> If you have a secure hash function taking some string into a point of elliptic curve E, multiplying said point by the cofactor is also a secure hash function

> If you have a secure hash function taking some string into a point of elliptic curve E, multiplying said point by the cofactor is also a secure hash function into the relevant subgroup of E. Fair enough. Though this requires an additional multiplication (at least it's a cheap one). I'm pretty sure some protocols have missed this.