An Efficient Multiplier/Divider Design for Elliptic Curve Cryptosystem over GF(2(superscript m))

Using the concept of reciprocal polynomial, this paper shows that a field multiplication over GF(2(superscript m)) can be implemented by extended Stein's algorithm, one of the algorithms used to accomplish division. In this way, a field multiplier can be efficiently embedded into a divider with very little hardware overhead for operand selection based on a fundamental change at the algorithmic level. When applying the developed combined multiplication and division (CMD) algorithm to Elliptic Curve Cryptography (ECC) using affine coordinates, we achieve about 13.8% reduction on the area requirement with almost no performance degradation compared to the one implemented with two distinct components. Experimental results also demonstrate that not only our CMD circuit has the area advantage (up to 12.7%) in comparison with other low-cost design but also the resulting area-efficient design of ECC system exhibits considerable improvement on the area-time (AT) complexity of previous work.

並列關鍵字

elliptic curve cryptography ECC ； affine coordinates ； combined multiplier and divider CMD design ； extended stein's division algorithm ； MSB-first multiplier ； polynomial basis

被引用紀錄

王鵬舜（2006）。含高反射率印刷網點之側照式背光模組性能之研究〔碩士論文，國立清華大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0016-1303200709293817

國際替代計量

An Efficient Multiplier/Divider Design for Elliptic Curve Cryptosystem over GF(2(superscript m))

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