Introduction to finite fields and their applications
Introduction to finite fields and their applications
ACISP '97 Proceedings of the Second Australasian Conference on Information Security and Privacy
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Optimal Extension Fields for XTR
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Comments on a Signature Scheme Based on the Third Order LFSR Proposed at ACISP2001
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
On the Computational Efficiency of XTR+
Information Security and Cryptology
Fast irreducibility testing for XTR using a gaussian normal basis of low complexity
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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A. K. Lenstra and E. R. Verheul in [2] 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 [2], 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.