论文信息 - XTR Extended to GF(p6m)

XTR Extended to GF(p6m)

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.

Seungjoo Kim | Jaemoon Kim | Ikkwon Yie | Seongan Lim | Hongsub Lee

[1] Arjen K. Lenstra,et al. Key Improvements to XTR , 2000, ASIACRYPT.

[2] Arjen K. Lenstra,et al. Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems Over Finite Fields , 1997, ACISP.

[3] Arjen K. Lenstra,et al. Selecting Cryptographic Key Sizes , 2000, Public Key Cryptography.

[4] Walter M. Lioen,et al. Factorization of RSA-140 Using the Number Field Sieve , 1999, CRYPTO 1999.

[5] Andries E. Brouwer,et al. Doing More with Fewer Bits , 1999, ASIACRYPT.

[6] Harald Niederreiter,et al. Introduction to finite fields and their applications: List of Symbols , 1986 .

[7] Arjen K. Lenstra,et al. The XTR Public Key System , 2000, CRYPTO.

[8] Colin Boyd,et al. Advances in Cryptology - ASIACRYPT 2001 , 2001 .

[9] Michael Wiener,et al. Advances in Cryptology — CRYPTO’ 99 , 1999 .

[10] Arjen K. Lenstra,et al. Fast Irreducibility and Subgroup Membership Testing in XTR , 2001, Public Key Cryptography.