Optimal Extension Fields for XTR [chapter]

Dong-Guk Han, Ki Soon Yoon, Young-Ho Park, Chang Han Kim, Jongin Lim
2003 Lecture Notes in Computer Science  
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 (p 6 ) and it can be generalized to the field GF (p 6m ) [6, 9] . This paper proposes optimal extension fields for XTR among Galois fields GF (p 6m ) which can be applied to XTR. In order to select such fields, we introduce a new notion
more » ... of Generalized Optimal Extension Fields(GOEFs) and suggest a condition of prime p, a defining polynomial of GF (p 2m ) and a fast method of multiplication in GF (p 2m ) to achieve fast finite field arithmetic in GF (p 2m ). From our implementation results, GF (p 36 ) → GF (p 12 ) is the most efficient extension fields for XTR and computing T r(g n ) given T r(g) in GF (p 12 ) is on average more than twice faster than that of the XTR system[6,10] on Pentium III/700MHz which has 32-bit architecture.
doi:10.1007/3-540-36492-7_24 fatcat:qn2xh5z3h5fs7bjgk4pgd3u3uu