**A new aspect of dual basis for efficient field arithmetic
Chang-Hyi Lee and Jong-In Lim, August 1998.**

In this manuscript we consider the special type of dual basis for
finite fields, *GF*(2* ^{m}*),
where the varients of

- the field multiplication can be constructed only by
*k*(<=*m*/2) rotations and the same amount of vector XOR processes, - there is needed no additional work load as basis changing (from standard to the dual basis or from the dual basis to standard basis as the conventional dual based arithmetic does),
- the field squaring is only bit-by-bit permutation and it has a good regularity for its implementation, and
- the field inversion process is available for both cases of its
implementation using Fermat's Theorem and of its implementation using
*almost inverse*algorithm [14], especially the case of using the*almost inverse*algorithm has an additional advantage in finding (computing) its complete inverse element.

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**Technique for Generating Provable Primes
Preda Mihailescu, May 1998.**

We suggest a technique for generating provable primes for cryptographical use, for the P1363 standard. The method not only provides a certificate for the primes generated, it is also faster than similar probabilistic generation algorithms. The security concerns are also covered. Detailed descriptions and analysis may be found in [Mi], [Mi1].

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**Efficient Finite Field Basis Conversion Techniques**

Burt Kaliski, Moses Liskov and Yiqun Lisa Yin, April 1999.

This summary of finite field basis conversion techniques is proposed for inclusion in IEEE P1363 Annex A. Included are some conventional basis conversion techniques, as well as some new storage-efficient basis conversion techniques.

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**Usage of Optimal Extension Fields for Elliptic
Curve Cryptosystems****
Tetsutaro Kobayashi, Kazumaro Aoki, Fumitaka Hoshino, Kunio Kobayashi
and Hikaru Morita, August 1999.**
Presented at the August 1999
and October 1999 meetings.

In IEEE P1363, two kinds of finite fields, ``Prime Finite Fields'' and ``Characteristic Two Finite Fields'' have been standardized. We propose ``Optimal Extension Fields (OEF)'' in addition to the two fields. OEF is efficient to compute [1-3].

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Daniel V. Bailey and Christof Paar, February 18, 2000.

This contribution proposes text for possible inclusion in IEEE P1363a specifying support for additional finite fields in the DL and EC settings. In particular, this contribution generalizes IEEE P1363 to support all finite fields. Like IEEE P1363a, it is written as updates to the IEEE P1363 document. It is intended for discussion and review at the March 16-17, 2000, IEEE P1363 working group meeting. The contribution has not yet been approved by the working group.

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Preda Mihailescu, February 2000.

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Leo Reyzin and Burt Kaliski, February 18, 2000.

This contribution proposes text for possible inclusion in IEEE P1363a specifying storage-efficient finite field basis conversion techniques. Like IEEE P1363a, it is written as updates to the IEEE P1363 document. It is intended for discussion and review at the March 16-17, 2000, IEEE P1363 working group meeting. The contribution has not yet been approved by the working group.

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