Address validation

6 files changed, 1336 insertions, 9 deletions

diff --git a/public/js/2.5.3-crypto-sha256.js b/public/js/2.5.3-crypto-sha256.js
new file mode 100644
index 00000000..277152e7
--- /dev/null
+++ b/public/js/2.5.3-crypto-sha256.js
@@ -0,0 +1,14 @@
+/*
+ * Crypto-JS v2.5.3
+ * http://code.google.com/p/crypto-js/
+ * (c) 2009-2012 by Jeff Mott. All rights reserved.
+ * http://code.google.com/p/crypto-js/wiki/License
+ */
+(typeof Crypto=="undefined"||!Crypto.util)&&function(){var f=window.Crypto={},l=f.util={rotl:function(b,a){return b<<a|b>>>32-a},rotr:function(b,a){return b<<32-a|b>>>a},endian:function(b){if(b.constructor==Number)return l.rotl(b,8)&16711935|l.rotl(b,24)&4278255360;for(var a=0;a<b.length;a++)b[a]=l.endian(b[a]);return b},randomBytes:function(b){for(var a=[];b>0;b--)a.push(Math.floor(Math.random()*256));return a},bytesToWords:function(b){for(var a=[],c=0,d=0;c<b.length;c++,d+=8)a[d>>>5]|=(b[c]&255)<<
+24-d%32;return a},wordsToBytes:function(b){for(var a=[],c=0;c<b.length*32;c+=8)a.push(b[c>>>5]>>>24-c%32&255);return a},bytesToHex:function(b){for(var a=[],c=0;c<b.length;c++)a.push((b[c]>>>4).toString(16)),a.push((b[c]&15).toString(16));return a.join("")},hexToBytes:function(b){for(var a=[],c=0;c<b.length;c+=2)a.push(parseInt(b.substr(c,2),16));return a},bytesToBase64:function(b){if(typeof btoa=="function")return btoa(g.bytesToString(b));for(var a=[],c=0;c<b.length;c+=3)for(var d=b[c]<<16|b[c+1]<<
+8|b[c+2],p=0;p<4;p++)c*8+p*6<=b.length*8?a.push("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/".charAt(d>>>6*(3-p)&63)):a.push("=");return a.join("")},base64ToBytes:function(b){if(typeof atob=="function")return g.stringToBytes(atob(b));for(var b=b.replace(/[^A-Z0-9+\/]/ig,""),a=[],c=0,d=0;c<b.length;d=++c%4)d!=0&&a.push(("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/".indexOf(b.charAt(c-1))&Math.pow(2,-2*d+8)-1)<<d*2|"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/".indexOf(b.charAt(c))>>>
+6-d*2);return a}},f=f.charenc={};f.UTF8={stringToBytes:function(b){return g.stringToBytes(unescape(encodeURIComponent(b)))},bytesToString:function(b){return decodeURIComponent(escape(g.bytesToString(b)))}};var g=f.Binary={stringToBytes:function(b){for(var a=[],c=0;c<b.length;c++)a.push(b.charCodeAt(c)&255);return a},bytesToString:function(b){for(var a=[],c=0;c<b.length;c++)a.push(String.fromCharCode(b[c]));return a.join("")}}}();
+(function(){var f=Crypto,l=f.util,g=f.charenc,b=g.UTF8,a=g.Binary,c=[1116352408,1899447441,3049323471,3921009573,961987163,1508970993,2453635748,2870763221,3624381080,310598401,607225278,1426881987,1925078388,2162078206,2614888103,3248222580,3835390401,4022224774,264347078,604807628,770255983,1249150122,1555081692,1996064986,2554220882,2821834349,2952996808,3210313671,3336571891,3584528711,113926993,338241895,666307205,773529912,1294757372,1396182291,1695183700,1986661051,2177026350,2456956037,2730485921,
+2820302411,3259730800,3345764771,3516065817,3600352804,4094571909,275423344,430227734,506948616,659060556,883997877,958139571,1322822218,1537002063,1747873779,1955562222,2024104815,2227730452,2361852424,2428436474,2756734187,3204031479,3329325298],d=f.SHA256=function(b,c){var e=l.wordsToBytes(d._sha256(b));return c&&c.asBytes?e:c&&c.asString?a.bytesToString(e):l.bytesToHex(e)};d._sha256=function(a){a.constructor==String&&(a=b.stringToBytes(a));var d=l.bytesToWords(a),e=a.length*8,a=[1779033703,3144134277,
