Score:1

Is it possible to recover the private key if the same message is signed twice with different nonce?

nz flag

Sorry if this question is misguided, I'm a software developer and not a cryptographer.

Let's say I have a public key, and 2 signed messages.

Signed message 1:

message_hash_1
signature_1.r
signature_1.s

Signed message 2:

message_hash_2
signature_2.r
signature_2.s

Assumptions:

message_hash_1 == message_hash_2
signature_1.r != signature_2.r
signature_1.s != signature_2.s

I've read in https://www.bertcmiller.com/2021/12/28/glimpse_nonce_reuse.html that it is possible to recover the private key if r is the same across the signed messages, but s is different.

Is it possible to recover the private key if the message_hash is the same, but signature_1.r/signature_2.r and signature_1.s/signature_2.r are both different? So the nonce with which the message was signed was different, but the message and private key were the same across both signatures.

I'm using NIST P-256 elliptic curve.

kelalaka avatar
in flag
For ECDSA we have a dupe for this. could you search for it? in one minute..
nz flag
Awesome, thanks!
kelalaka avatar
in flag
Welcome. You might be interested in these, too. 1) [secp256k1: is it theoretically possible to generate same signature with different key, message hash and k?](https://crypto.stackexchange.com/q/89809/18298) 2) [How does the "biased-k attack" on (EC)DSA work?](https://crypto.stackexchange.com/q/44644/18298)
kelalaka avatar
in flag
Here a +1 for you as a fast accept and don't forget to upvote the helpful answers on your cause.
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