Optimal extension fields for XTR

Dong Guk Han; Ki Soon Yoon; Young Ho Park; Chang Han Kim; Jongin Lim

doi:10.1007/3-540-36492-7_24

Optimal extension fields for XTR

Dong Guk Han, Ki Soon Yoon, Young Ho Park, Chang Han Kim, Jongin Lim

School of Cybersecurity

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

4 Citations (Scopus)

Abstract

Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security [6]. XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF(p⁶) and it can be generalized to the field GF(p^6m) [6,9]. This paper proposes optimal extension fields for XTR among Galois fields GF(p^6m) which can be applied to XTR. In order to select such fields, we introduce a new notion of Generalized Optimal Extension Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF(p^2m) and a fast method of multiplication in GF(p^2m) to achieve fast finite field arithmetic in GF(p^2m). From our implementation results, GF(p³⁶) → GF(p¹²) is the most efficient extension fields for XTR and computing Tr(gⁿ) given Tr(g) in GF(p¹²) is on average more than twice faster than that of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Kaisa Nyberg, Howard Heys
Publisher	Springer Verlag
Pages	369-384
Number of pages	16
ISBN (Print)	9783540006220
DOIs	https://doi.org/10.1007/3-540-36492-7_24
Publication status	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2595
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Karatsuba's method
Pseudo-Mersenne prime
XTR public key system

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-36492-7_24

Cite this

Han, D. G., Yoon, K. S., Park, Y. H., Kim, C. H., & Lim, J. (2003). Optimal extension fields for XTR. In K. Nyberg, & H. Heys (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 369-384). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2595). Springer Verlag. https://doi.org/10.1007/3-540-36492-7_24

Optimal extension fields for XTR. / Han, Dong Guk; Yoon, Ki Soon; Park, Young Ho et al.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Kaisa Nyberg; Howard Heys. Springer Verlag, 2003. p. 369-384 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2595).

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

Han, DG, Yoon, KS, Park, YH, Kim, CH & Lim, J 2003, Optimal extension fields for XTR. in K Nyberg & H Heys (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2595, Springer Verlag, pp. 369-384. https://doi.org/10.1007/3-540-36492-7_24

Han DG, Yoon KS, Park YH, Kim CH, Lim J. Optimal extension fields for XTR. In Nyberg K, Heys H, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 369-384. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-36492-7_24

Han, Dong Guk ; Yoon, Ki Soon ; Park, Young Ho et al. / Optimal extension fields for XTR. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Kaisa Nyberg ; Howard Heys. Springer Verlag, 2003. pp. 369-384 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security [6]. XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF(p6) and it can be generalized to the field GF(p6m) [6,9]. This paper proposes optimal extension fields for XTR among Galois fields GF(p6m) which can be applied to XTR. In order to select such fields, we introduce a new notion of Generalized Optimal Extension Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF(p2m) and a fast method of multiplication in GF(p2m) to achieve fast finite field arithmetic in GF(p2m). From our implementation results, GF(p36) → GF(p12) is the most efficient extension fields for XTR and computing Tr(gn) given Tr(g) in GF(p12) is on average more than twice faster than that of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.",

keywords = "Karatsuba's method, Pseudo-Mersenne prime, XTR public key system",

author = "Han, {Dong Guk} and Yoon, {Ki Soon} and Park, {Young Ho} and Kim, {Chang Han} and Jongin Lim",

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AB - Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security [6]. XTR is a new method to represent elements of a subgroup of a multiplicative group of a finite field GF(p6) and it can be generalized to the field GF(p6m) [6,9]. This paper proposes optimal extension fields for XTR among Galois fields GF(p6m) which can be applied to XTR. In order to select such fields, we introduce a new notion of Generalized Optimal Extension Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF(p2m) and a fast method of multiplication in GF(p2m) to achieve fast finite field arithmetic in GF(p2m). From our implementation results, GF(p36) → GF(p12) is the most efficient extension fields for XTR and computing Tr(gn) given Tr(g) in GF(p12) is on average more than twice faster than that of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.

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Optimal extension fields for XTR

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