+1013904242,2773480762,1359893119,2600822924,528734635,1541459225],f=[],g,m,q,i,n,o,r,s,h,k,j;d[e>>5]|=128<<24-e%32;d[(e+64>>9<<4)+15]=e;for(s=0;s<d.length;s+=16){e=a[0];g=a[1];m=a[2];q=a[3];i=a[4];n=a[5];o=a[6];r=a[7];for(h=0;h<64;h++){h<16?f[h]=d[h+s]:(k=f[h-15],j=f[h-2],f[h]=((k<<25|k>>>7)^(k<<14|k>>>18)^k>>>3)+(f[h-7]>>>0)+((j<<15|j>>>17)^(j<<13|j>>>19)^j>>>10)+(f[h-16]>>>0));j=e&g^e&m^g&m;var t=(e<<30|e>>>2)^(e<<19|e>>>13)^(e<<10|e>>>22);k=(r>>>0)+((i<<26|i>>>6)^(i<<21|i>>>11)^(i<<7|i>>>25))+
+(i&n^~i&o)+c[h]+(f[h]>>>0);j=t+j;r=o;o=n;n=i;i=q+k>>>0;q=m;m=g;g=e;e=k+j>>>0}a[0]+=e;a[1]+=g;a[2]+=m;a[3]+=q;a[4]+=i;a[5]+=n;a[6]+=o;a[7]+=r}return a};d._blocksize=16;d._digestsize=32})();
diff --git a/public/js/calculator.coffee b/public/js/calculator.coffee
index 3d1d61b4..7e01e504 100644
--- a/public/js/calculator.coffee
+++ b/public/js/calculator.coffee
@@ -2,8 +2,15 @@
 #= require moment.min.js
 #= require qr.js
 #= require bootstrap.min.js
+#= require 2.5.3-crypto-sha256.js
+#= require jsbn.js
+#= require jsbn2.js
+#= require check_address.js
 
 g = exports ? this
+EXCHANGE_FAIL = "Error fetching exchange rate"
+SOCKET_FAIL = "Error connecting to payment server"
+ADDRESS_FAIL = "Invalid address"
 
 $(->
   g.websocket = null
@@ -21,8 +28,10 @@ $(->
 
   if user? and user
     $.getJSON(user + '.json', (data) ->
+      return unless data?
       g.name = data.name
       g.address = data.address 
+      g.symbol = data.symbol
       g.commission = data.commission 
       g.logo = data.logo 
       setupPage()
@@ -50,7 +59,7 @@ updateTotal = ->
   displayQR('bitcoin:' + g.address + '?amount=' + total.toString())
 
 exchangeFail = ->
-  $('#error').show().html("Error fetching exchange rate")
+  $('#error').show().html(EXCHANGE_FAIL)
   $('#calculator').hide()
 
 fetchExchangeRate = ->
@@ -66,11 +75,22 @@ fetchExchangeRate = ->
       $('#exchange').val(g.exchange.toFixed(2))
       updateTotal()
 
-      $('#error').hide()
-      $('#calculator').fadeIn('slow')
+      clear(EXCHANGE_FAIL)
+
+      if $('#error').html() is ""
+        $('#error').hide()
+        $('#calculator').fadeIn('slow')
   ).error(exchangeFail)
   setTimeout(fetchExchangeRate, 900000)
 
+fail = (err) ->
+  $('#calculator').hide()
+  $('#error').html(err).show()
+  
+clear = (msg) ->
+  if $('#error').html() is msg
+    $('#error').html("")
+
 setupPage = ->
   g.address or= '1VAnbtCAnYccECnjaMCPnWwt81EHCVgNr'
   g.commission or= 3
@@ -83,7 +103,11 @@ setupPage = ->
   else
     $('#name').html(g.name).show()
 
-  $('#address').html(g.address)
+  if check_address(g.address)
+    $('#address').html(g.address)
+  else
+    fail(ADDRESS_FAIL)
+    
   $('#symbol').html(g.symbol + " - " + commission.toFixed(0) + "%")
   $('#currency').html(g.symbol.slice(-3))
   $('#received').hide()
@@ -99,11 +123,8 @@ setupSocket = ->
     g.websocket.onopen = -> 
       g.websocket.send('{"op":"addr_sub", "addr":"' + g.address + '"}')
     
-
     g.websocket.onerror = g.websocket.onclose = ->
-      $('#calculator').hide()
-      $('#error').show().html("Error connecting to payment server")
-    
+      fail(SOCKET_FAIL)
 
     g.websocket.onmessage = (e) ->
       results = eval('(' + e.data + ')')
diff --git a/public/js/check_address.js b/public/js/check_address.js
new file mode 100644
index 00000000..0ec3de3c
--- /dev/null
+++ b/public/js/check_address.js
@@ -0,0 +1,66 @@
+BigInteger.valueOf = nbv;
+BigInteger.prototype.toByteArrayUnsigned = function () {
+    var ba = this.toByteArray();
+    if (ba.length) {
+        if (ba[0] == 0)
+            ba = ba.slice(1);
+        return ba.map(function (v) {
+            return (v < 0) ? v + 256 : v;
+        });
+    } else
+        return ba;
+};        
+var Bitcoin = {};
+(function () {
+    var B58 = Bitcoin.Base58 = {
