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calculator.html
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<html>
<head>
<title>Elliptic curve calculator</title>
<meta charset=utf-8 />
<meta http-equiv=“Pragma” content=”no-cache”>
<meta http-equiv=“Expires” content=”-1″>
<meta http-equiv=“CACHE-CONTROL” content=”NO-CACHE”>
<meta name="keywords" content="bitcoin,ecdsa,example,calculations,math">
<meta name="author" content="Willem Hengeveld, [email protected]">
<meta name="description" content="Elliptic curve calculator.">
<style>
h2 { background-color: lightgreen; }
</style>
<script src="bignum.js"></script>
<script src="gfp.js"></script>
<script src="ec.js"></script>
<script src="ecdsa.js"></script>
<script src="utils.js"></script>
<script src="jsutils.js"></script>
<script src="bccurve.js"></script>
<script src="expression.js"></script>
<script language=javascript>
'use strict';
var B = secp256k1();
function setvalue(base, id, value)
{
var av = base.querySelector("#"+id);
av.value = value;
av.innerHTML = value;
}
function getnumber(base, id)
{
var av = base.querySelector("#"+id);
if (!av)
throw "invalid selector";
var val = av.value;
if (!val)
return B.scalar(BigInt(0));
if (!val.startsWith("0x"))
val = "0x" + val;
return B.scalar(BigInt(val));
}
class ECContext {
constructor()
{
this.constants = { G: B.G, n: B.ec.order.p, p: B.ec.field.p };
// the current variables
this.d = {};
}
// functions evaluating the various operators
add(a, b) {
if ((a instanceof Point && b instanceof Point)
|| (a instanceof Value && b instanceof Value))
return a.add(b);
throw "You can only add points to points, or scalars to scalars";
}
sub(a, b) {
if ((a instanceof Point && b instanceof Point)
|| (a instanceof Value && b instanceof Value))
return a.sub(b);
throw "You can only subtract points from points, or scalars from scalars";
}
mul(a, b) {
if (a instanceof Point && b instanceof Point)
throw "points cannot be multiplied together";
// 'scalar * point' is the same as 'point * scalar'
if (b instanceof Point)
return b.mul(a);
// handles both 'scalar * scalar', and 'point * scalar'
return a.mul(b);
}
div(a, b) {
if (b instanceof Point)
throw "You cannot divide by a point";
return a.div(B.scalar(b));
}
pow(a, b) {
if (a instanceof Point || b instanceof Point)
throw "You cannot exponentiate Points";
// todo: make sure 2^(-1) translates to 1/2
// todo: make sure 2^(1/2) translates to sqrt(2)
return a.pow(b);
}
// the builtin functions
sqrt(a, flag) {
// todo: sometimes this results in a negative number.
return a.sqrt(Number(numval(flag)));
}
cubert(a, flag) { return a.cubert(Number(numval(flag))); }
coord(a) { return B.ec.coord(a); }
fromx(x, flag) { return B.ec.decompress(B.ec.coord(x), Number(numval(flag))); }
fromy(y, flag) { return B.ec.ydecompress(B.ec.coord(y), Number(numval(flag))); }
generate(start, n, expr) {
if (!["inc", "dbl"].includes(expr))
throw "generate must have either \"inc\", or \"dbl\" as its third argument.";
// generate start, start+G, start+2*G, ...
// todo: make it possible to pass expressions as a lambda.
n = numval(n);
var P = start;
var r = [];
for (var i=0 ; i < n ; i++) {
r.push(P);
if (expr==="inc")
P = P.add(B.G);
else if (expr==="dbl")
P = P.add(P);
}
return r;
}
// function for evaluating a number
numbervalue(a) { return B.scalar(BigInt(a)); }
// function for evaluating a string
textvalue(a) { return a; }
// function for evaluating a list
listvalue(t, a) {
// "(x, y)" evaulates to a curve point
if (a.length==2 && t=="()")
return B.ec.point(a[0], a[1]);
throw "value not supported";
}
get(name) {
if (name in this.constants)
return this.constants[name];
var parts = name.split(".");
if (parts.length==2)
return this.getfrompage(parts[0], parts[1]);
if (!(name in this.d))
this.d[name] = 0;
return this.d[name];
}
getfrompage(tabname, itemname)
{
var tab = document.getElementById(tabname);
return getnumber(tab, itemname);
}
// variable assignment
set(name, value)
{
if (name in this.constants) {
console.log("cannot change constant");
return;
}
var parts = name.split(".");
if (parts.length==2)
return this.setinpage(parts[0], parts[1], value);
this.d[name] = value;
}
setinpage(tabname, itemname, value)
{
var tab = document.getElementById(tabname);
var txt = null;
if (value instanceof Point)
txt = value.toString();
else if (value instanceof Value)
txt = value.toString();
else if (value)
console.log("unhandled: " ,value);
if (txt)
setvalue(tab, itemname, txt);
}
// TODO: change naming convention for points, so I can refer to a point like 'divpt.p1'
