Digital signature schemes often use domain parameters such as prime numbers or elliptic curves. They can be subject to security threats when they are not treated like public keys. In this paper we formalize the notion of "signature scheme with domain parameter" together with a new adversarial model: the "domain parameter shifting attack". We take ECDSA as a case study. We make a domain parameter shifting attack against ECDSA: an attacker can impersonate a honest signer either by trying to modify the subgroup generator G or, when using point compression representation, by trying to modify the elliptic curve a and b domain parameters. We further propose to fix this ECDSA issue.