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Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields.

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Title: Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields.
Authors: Dupont, Régis1 dupont@lix.polytechnique.fr, Enge, Andreas1 enge@lix.polytechnique.fr, Morain, François1 morain@lix.polytechnique.fr
Source: Journal of Cryptology. Spring2005, Vol. 18 Issue 2, p79-89. 11p.
Subjects: Elliptic curves, Complex multiplication, Algebraic geometry, Algebraic curves, Discriminant analysis, Logarithmic functions
Abstract: We present a fast algorithm for building ordinary elliptic curves over finite prime fields having arbitrary small MOV degree. The elliptic curves are obtained using complex multiplication by any desired discriminant. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Cryptology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields.
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  Data: <searchLink fieldCode="AR" term="%22Dupont%2C+Régis%22">Dupont, Régis</searchLink><relatesTo>1</relatesTo><i> dupont@lix.polytechnique.fr</i><br /><searchLink fieldCode="AR" term="%22Enge%2C+Andreas%22">Enge, Andreas</searchLink><relatesTo>1</relatesTo><i> enge@lix.polytechnique.fr</i><br /><searchLink fieldCode="AR" term="%22Morain%2C+François%22">Morain, François</searchLink><relatesTo>1</relatesTo><i> morain@lix.polytechnique.fr</i>
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  Data: <searchLink fieldCode="DE" term="%22Elliptic+curves%22">Elliptic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+multiplication%22">Complex multiplication</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+geometry%22">Algebraic geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+curves%22">Algebraic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Discriminant+analysis%22">Discriminant analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Logarithmic+functions%22">Logarithmic functions</searchLink>
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  Data: We present a fast algorithm for building ordinary elliptic curves over finite prime fields having arbitrary small MOV degree. The elliptic curves are obtained using complex multiplication by any desired discriminant. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Cryptology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00145-004-0219-7
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        Text: English
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      – SubjectFull: Complex multiplication
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      – SubjectFull: Algebraic geometry
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      – SubjectFull: Algebraic curves
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      – SubjectFull: Discriminant analysis
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      – SubjectFull: Logarithmic functions
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      – TitleFull: Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields.
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