Not sure this might help you,
I wrote this code from scratch in few minutes.
Though it isn't very smooth, but please give it a try
markup :
<canvas id="canvas"></canvas>
JavaScript :
window.onload = function() {
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 ;
this.color = rgb();
}, 0);
canvas.addEventListener('mouseup', function() {
this.down = false;
}, 0);
canvas.addEventListener('mousemove', function(e) {
this.style.cursor = 'pointer';
if(this.down) {
with(ctx) {
beginPath();
moveTo(this.X, this.Y);
lineTo(e.pageX , e.pageY );
strokeStyle = this.color;
stroke();
}
this.X = e.pageX ;
this.Y = e.pageY ;
}
}, 0);
function rgb() {
color = 'rgb(';
for(var i = 0; i< 3; i++) {
color += Math.floor(Math.random() * 255)+',';
}
return color.replace(/\,$/,')')
}
};
Test this code http://jsbin.com/ateho3