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3

The problem is that, imagine you sign a message $m$ using ECDSA and SHA-1 as hash algorithm. If an attacker manages to find a message $m'$ such as SHA-1$(m)$ = SHA-1$(m')$ then the computed signature for $m$ will be valid for $m'$. So the attacker can substitute $m$ for $m'$ while keeping the same signature value. The receiver who will try to validate the ...


2

I think that I've found a good solution to this problem. In short terms it consists in generating an ECDSA signature using the point $R$ as generator, $s$ as private key and the result of $s*R$ as public key. So the $r$ part of the signature would be revealed but the $s$ part is still kept secret. The usual ECDSA signature generation consists in proving ...


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That wikipedia article is about TLS, and lists separately only EC curves that have assigned numbers in TLS; for TLS all other curves fall under "arbitrary prime" or "arbitrary 2^m". OpenSSL supports for non-TLS operations including ECDSA quite a few curves not numbered for use in TLS, including the three you list. As requested, I do not comment on their ...



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