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.
| Original language | English |
|---|---|
| Pages (from-to) | 369-384 |
| Number of pages | 16 |
| Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Volume | 2595 |
| Publication status | Published - 2003 Dec 1 |
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Keywords
- Karatsuba's method
- Pseudo-Mersenne prime
- XTR public key system
ASJC Scopus subject areas
- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science
Cite this
Optimal extension fields for XTR. / Han, Dong Guk; Yoon, Ki Soon; Park, Young Ho; Kim, Chang Han; Lim, Jong In.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2595, 01.12.2003, p. 369-384.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimal extension fields for XTR
AU - Han, Dong Guk
AU - Yoon, Ki Soon
AU - Park, Young Ho
AU - Kim, Chang Han
AU - Lim, Jong In
PY - 2003/12/1
Y1 - 2003/12/1
N2 - 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.
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.
KW - Karatsuba's method
KW - Pseudo-Mersenne prime
KW - XTR public key system
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UR - http://www.scopus.com/inward/citedby.url?scp=17144380568&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:17144380568
VL - 2595
SP - 369
EP - 384
JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SN - 0302-9743
ER -