Draw on a Canvas via mouse and touch

I want to draw on a canvas, works great with a mouse, but how do I have to modify the code to make it run on iPad or Nexus as well?

link

 var canvas = document.getElementById('canvas');
    var ctx = canvas.getContext('2d');
    var width  = window.innerWidth;
    var height = window.innerHeight;
    canvas.height = height;
    canvas.width = width;

    canvas.addEventListener('mousedown', function(e) {
        this.down = true;   
        this.X = e.pageX ;
        this.Y = e.pageY ;
    }, 0);

    canvas.addEventListener('mouseup', function() {
        this.down = false;          
    }, 0);

    canvas.addEventListener('mousemove', function(e) {
      
        if(this.down) {
             with(ctx) {
                beginPath();
                moveTo(this.X, this.Y);
                lineTo(e.pageX , e.pageY );
                ctx.lineWidth=1;
                stroke();
             }
             this.X = e.pageX ;
             this.Y = e.pageY ;
        }
    }, 0);