Edit in JSFiddle

// Canvas Drawing Pad
;(function($){
  var app = this.app || (this.app={});

  var canvas = $('canvas');

  var drawingPad = app.drawingPad = {
    context: canvas[0].getContext('2d'),
    drawLine: function(x1, y1, x2, y2, thickness, strokeStyle) {
      this.context.beginPath();
      this.context.moveTo(x1,y1);
      this.context.lineTo(x2,y2);
      this.context.lineWidth = thickness || 1;
      this.context.strokeStyle = strokeStyle || "#222";
      this.context.stroke();
    }
  };

  // interaction
  (function(){
    var isDrawing = false;
    var startX = startY = 0;

    // Pen Down
    canvas.bind('touchstart mousedown', function(e){
      isDrawing = true;
      if (e.originalEvent.touches) { // touch device
        var mouseX = e.originalEvent.touches[0].pageX - canvas.offset().left;
        var mouseY = e.originalEvent.touches[0].pageY - canvas.offset().top;
      } else { // mouse device
        var mouseX = e.pageX - canvas.offset().left;
        var mouseY = e.pageY - canvas.offset().top;
      }
      startX = mouseX;
      startY = mouseY;
    });

    // Pen Move
    canvas.bind('touchmove mousemove', function(e){
      if (isDrawing)
      {
        if (e.originalEvent.touches) { // touch device
          var mouseX = e.originalEvent.touches[0].pageX - canvas.offset().left;
          var mouseY = e.originalEvent.touches[0].pageY - canvas.offset().top;
        } else { // mouse device
          var mouseX = e.pageX - canvas.offset().left;
          var mouseY = e.pageY - canvas.offset().top;
        }
        drawingPad.drawLine(startX, startY, mouseX, mouseY, 3);
        drawingPad.drawLine(320-startX, startY, 320-mouseX, mouseY, 3);
        startX = mouseX;
        startY = mouseY;
      }
    });

    // Pen Up
    canvas.bind('touchend mouseup', function(e) {
      isDrawing = false;
    });
  })();

}).call(this, jQuery);

<canvas id='canvas' width='300' height='300'></canvas>

body {
    margin: 0;
    padding: 0;
}
canvas {
  border: 1px solid #666;
}