+        alphabet: "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz",
+        base: BigInteger.valueOf(58),
+        decode: function (input) {
+            bi = BigInteger.valueOf(0);
+            var leadingZerosNum = 0;
+            for (var i = input.length - 1; i >= 0; i--) {
+                var alphaIndex = B58.alphabet.indexOf(input[i]);
+                if (alphaIndex < 0) {
+                    throw "Invalid character";
+                }
+                bi = bi.add(BigInteger.valueOf(alphaIndex)
+                .multiply(B58.base.pow(input.length - 1 - i)));
+                if (input[i] == "1") leadingZerosNum++;
+                else leadingZerosNum = 0;
+            }
+            var bytes = bi.toByteArrayUnsigned();
+            while (leadingZerosNum-- > 0) bytes.unshift(0);
+            return bytes;
+        }
+    };
+})();
+Bitcoin.Address = function (bytes) {
+    if ("string" == typeof bytes)
+        bytes = Bitcoin.Address.decodeString(bytes);
+    this.hash = bytes;
+    this.version = Bitcoin.Address.networkVersion;
+};
+Bitcoin.Address.networkVersion = 0x00; // mainnet
+Bitcoin.Address.decodeString = function (string) {
+    var bytes = Bitcoin.Base58.decode(string);
+    var hash = bytes.slice(0, 21);
+    var checksum = Crypto.SHA256(Crypto.SHA256(hash, { asBytes: true }), { asBytes: true });
+    if (checksum[0] != bytes[21] ||
+        checksum[1] != bytes[22] ||
+        checksum[2] != bytes[23] ||
+        checksum[3] != bytes[24])
+        throw "Checksum validation failed!";
+    var version = hash.shift();
+    if (version != 0)
+        throw "Version " + version + " not supported!";
+    return hash;
+};
+
+function check_address(address) {
+    try {
+        Bitcoin.Address(address);
+        return true;
+    } catch (err) {
+        return false;
+    }
+}
diff --git a/public/js/index.coffee b/public/js/index.coffee
index d832c4ed..a5821e90 100644
--- a/public/js/index.coffee
+++ b/public/js/index.coffee
@@ -1,9 +1,20 @@
 #= require jquery-1.8.2.min.js
+#= require 2.5.3-crypto-sha256.js
+#= require jsbn.js
+#= require jsbn2.js
+#= require check_address.js
 
 $(->
   symbols = ['mtgoxUSD', 'btceUSD', 'bitstampUSD', 'virwoxSLL', 'btcdeEUR', 'mtgoxEUR', 'btc24EUR', 'mtgoxAUD', 'cryptoxAUD', 'mtgoxGBP', 'btcnCNY', 'intrsngEUR', 'virtexCAD', 'mtgoxPLN', 'cbxUSD', 'bitcurexPLN', 'bitmarketEUR', 'bitfloorUSD', 'mrcdBRL', 'bcEUR']
 
   $.each(symbols, (i, v) ->
-    $('#symbol').append("<option>#{v}</option>")
+    $('#symbol').append("<option value='#{v}'>#{v}</option>")
+  )
+
+  $('#address').change(->
+    if check_address($(this).val())
+      $(this).css('color', 'black')
+    else
+      $(this).css('color', 'red')
   )
 )
diff --git a/public/js/jsbn.js b/public/js/jsbn.js
new file mode 100644
index 00000000..40bb9e2b
--- /dev/null
+++ b/public/js/jsbn.js
@@ -0,0 +1,559 @@
+// Copyright (c) 2005  Tom Wu
+// All Rights Reserved.
+// See "LICENSE" for details.
+
+// Basic JavaScript BN library - subset useful for RSA encryption.
+
+// Bits per digit
+var dbits;
+
+// JavaScript engine analysis
+var canary = 0xdeadbeefcafe;
+var j_lm = ((canary&0xffffff)==0xefcafe);
+
+// (public) Constructor
+function BigInteger(a,b,c) {
+  if(a != null)
+    if("number" == typeof a) this.fromNumber(a,b,c);
+    else if(b == null && "string" != typeof a) this.fromString(a,256);
+    else this.fromString(a,b);
+}
+
+// return new, unset BigInteger
+function nbi() { return new BigInteger(null); }
+
+// am: Compute w_j += (x*this_i), propagate carries,
+// c is initial carry, returns final carry.
+// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
+// We need to select the fastest one that works in this environment.
+
+// am1: use a single mult and divide to get the high bits,
+// max digit bits should be 26 because
+// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
+function am1(i,x,w,j,c,n) {
+  while(--n >= 0) {
+    var v = x*this[i++]+w[j]+c;
+    c = Math.floor(v/0x4000000);
+    w[j++] = v&0x3ffffff;
+  }
+  return c;
+}
+// am2 avoids a big mult-and-extract completely.
+// Max digit bits should be <= 30 because we do bitwise ops
+// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
+function am2(i,x,w,j,c,n) {
+  var xl = x&0x7fff, xh = x>>15;
+  while(--n >= 0) {
+    var l = this[i]&0x7fff;
+    var h = this[i++]>>15;
+    var m = xh*l+h*xl;
+    l = xl*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);
+    c = (l>>>30)+(m>>>15)+xh*h+(c>>>30);
+    w[j++] = l&0x3fffffff;
+  }
+  return c;
+}
+// Alternately, set max digit bits to 28 since some
+// browsers slow down when dealing with 32-bit numbers.
+function am3(i,x,w,j,c,n) {
+  var xl = x&0x3fff, xh = x>>14;
+  while(--n >= 0) {
+    var l = this[i]&0x3fff;
+    var h = this[i++]>>14;
+    var m = xh*l+h*xl;
+    l = xl*l+((m&0x3fff)<<14)+w[j]+c;
+    c = (l>>28)+(m>>14)+xh*h;
+    w[j++] = l&0xfffffff;
+  }
+  return c;
+}
+if(j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
+  BigInteger.prototype.am = am2;
+  dbits = 30;
+}
+else if(j_lm && (navigator.appName != "Netscape")) {
+  BigInteger.prototype.am = am1;
+  dbits = 26;
+}
+else { // Mozilla/Netscape seems to prefer am3
+  BigInteger.prototype.am = am3;
+  dbits = 28;
+}
+
+BigInteger.prototype.DB = dbits;
+BigInteger.prototype.DM = ((1<<dbits)-1);
+BigInteger.prototype.DV = (1<<dbits);
+
+var BI_FP = 52;
+BigInteger.prototype.FV = Math.pow(2,BI_FP);
+BigInteger.prototype.F1 = BI_FP-dbits;
+BigInteger.prototype.F2 = 2*dbits-BI_FP;
+
+// Digit conversions
+var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
+var BI_RC = new Array();
+var rr,vv;
+rr = "0".charCodeAt(0);
+for(vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
+rr = "a".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+rr = "A".charCodeAt(0);
+for(vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
+
+function int2char(n) { return BI_RM.charAt(n); }
+function intAt(s,i) {
+  var c = BI_RC[s.charCodeAt(i)];
+  return (c==null)?-1:c;
+}
+
+// (protected) copy this to r
+function bnpCopyTo(r) {
+  for(var i = this.t-1; i >= 0; --i) r[i] = this[i];
+  r.t = this.t;
+  r.s = this.s;
+}
+
+// (protected) set from integer value x, -DV <= x < DV
+function bnpFromInt(x) {
+  this.t = 1;
+  this.s = (x<0)?-1:0;
+  if(x > 0) this[0] = x;
+  else if(x < -1) this[0] = x+DV;
+  else this.t = 0;
+}
+
+// return bigint initialized to value
+function nbv(i) { var r = nbi(); r.fromInt(i); return r; }
+
+// (protected) set from string and radix
+function bnpFromString(s,b) {
+  var k;
+  if(b == 16) k = 4;
+  else if(b == 8) k = 3;
+  else if(b == 256) k = 8; // byte array
+  else if(b == 2) k = 1;
+  else if(b == 32) k = 5;
+  else if(b == 4) k = 2;
+  else { this.fromRadix(s,b); return; }
+  this.t = 0;
+  this.s = 0;
+  var i = s.length, mi = false, sh = 0;
+  while(--i >= 0) {
+    var x = (k==8)?s[i]&0xff:intAt(s,i);
+    if(x < 0) {
+      if(s.charAt(i) == "-") mi = true;
+      continue;
+    }
+    mi = false;
+    if(sh == 0)
+      this[this.t++] = x;
