Scopus subject areas

Industrial and Manufacturing Engineering

Access to Document

10.1007/978-94-007-2792-2_10

Cite this

Cho, YI, Chang, NS, Kim, CH & Hong, S 2012, Extended NIST prime family for efficient modular reduction. in Computer Science and Convergence, CSA 2011 and WCC 2011 Proceedings. Lecture Notes in Electrical Engineering, vol. 114 LNEE, pp. 105-111, 3rd International Conference on Computer Science and Its Applications, CSA 2011 and 2011 FTRA World Convergence Conference, WCC 2011, Jeju, Korea, Republic of, 11/12/12. https://doi.org/10.1007/978-94-007-2792-2_10

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title = "Extended NIST prime family for efficient modular reduction",

abstract = "The FIPS 186-2 standard recommends five prime fields with a modulus so-called NIST primes for elliptic curve cryptosystems. Primes of the special form such as NIST primes have a property yields modular reduction algorithms that are significantly fast. However the number of NIST primes are not large enough. In this paper, we further extend the idea of NIST primes. Then we find more primes can provide fast modular reduction computation that NIST prime family does not support. Our method provides more efficient modular arithmetic than Montgomery algorithm in prime fields that NIST primes does not support.",

keywords = "Finite field arithmetic, Modular arithmetic, NIST prime",

author = "Cho, {Young In} and Chang, {Nam Su} and Kim, {Chang Han} and Seokhie Hong",

year = "2012",

doi = "10.1007/978-94-007-2792-2_10",

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series = "Lecture Notes in Electrical Engineering",

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AU - Hong, Seokhie

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AB - The FIPS 186-2 standard recommends five prime fields with a modulus so-called NIST primes for elliptic curve cryptosystems. Primes of the special form such as NIST primes have a property yields modular reduction algorithms that are significantly fast. However the number of NIST primes are not large enough. In this paper, we further extend the idea of NIST primes. Then we find more primes can provide fast modular reduction computation that NIST prime family does not support. Our method provides more efficient modular arithmetic than Montgomery algorithm in prime fields that NIST primes does not support.

KW - Finite field arithmetic

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Extended NIST prime family for efficient modular reduction

Abstract

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Keywords

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