Secure and Compact Elliptic Curve Cryptosystems

• Item type: SIG Technical Reports(1)
• 公開日: 2019-05-16
• タイトル: Secure and Compact Elliptic Curve Cryptosystems
• タイトル / 言語: en
• タイトル: Secure and Compact Elliptic Curve Cryptosystems
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Graduate School of Engineering Osaka University
• 著者所属: Graduate School of Engineering Osaka University
• 著者所属(英): en
• 著者所属(英): Graduate School of Engineering Osaka University
• 著者所属(英): en
• 著者所属(英): Graduate School of Engineering Osaka University
• 著者名: Yaoan, Jin; Atsuko, Miyaji
• 著者名(英): Yaoan, Jin; Atsuko, Miyaji
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Elliptic curve cryptosystems (ECCs) are widely used because of their short key size． They can ensure enough security with shorter keys， and use less memory space to reduce parameters． Hence， an elliptic curve is typically used in embedded systems． The dominant computation of an ECC is scalar multiplication Q = kP， P ∈ E(Fq)． Thus， the security and efficiency of scalar multiplication are paramount． To render secure ECCs， complete addition formulae can be employed for a secure scalar multiplication． However， this requires significant memory and is thus not suitable for compact devices． Several coordinates exist for elliptic curves such as affine， Jacobian， projective． The complete addition formulae are not based on affine coordinates and thus require considerable memory． In this study， we achieved a compact ECC by focusing on affine coordinates． In fact， affine coordinates are highly advantageous in terms of memory but require many if statements for scalar multiplication owing to exceptional points． We improve the scalar multiplication and reduce the limitations for input k． Furthermore， we extend the affine addition formulae to delete some exceptional inputs for scalar multiplication． Our compact ECC reduces memory complexity up to 26 % and is much more efficient compared to Joye's RL 2-ary algorithm with the complete addition of formulae when the ratio I/M of computational complexity of inversion (I) to multiplication (M) is less than 7．2．
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Elliptic curve cryptosystems (ECCs) are widely used because of their short key size. They can ensure enough security with shorter keys, and use less memory space to reduce parameters. Hence, an elliptic curve is typically used in embedded systems. The dominant computation of an ECC is scalar multiplication Q = kP, P ∈ E(Fq). Thus, the security and efficiency of scalar multiplication are paramount. To render secure ECCs, complete addition formulae can be employed for a secure scalar multiplication. However, this requires significant memory and is thus not suitable for compact devices. Several coordinates exist for elliptic curves such as affine, Jacobian, projective. The complete addition formulae are not based on affine coordinates and thus require considerable memory. In this study, we achieved a compact ECC by focusing on affine coordinates. In fact, affine coordinates are highly advantageous in terms of memory but require many if statements for scalar multiplication owing to exceptional points. We improve the scalar multiplication and reduce the limitations for input k. Furthermore, we extend the affine addition formulae to delete some exceptional inputs for scalar multiplication. Our compact ECC reduces memory complexity up to 26 % and is much more efficient compared to Joye's RL 2-ary algorithm with the complete addition of formulae when the ratio I/M of computational complexity of inversion (I) to multiplication (M) is less than 7.2.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AA12326962
• 書誌情報: 研究報告インターネットと運用技術（IOT）; 巻 2019-IOT-45, 号 17, p. 1-6, 発行日 2019-05-16
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 2188-8787
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会