+    else if(sh+k > this.DB) {
+      this[this.t-1] |= (x&((1<<(this.DB-sh))-1))<<sh;
+      this[this.t++] = (x>>(this.DB-sh));
+    }
+    else
+      this[this.t-1] |= x<<sh;
+    sh += k;
+    if(sh >= this.DB) sh -= this.DB;
+  }
+  if(k == 8 && (s[0]&0x80) != 0) {
+    this.s = -1;
+    if(sh > 0) this[this.t-1] |= ((1<<(this.DB-sh))-1)<<sh;
+  }
+  this.clamp();
+  if(mi) BigInteger.ZERO.subTo(this,this);
+}
+
+// (protected) clamp off excess high words
+function bnpClamp() {
+  var c = this.s&this.DM;
+  while(this.t > 0 && this[this.t-1] == c) --this.t;
+}
+
+// (public) return string representation in given radix
+function bnToString(b) {
+  if(this.s < 0) return "-"+this.negate().toString(b);
+  var k;
+  if(b == 16) k = 4;
+  else if(b == 8) k = 3;
+  else if(b == 2) k = 1;
+  else if(b == 32) k = 5;
+  else if(b == 4) k = 2;
+  else return this.toRadix(b);
+  var km = (1<<k)-1, d, m = false, r = "", i = this.t;
+  var p = this.DB-(i*this.DB)%k;
+  if(i-- > 0) {
+    if(p < this.DB && (d = this[i]>>p) > 0) { m = true; r = int2char(d); }
+    while(i >= 0) {
+      if(p < k) {
+        d = (this[i]&((1<<p)-1))<<(k-p);
+        d |= this[--i]>>(p+=this.DB-k);
+      }
+      else {
+        d = (this[i]>>(p-=k))&km;
+        if(p <= 0) { p += this.DB; --i; }
+      }
+      if(d > 0) m = true;
+      if(m) r += int2char(d);
+    }
+  }
+  return m?r:"0";
+}
+
+// (public) -this
+function bnNegate() { var r = nbi(); BigInteger.ZERO.subTo(this,r); return r; }
+
+// (public) |this|
+function bnAbs() { return (this.s<0)?this.negate():this; }
+
+// (public) return + if this > a, - if this < a, 0 if equal
+function bnCompareTo(a) {
+  var r = this.s-a.s;
+  if(r != 0) return r;
+  var i = this.t;
+  r = i-a.t;
+  if(r != 0) return (this.s<0)?-r:r;
+  while(--i >= 0) if((r=this[i]-a[i]) != 0) return r;
+  return 0;
+}
+
+// returns bit length of the integer x
+function nbits(x) {
+  var r = 1, t;
+  if((t=x>>>16) != 0) { x = t; r += 16; }
+  if((t=x>>8) != 0) { x = t; r += 8; }
+  if((t=x>>4) != 0) { x = t; r += 4; }
+  if((t=x>>2) != 0) { x = t; r += 2; }
+  if((t=x>>1) != 0) { x = t; r += 1; }
+  return r;
+}
+
+// (public) return the number of bits in "this"
+function bnBitLength() {
+  if(this.t <= 0) return 0;
+  return this.DB*(this.t-1)+nbits(this[this.t-1]^(this.s&this.DM));
+}
+
+// (protected) r = this << n*DB
+function bnpDLShiftTo(n,r) {
+  var i;
+  for(i = this.t-1; i >= 0; --i) r[i+n] = this[i];
+  for(i = n-1; i >= 0; --i) r[i] = 0;
+  r.t = this.t+n;
+  r.s = this.s;
+}
+
+// (protected) r = this >> n*DB
+function bnpDRShiftTo(n,r) {
+  for(var i = n; i < this.t; ++i) r[i-n] = this[i];
+  r.t = Math.max(this.t-n,0);
+  r.s = this.s;
+}
+
+// (protected) r = this << n
+function bnpLShiftTo(n,r) {
+  var bs = n%this.DB;
+  var cbs = this.DB-bs;
+  var bm = (1<<cbs)-1;
+  var ds = Math.floor(n/this.DB), c = (this.s<<bs)&this.DM, i;
+  for(i = this.t-1; i >= 0; --i) {
+    r[i+ds+1] = (this[i]>>cbs)|c;
+    c = (this[i]&bm)<<bs;
+  }
+  for(i = ds-1; i >= 0; --i) r[i] = 0;
+  r[ds] = c;
+  r.t = this.t+ds+1;
+  r.s = this.s;
+  r.clamp();
+}
+
+// (protected) r = this >> n
+function bnpRShiftTo(n,r) {
+  r.s = this.s;
+  var ds = Math.floor(n/this.DB);
+  if(ds >= this.t) { r.t = 0; return; }
+  var bs = n%this.DB;
+  var cbs = this.DB-bs;
+  var bm = (1<<bs)-1;
+  r[0] = this[ds]>>bs;
+  for(var i = ds+1; i < this.t; ++i) {
+    r[i-ds-1] |= (this[i]&bm)<<cbs;
