XTR extended to GF(P6m)

Seongan Lim; Seungjoo Kim; Ikkwon Yie; Jaemoon Kim; Hongsub Lee

doi:10.1007/3-540-45537-x_23

XTR extended to GF(P6m)

Seongan Lim, Seungjoo Kim, Ikkwon Yie, Jaemoon Kim, Hongsub Lee

Graduate School of Information Study

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

14 Citations (Scopus)

Abstract

A. K. Lenstra and E. R. Verheul in [2] proposed a very efficient way called XTR in which certain subgroup of the Galois field GF(p⁶) can be represented by elements in GF(p2). At the end of their paper [2], they briefly mentioned on a method of generalizing their idea to the field GF(p^6m). In this paper, we give a systematic design of this generalization and discuss about optimal choices for p and m with respect to performances. If we choose m large enough, we can reduce the size of p as small as the word size of common processors. In such a case, this extended XTR is well suited for the processors with optimized arithmetic on integers of word size.

Original language	English
Title of host publication	Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers
Editors	Serge Vaudenay, Amr M. Youssef
Publisher	Springer Verlag
Pages	301-312
Number of pages	12
ISBN (Print)	9783540430667
DOIs	https://doi.org/10.1007/3-540-45537-x_23
Publication status	Published - 2001
Event	8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001 - Toronto, Canada Duration: 2001 Aug 16 → 2001 Aug 17

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2259
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001
Country	Canada
City	Toronto
Period	01/8/16 → 01/8/17

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/3-540-45537-x_23

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Cite this

Lim, S., Kim, S., Yie, I., Kim, J., & Lee, H. (2001). XTR extended to GF(P6m). In S. Vaudenay, & A. M. Youssef (Eds.), Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers (pp. 301-312). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2259). Springer Verlag. https://doi.org/10.1007/3-540-45537-x_23

XTR extended to GF(P6m). / Lim, Seongan; Kim, Seungjoo; Yie, Ikkwon; Kim, Jaemoon; Lee, Hongsub.

Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. ed. / Serge Vaudenay; Amr M. Youssef. Springer Verlag, 2001. p. 301-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2259).

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

Lim, S, Kim, S, Yie, I, Kim, J & Lee, H 2001, XTR extended to GF(P6m). in S Vaudenay & AM Youssef (eds), Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2259, Springer Verlag, pp. 301-312, 8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001, Toronto, Canada, 01/8/16. https://doi.org/10.1007/3-540-45537-x_23

Lim S, Kim S, Yie I, Kim J, Lee H. XTR extended to GF(P6m). In Vaudenay S, Youssef AM, editors, Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. Springer Verlag. 2001. p. 301-312. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45537-x_23

Lim, Seongan ; Kim, Seungjoo ; Yie, Ikkwon ; Kim, Jaemoon ; Lee, Hongsub. / XTR extended to GF(P6m). Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers. editor / Serge Vaudenay ; Amr M. Youssef. Springer Verlag, 2001. pp. 301-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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AB - A. K. Lenstra and E. R. Verheul in [2] proposed a very efficient way called XTR in which certain subgroup of the Galois field GF(p6) can be represented by elements in GF(p2). At the end of their paper [2], they briefly mentioned on a method of generalizing their idea to the field GF(p6m). In this paper, we give a systematic design of this generalization and discuss about optimal choices for p and m with respect to performances. If we choose m large enough, we can reduce the size of p as small as the word size of common processors. In such a case, this extended XTR is well suited for the processors with optimized arithmetic on integers of word size.

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