hash function for elliptic curve co-ordinates Is there any hash function which takes the co-ordinates of an elliptic curve $E_p(a,b)$ as input and gives an integer value i.e.

$h(.) : \{(x,y) \in E_p(a,b)\} \rightarrow \mathbb{Z}$
Let $k$ denote the bit-size of $p$.  Let also a hash function $H \colon \{0,1\}^{2k} \to \{0,1\}^\ell$.  We define the hash value of a point $P = (x,y)$ on an elliptic curve over $\mathbb{F}_p$ as
$$h \colon E_p(a,b) \to \mathbb{Z}, (x,y) \mapsto H(x + 2^k y)$$

One-wayness follows from hash function $H$ (for example SHA-3).

Note. There is a slight abuse of notation above, integer $x+2^ky$ should be seen as a binary string when applying hash function $H$; and the output (namely, $H(x + 2^k y)$) should be regarded as an integer.  This is done by the canonical representation: a $t$-bit integer $a \in \mathbb{Z}$ can uniquely be represented as $a = \sum_{i=0}^{t-1} a_i 2^i$ with $a_i \in \{0,1\}$, which in turn can be seen as the $t$-bit binary string $a_{t-1}a_{t-2}\ldots a_0$, and conversely.