If the attacker - some guy who really, really wants to steal bitcoins - somehow finds the ephemeral key used in an 256-bit ECDSA signature, can he recover the private key?

If so, would knowing the partial bits of the ephemeral key be sufficient to recover the private key entirely?

  • 1
    $\begingroup$ secp256k1 is an Elliptic Curve, not a signature algorithm. secp256k1 is used with several signature algorithms, including ECDSA (mostly) and Schnorr (sometime, but increasingly). That has an importance, for the former seems more sensitive than the later to leak of the ephemeral secret (which the question names ephemeral key). But in both cases the short answer is yes, and addressed elsewhere; there for ECDSA. Also: the question is unrelated to encryption. $\endgroup$
    – fgrieu
    Jan 10 '20 at 17:29
  • $\begingroup$ @fgrieu Thank you. I confused secp256k1 with ECDSA. I have edited the answer to fix this $\endgroup$ Jan 10 '20 at 23:39
  • $\begingroup$ The static keys are usually used for signatures, and the ephemeral keys for encryption. Anyways, is the signature key not the private key?? $\endgroup$
    – SamG101
    Jan 13 '20 at 8:30

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