+    r[i-ds] = this[i]>>bs;
+  }
+  if(bs > 0) r[this.t-ds-1] |= (this.s&bm)<<cbs;
+  r.t = this.t-ds;
+  r.clamp();
+}
+
+// (protected) r = this - a
+function bnpSubTo(a,r) {
+  var i = 0, c = 0, m = Math.min(a.t,this.t);
+  while(i < m) {
+    c += this[i]-a[i];
+    r[i++] = c&this.DM;
+    c >>= this.DB;
+  }
+  if(a.t < this.t) {
+    c -= a.s;
+    while(i < this.t) {
+      c += this[i];
+      r[i++] = c&this.DM;
+      c >>= this.DB;
+    }
+    c += this.s;
+  }
+  else {
+    c += this.s;
+    while(i < a.t) {
+      c -= a[i];
+      r[i++] = c&this.DM;
+      c >>= this.DB;
+    }
+    c -= a.s;
+  }
+  r.s = (c<0)?-1:0;
+  if(c < -1) r[i++] = this.DV+c;
+  else if(c > 0) r[i++] = c;
+  r.t = i;
+  r.clamp();
+}
+
+// (protected) r = this * a, r != this,a (HAC 14.12)
+// "this" should be the larger one if appropriate.
+function bnpMultiplyTo(a,r) {
+  var x = this.abs(), y = a.abs();
+  var i = x.t;
+  r.t = i+y.t;
+  while(--i >= 0) r[i] = 0;
+  for(i = 0; i < y.t; ++i) r[i+x.t] = x.am(0,y[i],r,i,0,x.t);
+  r.s = 0;
+  r.clamp();
+  if(this.s != a.s) BigInteger.ZERO.subTo(r,r);
+}
+
+// (protected) r = this^2, r != this (HAC 14.16)
+function bnpSquareTo(r) {
+  var x = this.abs();
+  var i = r.t = 2*x.t;
+  while(--i >= 0) r[i] = 0;
+  for(i = 0; i < x.t-1; ++i) {
+    var c = x.am(i,x[i],r,2*i,0,1);
+    if((r[i+x.t]+=x.am(i+1,2*x[i],r,2*i+1,c,x.t-i-1)) >= x.DV) {
+      r[i+x.t] -= x.DV;
+      r[i+x.t+1] = 1;
+    }
+  }
+  if(r.t > 0) r[r.t-1] += x.am(i,x[i],r,2*i,0,1);
+  r.s = 0;
+  r.clamp();
+}
+
+// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
+// r != q, this != m.  q or r may be null.
+function bnpDivRemTo(m,q,r) {
+  var pm = m.abs();
+  if(pm.t <= 0) return;
+  var pt = this.abs();
+  if(pt.t < pm.t) {
+    if(q != null) q.fromInt(0);
+    if(r != null) this.copyTo(r);
+    return;
+  }
+  if(r == null) r = nbi();
+  var y = nbi(), ts = this.s, ms = m.s;
+  var nsh = this.DB-nbits(pm[pm.t-1]);	// normalize modulus
+  if(nsh > 0) { pm.lShiftTo(nsh,y); pt.lShiftTo(nsh,r); }
+  else { pm.copyTo(y); pt.copyTo(r); }
+  var ys = y.t;
+  var y0 = y[ys-1];
+  if(y0 == 0) return;
+  var yt = y0*(1<<this.F1)+((ys>1)?y[ys-2]>>this.F2:0);
+  var d1 = this.FV/yt, d2 = (1<<this.F1)/yt, e = 1<<this.F2;
+  var i = r.t, j = i-ys, t = (q==null)?nbi():q;
+  y.dlShiftTo(j,t);
+  if(r.compareTo(t) >= 0) {
+    r[r.t++] = 1;
+    r.subTo(t,r);
+  }
+  BigInteger.ONE.dlShiftTo(ys,t);
+  t.subTo(y,y);	// "negative" y so we can replace sub with am later
+  while(y.t < ys) y[y.t++] = 0;
+  while(--j >= 0) {
+    // Estimate quotient digit
+    var qd = (r[--i]==y0)?this.DM:Math.floor(r[i]*d1+(r[i-1]+e)*d2);
+    if((r[i]+=y.am(0,qd,r,j,0,ys)) < qd) {	// Try it out
+      y.dlShiftTo(j,t);
+      r.subTo(t,r);
+      while(r[i] < --qd) r.subTo(t,r);
+    }
+  }
+  if(q != null) {
+    r.drShiftTo(ys,q);
+    if(ts != ms) BigInteger.ZERO.subTo(q,q);
+  }
+  r.t = ys;
+  r.clamp();
+  if(nsh > 0) r.rShiftTo(nsh,r);	// Denormalize remainder
+  if(ts < 0) BigInteger.ZERO.subTo(r,r);
+}
+
+// (public) this mod a
+function bnMod(a) {
+  var r = nbi();
+  this.abs().divRemTo(a,null,r);
+  if(this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r,r);
+  return r;
+}
+
+// Modular reduction using "classic" algorithm
+function Classic(m) { this.m = m; }
+function cConvert(x) {
+  if(x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
+  else return x;
+}
+function cRevert(x) { return x; }
