# Message mapping to elliptic curve in BLS signature

In the BLS signature the subgroup $$G$$ of elliptic curve constructed with point $$P$$ with prime order $$q$$ by $$G=\langle P\rangle$$. The $$h(x)$$ is a hash function. The point $$S$$ is map (image) of $$h(m)$$ on elliptic curve. The signature is multiplying the private key in the point $$S$$.

Is the point $$S$$, also in $$G$$ and a multiple of point $$P$$ such as $$kP$$?

• "The point $S$ is a map..." What do you mean by this? Sep 16, 2020 at 19:28

It depends on whether the pairing is a type 1 pairing or some other type of pairing. In a type 1 pairing, $$S$$ is a multiple of $$P$$. In any other type of pairing, $$S$$ is not a multiple of $$P$$.