As Peter Wuille [mentions here](https://bitcoin.stackexchange.com/questions/38351/ecdsa-v-r-s-what-is-v/38909#comment46061_38909), the ECDSA signature values (r, s) are modulo `N` (eg verifying ECDSA signatures, where `u1 = z * w % N`), whereas the rest of the ECDSA functionality in Bitcoin seems to be modulo **`P`**.

Why is this so?