# Finding the private key with the transaction signature [duplicate]

I have two ETH transactions (both belonging to the same address) that both have the same r value in the transaction signature, is it possible to extract the private key from it? Details of both transactions below:

transaction hash(1): 0x374180005946ef3b1906ee1677f85fa62eb5a834aa0241b4c9c74174bca26a07

r: 0x41d43fd626c24e449ac54257eeff271edb438bbabbc9bee3d60a5bd78dc39d6d

s: 0x0f8062db22b4f8b654c01d6114616c1a7972453ab509a5fe5192a8ae28d7f351 —————————————————————- transaction hash(2): 0x670f66ff71882ae35436cd399adf57805745177b465fdb44a60b31b7c32e4d16

r: 0x41d43fd626c24e449ac54257eeff271edb438bbabbc9bee3d60a5bd78dc39d6d

s: 0x796fd3c7e31cb6f799d00d5a4c63185baa70e2ba10a7104a3a48d43d82738ef9

• "I have two ETH transactions (both belonging to the same address) that both have the same r value in the transaction signature, is it possible to extract the private key from it?" is directly about an on-topic cryptographic problem; but it's a duplicate. The values of the hashes and signatures are off-topic, per policy on questions consisting mostly of ciphertext/values.
– fgrieu
Oct 20, 2022 at 6:40

As the standard notes, it is not only required for $$k$$ to be secret, but it is also crucial to select different $$k$$ for different signatures, otherwise the equation in step 6. can be solved for $$d_A$$, the private key: given two signatures $$(r,s)$$ and $$(r, s')$$, employing the same unknown $$k$$ for different known messages $$m$$ and $$m'$$, an attacker can calculate $$z$$ and $$z'$$, and since $$s-s' = k^{-1}(z-z')$$ (all operations in this paragraph are done modulo $$n$$) the attacker can find $$k = \frac{z-z'}{s-s'}$$. Since $$s = k^{-1}(z + rd_A)$$, the attacker can now calculate the private key $$d_A = \frac{sk - z}{r}$$.