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Prikladnaya Diskretnaya Matematika, 2011, Number 3(13), Pages 17–54
(Mi pdm335)
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Theoretical Foundations of Applied Discrete Mathematics
Method for constructing elliptic curves using complex multiplication and its optimizations
E. A. Grechnikov M. V. Lomonosov Moscow State University, Moscow, Russia
Abstract:
Elliptic curves over finite fields with predefined conditions on the order are practically constructed using the theory of complex multiplication. A stage with the longest calculations in this method reconstructs some polynomial with integer coefficients. We prove some theoretical results and give a detailed account of the method itself and show how one can use a divisor of the mentioned polynomial with coefficients in an extension of the rational number field.
Keywords:
elliptic curves, finite fields, complex multiplication, simultaneous approximations.
Citation:
E. A. Grechnikov, “Method for constructing elliptic curves using complex multiplication and its optimizations”, Prikl. Diskr. Mat., 2011, no. 3(13), 17–54
Linking options:
https://www.mathnet.ru/eng/pdm335 https://www.mathnet.ru/eng/pdm/y2011/i3/p17
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Abstract page: | 370 | Full-text PDF : | 166 | References: | 40 | First page: | 1 |
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