# ECDSA - why is the first part of the signature used in the second?

Using the terminology of https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm

Why is the second part of the ECDSA signature defined as:

$$s = k^{-1}(z+rd_A)\text{ mod n}$$

Could the scheme not work just as well without multiplying $$d_A$$ by $$r$$?

In other words we would have:

$$s = k^{-1}(z+d_A)\text{ mod n}$$

• Hint: how would you proceed with verification of a signature? – fgrieu Feb 25 '19 at 15:12
• (again using terminology of wikipedia) would just define $u_2 = w$ (instead of $u_2 = rw$) and should work no? – Yoni Berger Feb 26 '19 at 7:42