+function cReduce(x) { x.divRemTo(this.m,null,x); }
+function cMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+function cSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+Classic.prototype.convert = cConvert;
+Classic.prototype.revert = cRevert;
+Classic.prototype.reduce = cReduce;
+Classic.prototype.mulTo = cMulTo;
+Classic.prototype.sqrTo = cSqrTo;
+
+// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
+// justification:
+//         xy == 1 (mod m)
+//         xy =  1+km
+//   xy(2-xy) = (1+km)(1-km)
+// x[y(2-xy)] = 1-k^2m^2
+// x[y(2-xy)] == 1 (mod m^2)
+// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
+// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
+// JS multiply "overflows" differently from C/C++, so care is needed here.
+function bnpInvDigit() {
+  if(this.t < 1) return 0;
+  var x = this[0];
+  if((x&1) == 0) return 0;
+  var y = x&3;		// y == 1/x mod 2^2
+  y = (y*(2-(x&0xf)*y))&0xf;	// y == 1/x mod 2^4
+  y = (y*(2-(x&0xff)*y))&0xff;	// y == 1/x mod 2^8
+  y = (y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;	// y == 1/x mod 2^16
+  // last step - calculate inverse mod DV directly;
+  // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
+  y = (y*(2-x*y%this.DV))%this.DV;		// y == 1/x mod 2^dbits
+  // we really want the negative inverse, and -DV < y < DV
+  return (y>0)?this.DV-y:-y;
+}
+
+// Montgomery reduction
+function Montgomery(m) {
+  this.m = m;
+  this.mp = m.invDigit();
+  this.mpl = this.mp&0x7fff;
+  this.mph = this.mp>>15;
+  this.um = (1<<(m.DB-15))-1;
+  this.mt2 = 2*m.t;
+}
+
+// xR mod m
+function montConvert(x) {
+  var r = nbi();
+  x.abs().dlShiftTo(this.m.t,r);
+  r.divRemTo(this.m,null,r);
+  if(x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r,r);
+  return r;
+}
+
+// x/R mod m
+function montRevert(x) {
+  var r = nbi();
+  x.copyTo(r);
+  this.reduce(r);
+  return r;
+}
+
+// x = x/R mod m (HAC 14.32)
+function montReduce(x) {
+  while(x.t <= this.mt2)	// pad x so am has enough room later
+    x[x.t++] = 0;
+  for(var i = 0; i < this.m.t; ++i) {
+    // faster way of calculating u0 = x[i]*mp mod DV
+    var j = x[i]&0x7fff;
+    var u0 = (j*this.mpl+(((j*this.mph+(x[i]>>15)*this.mpl)&this.um)<<15))&x.DM;
+    // use am to combine the multiply-shift-add into one call
+    j = i+this.m.t;
+    x[j] += this.m.am(0,u0,x,i,0,this.m.t);
+    // propagate carry
+    while(x[j] >= x.DV) { x[j] -= x.DV; x[++j]++; }
+  }
+  x.clamp();
+  x.drShiftTo(this.m.t,x);
+  if(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
+}
+
+// r = "x^2/R mod m"; x != r
+function montSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+// r = "xy/R mod m"; x,y != r
+function montMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+
+Montgomery.prototype.convert = montConvert;
+Montgomery.prototype.revert = montRevert;
+Montgomery.prototype.reduce = montReduce;
+Montgomery.prototype.mulTo = montMulTo;
+Montgomery.prototype.sqrTo = montSqrTo;
+
+// (protected) true iff this is even
+function bnpIsEven() { return ((this.t>0)?(this[0]&1):this.s) == 0; }
+
+// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
+function bnpExp(e,z) {
+  if(e > 0xffffffff || e < 1) return BigInteger.ONE;
+  var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e)-1;
+  g.copyTo(r);
+  while(--i >= 0) {
+    z.sqrTo(r,r2);
+    if((e&(1<<i)) > 0) z.mulTo(r2,g,r);
+    else { var t = r; r = r2; r2 = t; }
+  }
+  return z.revert(r);
+}
+
