Isomorphism and Generation of Montgomery-Form Elliptic Curves Suitable for Cryptosystems

Isomorphism and Generation of Montgomery-Form Elliptic Curves Suitable for Cryptosystems

LIU Duo;SONG Tao;DAI Yiqi

【期刊名称】《清华大学学报（英文版）》 【年(卷),期】2005(010)002

【摘要】Many efficient algorithms of Montgomery-form elliptic curve cryptology have been investigated recently. At present, there are no reported studies of the isomorphic class of the Montgomery-form elliptic curve over a finite field. This paper investigates the isomorphism of Montgomery-form elliptic curves via the isomorphism of Weierstrass-form elliptic curves and gives a table of (nearly) all the forms of Montgomery-form elliptic curves suitable for cryptographic usage. Then, an algorithm for generating a secure elliptic curve with Montgomery-form is presented. The most important advantages of the new algorithm are that it avoids the transformation from an elliptic curve's Weierstrass-form to its Montgomery-form, and that it decreases the probability of collision. So, the proposed algorithem is quicker, simpler, and more efficient than the old ones. 【总页数】7页(145-151)

【关键词】elliptic curve;cryptography;Montgomery-form;isomorphism 【作者】LIU Duo;SONG Tao;DAI Yiqi

【作者单位】Department of Computer Science and Technology,

Tsinghua University, Beijing 100084, China;Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China;Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China 【正文语种】中文 【中图分类】TB1 【文献来源】

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