Finding elliptic curves with a subgroup of prescribed size
2016 ◽
Vol 13
(01)
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pp. 133-152
Keyword(s):
Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime [Formula: see text] and positive integer [Formula: see text], outputs an elliptic curve [Formula: see text] over the finite field [Formula: see text] for which the cardinality of [Formula: see text] is divisible by [Formula: see text]. The running time of the algorithm is [Formula: see text], and this leads to more efficient constructions of rational functions over [Formula: see text] whose image is small relative to [Formula: see text]. We also give an unconditional version of the algorithm that works for almost all primes [Formula: see text], and give a probabilistic algorithm with subexponential time complexity.
2015 ◽
Vol 18
(1)
◽
pp. 308-322
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2016 ◽
Vol 68
(4)
◽
pp. 721-761
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Keyword(s):
2002 ◽
Vol 66
(3)
◽
pp. 353-358
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2012 ◽
Vol 64
(1)
◽
pp. 151-182
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Keyword(s):
2005 ◽
Vol 72
(2)
◽
pp. 251-263
◽
2005 ◽
Vol 48
(1)
◽
pp. 16-31
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1995 ◽
Vol 38
(2)
◽
pp. 167-173
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Keyword(s):
2010 ◽
Vol 53
(1)
◽
pp. 1-12
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2012 ◽
Vol 149
(2)
◽
pp. 175-203
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1971 ◽
Vol 36
(1)
◽
pp. 267-278
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