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Only koblitz curves (secp256k1) seem to be secure?

On a related note, the Bernstein team designed Ed25519 with side channels attacks in mind. https://en.wikipedia.org/wiki/EdDSA#Features

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It would have been nice if the paper had discussed Ed25519. Anyone else know what the status is relative to this (and other, similar) work?

The paper attacks implementations, not algorithms. As far as I know, all of the of the major Ed25519 implementations are side channel protected and safe (no branches on secret data, no array indexing with secret data)

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