• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.129-131
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• 2004

Elliptic Curve Cryptography (ECC) coprocessors support massive scalar multiplications of a point. We research the design for multi-segment multipliers in fixed-size ECC coprocessors using the multi-segment Karatsuba algorithm on GF($2^m$). ECC coprocessors of the proposed multiplier is verified on the SoC-design verification kit which embeds ALTERA EXCALIBUR FPGAs. As a result of our experiment, the multi-segment Karatsuba multiplier, which has more efficient performance about twice times than the traditional multi-segment multiplier, can be implemented as adding few H/W resources. Therefore the multi-segment Karatsuba multiplier which satisfies performance for the cryptographic algorithm, is adequate for a low cost embedded system, and is implemented in the minimum area.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.1
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• pp.33-40
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• 2004

The divide-and-conquer method is efficiently used in parallel multiplier over finite field $GF(2^n)$. Leone Proposed optimal stop condition for iteration of Karatsuba-Ofman algerian(KOA). Ernst et al. suggested Multi-Segment Karatsuba(MSK) method. In this paper, we analyze the complexity of a parallel MSK multiplier based on the method. We propose a new parallel MSK multiplier whose space complexity is same to each other. Additionally, we propose optimal stop condition for iteration of the new MSK method. In some finite fields, our proposed multiplier is more efficient than the KOA.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.5 s.335
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• pp.23-30
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• 2005

In the construction of an extension field, there is a connection between the polynomial multiplication method and the degree of polynomial. The existing methods, KO and MSK methods, efficiently reduce the complexity of coefficient-multiplication. However, when we construct the multiplication of an extension field using KO and MSK methods, the polynomials are padded with necessary number of zero coefficients in general. In this paper, we propose basic properties of KO and MSK methods and algorithm that can reduce coefficient-multiplications. The proposed algorithm is more reducible than the original KO and MSK methods. This characteristic makes the employment of this multiplier particularly suitable for applications characterized by specific space constrains, such as those based on smart cards, token hardware, mobile phone or other devices.