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I would like to map integer values to points on Ed25519, and then back again.

Is there a technique that takes advantage of the specific structure of Ed25519?

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You might want to take a look at Elligator 2, but it has some limitations. –  CodesInChaos May 5 at 20:58
    
@CodesInChaos: Thank you! This looks very promising. –  Chris May 6 at 10:20

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