Elliptic curves with the montgomery-form and their cryptographic applications

Katsuyuki Okeya, Hiroyuki Kurumatani, Kouichi Sakurai

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

56 被引用数 (Scopus)

抄録

We show that the elliptic curve cryptosystems based on the Montgomery-form EM: BY2 = X3+ AX2 +X are immune to the timing-attacks by using our technique of randomized projective coordinates, while Montgomery originally introduced this type of curves for speeding up the Pollard and Elliptic Curve Methods of integer factorization [Math. Comp. Vol.48, No.177, (1987) pp.243-264]. However, it should be noted that not all the elliptic curves have the Montgomery-form, because the order of any elliptic curve with the Montgomery-form is divisible by “4”. Whereas recent ECC-standards [NIST,SEC-1] recommend that the cofactor of elliptic curve should be no greater than 4 for cryptographic applications. Therefore, we present an efficient algorithm for generating Montgomery-form elliptic curve whose cofactor is exactly “4”. Finally, we give the exact consition on the elliptic curves whether they can be represented as a Montgomery-form or not. We consider divisibility by “8” for Montgomery-form elliptic curves. We implement the proposed algorithm and give some numerical examples obtained by this.

本文言語英語
ホスト出版物のタイトルPublic Key Cryptography - 3rd International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2000, Proceedings
編集者Hideki Imai, Yuliang Zheng
出版社Springer Verlag
ページ238-257
ページ数20
ISBN(印刷版)3540669671, 9783540669678
DOI
出版ステータス出版済み - 2000
イベント3rd International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2000 - Melbourne, オーストラリア
継続期間: 1 18 20001 20 2000

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
1751
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他3rd International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2000
Countryオーストラリア
CityMelbourne
Period1/18/001/20/00

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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