@inbook{c0dddf54416849a08b619d514af12950,
title = "Optimal extension fields for XTR",
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",
note = "Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2003",
doi = "10.1007/3-540-36492-7_24",
language = "English",
isbn = "9783540006220",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "369--384",
editor = "Kaisa Nyberg and Howard Heys",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
}