A. Agashe, K. Lauter, R. Venkatesan, \Constructing elliptic curves with a given number of points over a nite eld," Cryptology ePrint Archive, Report 2001/096, http://eprint.iacr.org/2001/096/. Home/Search Document Details and Download
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Constructing Elliptic Curves with Prescribed Embedding Degrees - Barreto, Lynn, Scott (2002) (8 citations) (Correct)
....the Magma implementation of Tzanakis method, we were not able to nd any cryptographically signi cant examples of curves with k = 5; 8; 10; 12, the only such cases being those where D is too large for traditional CM methods. We have not tried more recent variants of the CM method like that of [1], so there is still hope that solutions of equation 1 with large D are actually practical. But even if this direct approach remains out of reach, there are successful ways to generate suitable eld and curve parameters, as we show next. 3.1 A particular case Let p be a prime (not to be confused ....
A. Agashe, K. Lauter, R. Venkatesan, \Constructing elliptic curves with a given number of points over a nite eld," Cryptology ePrint Archive, Report 2001/096, http://eprint.iacr.org/2001/096/.
Constructing Elliptic Curves with Prescribed Embedding Degrees - Barreto, Lynn, Scott (2002) (8 citations) (Correct)
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A. Agashe, K. Lauter, R. Venkatesan, \Constructing elliptic curves with a given number of points over a nite eld," Cryptology ePrint Archive, Report 2001/096, http://eprint.iacr.org/2001/096/.
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