# Why create a subkey in the digital signature algorithm

In the signing step, wikipedia, a subkey is created.

A key k is randomly chosen from 1..q-1.


What's the use of that k?

If the k is to make less exposure to the private x; however, x is inevitably used in the signing part when computing s.

• That's not a subkey. That's simply the randomness used in the signing process. – Maeher May 27 at 14:09
• I guess any answer that explains the reason for $k$ would suffice. I think we can agree with Maeher that $k$ is not a subkey. Something about security and calculation of the private key giving separate signatures, I predict. – Maarten Bodewes May 27 at 14:42

What's the use of that k?

The following lines of the wiki tell you:

Compute $$r := ( g^k \bmod p ) \bmod q$$

Compute $$s := ( k^{−1} ( H(m) + xr ) ) \bmod q$$

That is, it is used to compute both $$r$$ and $$s$$.