// which will then implicitly refer to (divpt.p1.x, divpt.p1.y)
};
var CTX = new ECContext();
function load_freeform()
{
var tab = document.getElementById("freeform");
setvalue(tab, "expr", [
"fromx(coord(0)-coord(3),0)",
"P=fromx(6,1)+fromx(2,0)",
"P/2",
"1/5"].join("\n"));
}
function makerow(k, v)
{
var tr = el('tr');
tr.append(el('td', k));
tr.append(el('td', v));
return tr;
}
function eval_expr(expr)
{
var e;
try {
e = parseexpr(expr);
console.log(e.toString());
}
catch(err) {
return "Error parsing expression: "+err.toString();
}
var r;
try {
r = evaluator(e, CTX);
}
catch(err) {
return "Error evaluating expression: "+err.toString();
}
var txt = null;
if (r instanceof Point)
txt = r.toString();
else if (r instanceof Value)
txt = r.toString();
else if (r instanceof Array) {
var res = "";
r.forEach( v => res += v.toString() + "\n" );
txt = res;
}
else if (r)
console.log(r);
return txt;
}
function make_url_for_expr(expr)
{
var baseurl = window.location.protocol + "//" + window.location.host + "/" + window.location.pathname;
return baseurl + "#" + btoa(expr);
}
function do_freeform()
{
var tab = document.getElementById("freeform");
var expr = tab.querySelector("#expr").value;
var href = tab.querySelector("#href");
href.href = make_url_for_expr(expr);
var results = [];
for (var e of expr.split("\n")) {
let r = eval_expr(e);
if (r)
results.push(r);
}
var otab = document.getElementById("output");
var bodies = [];
if (results) {
var tbody = el('tbody');
tbody.append(el('tr', el('td', el('hr'))));
results.forEach( txt => tbody.append(makerow("result:", txt)));
bodies.push(tbody);
}
var tbody = el('tbody');
Object.entries(CTX.d).forEach(([k,v])=>{tbody.append(makerow(k, v.toString())); });
bodies.push(tbody);
otab.replaceChildren(...bodies);
}
function start()
{
var tab = document.getElementById("freeform");
var expr = tab.querySelector("#expr");
var h = window.location.hash;
if (h.startsWith("#"))
h = h.slice(1);
expr.value = atob(h);
}
</script>
</head>
<body onLoad="start()">
Menu:
<a href="ecdsacrack.html">crack demo</a>
<a href="linearequations.html">using linear algebra</a>
<a href="calculator.html">curve calculator</a>
<a href="curve.html">curve demo</a>
<a href="transaction.html">bitcoin transaction</a>
<a href="unittest.html">unittest</a><br>
Author: Willem Hengeveld, <a href="mailto:[email protected]">[email protected]</a>,
Source: <a href="https://github.com/nlitsme/bitcoinexplainer">on github</a>.
<p>
Enter any kind of expression to do elliptic curve calculations. one expression per line. You can assign expressions to variables, which will be remembered.
You can also save a link to the calculation.
<br>
Calculations on numbers are done modulo the grouporder, Calculations on points are done in the <a href="https://en.bitcoin.it/wiki/Secp256k1">secp256k1</a> curve.
<br>
<br>
Predefined constants:
<ul>
<li><em>G</em> - the generator.
<li><em>n</em> - the group order.
<li><em>p</em> - the curve prime order.
</ul>
functions:
<ul>
<li><em>sqrt(value, flag)</em> - the square root, a number and a flag 0 or 1
<li><em>cubert(value, flag)</em> - the cube root, takes two params, a number and a flag 0, 1 or 2
<li><em>coord(value)</em> - force a value to be a coordinate, in the galois field of order <em>p</em>
<li><em>scalar(value)</em> - force a value to be a coordinate, in the galois field of order <em>n</em>
<li><em>fromx(xcoord, flag)</em> - 'decompress' a point from a x coord and a flag{0,1}.
<li><em>fromy(ycoord, flag)</em> - 'decompress' a point from a y coord and a flag{0,1,2}.
<li><em>generate(point, count, type)</em> - generate a sequence of curve points, type must be "inc" ( increment point ) or "dbl" (double point)
<li><em>(x,y)</em> - a curve point.
<li><em>1234</em> - a scalar value.
<li><em>0xabcd</em> - a hexadecimal scalar value.
</ul>
operators:
<ul>
<li><em>+</em> - addition: Point+Point, Scalar+Scalar
<li><em>-</em> - subtraction: Point-Point, Scalar-Scalar
<li><em>*</em> - multiplication: Point*Scalar, Scalar*Point, Scalar*Scalar
<li><em>/</em> - division: Point/Scalar, Scalar/Scalar
<li><em>^</em> - exponentiation: Scalar^Scalar
</ul>
<p>
<h2>Free form expressions.</h2>
<table id=freeform>
<tr>
<td valign=top>
<button onclick='do_freeform()'>calculate</button><br>
<button onclick='load_freeform()'>Load example</button><br>
<a id=href href=#>link this calculation</a><br>
</td>
<td><textarea rows=10 cols=80 id='expr'></textarea></td>
</tr>
</table>
<table id=output>
</table>
</body>
</html>