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8

It is not possible to double security level of Ed25519 any trivial way. Instead, doubling security level requires using another curve that is approximately 512 bit curve. In systems compliant with RFC 7748, i.e. some of IETF specifications, there is Curve448 curve (Ed448-goldilocks). It is almost twice as strong as Curve25519 (its strength is 224 bits). ...


4

When using RSA, I prefer 4096-bit keys, but I would like to use Ed25519. If you use Ed25519 (which is based on Curve25519), well, there's not a great deal you can do; you can find discrete logs for Curve25519 with about $O(2^{128})$ effort, and performing a discrete log allows you to recover the Ed25519 private key. Now, you could replace Curve25519 with ...



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