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I implemented and used the P-521 curve for ECDSA. Signatures are 132 bytes long. It seems that Edwards E-521 is safer but I did not investigated very deeper.

What is its signature length ?

How is it better ?

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  • $\begingroup$ Library recommendations are off topic, so I'm editing that part out. $\endgroup$ – otus Sep 1 '15 at 8:35
  • $\begingroup$ Do you want to compare ECDSA using P-521 with ECDSA using E-521 ? $\endgroup$ – Ruggero Sep 1 '15 at 10:23
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What is its signature length ?

Depends on what algorithms you use, but with ECDSA the signature length is twice the length of the order of the base point. For P-521 that's 1042 bits, or 132 bytes when using whole bytes for each part. For E-521 it's 1038 bits or 130 bytes.

How is it better ?

The design criteria for E-521 are stated in A note on high-security general-purpose elliptic curves:

The curves Curve25519 and Curve1174 have been engineered to facilitate simple, efficient and secure implementation of general-purpose elliptic curve cryptosystems, with impressive results [8]. On these grounds, it makes sense to look for similar curves at higher security levels.

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