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I have an error in reasoning regarding to the calculations on elliptic curves. The basic group operations are all calculated mod p. Ok right.
Then I construct for ECC a discrete logarithm problem with the point multiplication in a cyclic group. But why do I have do calculate in ECDSA everything mod q (order of the cyclic group) and not mod p (modulus)?
Are they seperate operations and not associated with each other?
And why is the modulus a domain parameter of an elliptic curve for ECDSA when I actually don't calculate mod p?