Why can't we use any random elliptic curve? What are the properties that need to be satisfied?
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Can you propose a procedure to pick "randomly" an elliptic curve? – Ievgeni Aug 22 '23 at 17:10
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1That's a complex subject. Useful references: safecurves, Brainpool requirements, sec2 §2.1. – fgrieu Aug 22 '23 at 17:30
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Far from being the only reason, but some curves can be implemented more efficiently than others. – swineone Aug 25 '23 at 02:50
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Does this answer your question? What is necessary for generating an elliptic curve? – kelalaka Aug 27 '23 at 13:25