Quote from: peakyclin77 on Today at 01:00:12 PM

Alright, thank you for your help. I managed to recover the dB key!

It turns out it was using the same K, but actually -K (so the same R, but with a negative K).

Now, I’ve identified other pairs of signatures (P2PKH addresses) that reuse the same R, but with different private keys, and I don’t know the values of the private keys or K in these cases.
These addresses seem to be related to the ones I just recovered, so likely generated in a similar context.

This time, I suspect that K is large.

So my question is: what would be the best approach to try sweeping these addresses and recovering the private keys?

Thanks in advance for your insights!

Well done on using -K to recover the key, it's a small but crucial detail the best course of action now depends on your assumptions about the nonce K you have discovered other signature pairs that reuse the same R (same r in the signature), but with different private keys and unknown K to create a relationship between the two private keys, you can set up the ECDSA equations and remove K if the same R appears in multiple messages in particular, you can derive an equation involving s1, s2, z1, z2, d1, and d2 for two signatures using the same r but different messages and private keys because s = k ^-1(z + r·d) mod n under some presumptions, such as small key theory, this can be rearranged into a two-variable equation Lattice attacks—such as LLL or Coppersmith's method can be used to resolve discrepancies or known structures. You can use d = (s·k - z)·r^-1 mod n to compute the corresponding private key if you suspect that K is reused exactly (or as -K, K + c, etc.) then, you can verify that the derived public key corresponds to the target address. You may also think about examining the entropy or structure of the nonces used if K is big but originates from a weak PRNG or predictable pattern, particularly if these signatures are from the same wallet or buggy implementation the best course of action is to look for nonce reuse patterns, create equations between the private keys, and then use algebraic or lattice-based methods to recover them