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I'm studying Elliptic Cruve Cryptograhpy. When I do a search on Google of ECC, I find some pdf where I see these curve's paramters: $q, h, r, exp1, exp2$. What are these parameters ? Are there tables (or a site) of these paramters ? I'm finding a corrispondence's table of (Curve, Paramters).

EDIT: Pairing Cryptography curiosity

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  • $\begingroup$ Chances are $q$ is the order of the subgroup generated by the chosen point and $h$ is the cofactor, ie the quotient out of curve order and subgroup order. As for the rest I don't know (-> no answer) w/o research. $\endgroup$ – SEJPM Sep 22 '16 at 18:07
  • $\begingroup$ There is a link where are the paramaters that I have mentioned:gas.dia.unisa.it/projects/jpbc/docs/curvegenerator.html. Can you give me a hint ? $\endgroup$ – JLo Sep 22 '16 at 20:52
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You seem to have strayed into the world of Pairing-Based Cryptography! This is not at all the same as regular Elliptic Curve Cryptography, and I suggest you back away slowly, making no sudden moves. Those parameters are for elliptic curves with Complex Multiplication, which is not what you want.

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  • $\begingroup$ Ok. But now maybe I can understand what are $q$ = is the order of field $F_q$; $r$ = prime factor of order $q+1$ -> Solinas prime; $h$ if I understand is the multipler of $q$. Now I don't undertand what are $exp1$ and $exp2$, and How can I retrive the bit's curve from these parameters. $\endgroup$ – JLo Sep 22 '16 at 23:09
  • $\begingroup$ @JLo: I don't know what they mean. But you don't have to know either, if all you are interested in is Elliptic Curve Cryptography. $\endgroup$ – TonyK Sep 22 '16 at 23:17
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Not sure if still relevant, but just to give the answer: in here it is explained that $r=2^{\text{exp1}}+\text{sign1}*2^{\text{exp2}}+\text{sign0}*1$, a Solinas prime. Also $r\cdot h=q+1$ where $q$ is prime and $h$ is a multiple of 12.

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