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. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Han, D. G., Yoon, K. S., Park, Y. H., Kim, C. H., & Lim, J. (2003). Optimal extension fields for XTR. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2595, 369–384. https://doi.org/10.1007/3-540-36492-7_24
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