Optimal Extension Fields for XTR
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Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security . 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) ,. 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 , on Pentium III/700MHz which has 32-bit architecture.
KeywordsXTR public key system Pseudo-Mersenne prime Karatsuba’s method
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