XTR Extended to GF(p6m)
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- Lim S., Kim S., Yie I., Kim J., Lee H. (2001) XTR Extended to GF(p6m). In: Vaudenay S., Youssef A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg
A. K. Lenstra and E. R. Verheul in  proposed a very efficient way called XTR in which certain subgroup of the Galois field GF(p6) can be represented by elements in GF(p2). At the end of their paper , they briefly mentioned on a method of generalizing their idea to the field GF(p6m). In this paper, we give a systematic design of this generalization and discuss about optimal choices for p and m with respect to performances. If we choose m large enough, we can reduce the size of p as small as the word size of common processors. In such a case, this extended XTR is well suited for the processors with optimized arithmetic on integers of word size.