+// (public) this^e % m, 0 <= e < 2^32
+function bnModPowInt(e,m) {
+  var z;
+  if(e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
+  return this.exp(e,z);
+}
+
+// protected
+BigInteger.prototype.copyTo = bnpCopyTo;
+BigInteger.prototype.fromInt = bnpFromInt;
+BigInteger.prototype.fromString = bnpFromString;
+BigInteger.prototype.clamp = bnpClamp;
+BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
+BigInteger.prototype.drShiftTo = bnpDRShiftTo;
+BigInteger.prototype.lShiftTo = bnpLShiftTo;
+BigInteger.prototype.rShiftTo = bnpRShiftTo;
+BigInteger.prototype.subTo = bnpSubTo;
+BigInteger.prototype.multiplyTo = bnpMultiplyTo;
+BigInteger.prototype.squareTo = bnpSquareTo;
+BigInteger.prototype.divRemTo = bnpDivRemTo;
+BigInteger.prototype.invDigit = bnpInvDigit;
+BigInteger.prototype.isEven = bnpIsEven;
+BigInteger.prototype.exp = bnpExp;
+
+// public
+BigInteger.prototype.toString = bnToString;
+BigInteger.prototype.negate = bnNegate;
+BigInteger.prototype.abs = bnAbs;
+BigInteger.prototype.compareTo = bnCompareTo;
+BigInteger.prototype.bitLength = bnBitLength;
+BigInteger.prototype.mod = bnMod;
+BigInteger.prototype.modPowInt = bnModPowInt;
+
+// "constants"
+BigInteger.ZERO = nbv(0);
+BigInteger.ONE = nbv(1);
diff --git a/public/js/jsbn2.js b/public/js/jsbn2.js
new file mode 100644
index 00000000..5b2b725c
--- /dev/null
+++ b/public/js/jsbn2.js
@@ -0,0 +1,656 @@
+// Copyright (c) 2005-2009  Tom Wu
+// All Rights Reserved.
+// See "LICENSE" for details.
+
+// Extended JavaScript BN functions, required for RSA private ops.
+
+// Version 1.1: new BigInteger("0", 10) returns "proper" zero
+// Version 1.2: square() API, isProbablePrime fix
+
+// (public)
+function bnClone() { var r = nbi(); this.copyTo(r); return r; }
+
+// (public) return value as integer
+function bnIntValue() {
+  if(this.s < 0) {
+    if(this.t == 1) return this[0]-this.DV;
+    else if(this.t == 0) return -1;
+  }
+  else if(this.t == 1) return this[0];
+  else if(this.t == 0) return 0;
+  // assumes 16 < DB < 32
+  return ((this[1]&((1<<(32-this.DB))-1))<<this.DB)|this[0];
+}
+
+// (public) return value as byte
+function bnByteValue() { return (this.t==0)?this.s:(this[0]<<24)>>24; }
+
+// (public) return value as short (assumes DB>=16)
+function bnShortValue() { return (this.t==0)?this.s:(this[0]<<16)>>16; }
+
+// (protected) return x s.t. r^x < DV
+function bnpChunkSize(r) { return Math.floor(Math.LN2*this.DB/Math.log(r)); }
+
+// (public) 0 if this == 0, 1 if this > 0
+function bnSigNum() {
+  if(this.s < 0) return -1;
+  else if(this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
+  else return 1;
+}
+
+// (protected) convert to radix string
+function bnpToRadix(b) {
+  if(b == null) b = 10;
+  if(this.signum() == 0 || b < 2 || b > 36) return "0";
+  var cs = this.chunkSize(b);
+  var a = Math.pow(b,cs);
+  var d = nbv(a), y = nbi(), z = nbi(), r = "";
+  this.divRemTo(d,y,z);
+  while(y.signum() > 0) {
+    r = (a+z.intValue()).toString(b).substr(1) + r;
+    y.divRemTo(d,y,z);
+  }
+  return z.intValue().toString(b) + r;
+}
+
+// (protected) convert from radix string
+function bnpFromRadix(s,b) {
+  this.fromInt(0);
+  if(b == null) b = 10;
+  var cs = this.chunkSize(b);
+  var d = Math.pow(b,cs), mi = false, j = 0, w = 0;
+  for(var i = 0; i < s.length; ++i) {
+    var x = intAt(s,i);
+    if(x < 0) {
+      if(s.charAt(i) == "-" && this.signum() == 0) mi = true;
+      continue;
+    }
+    w = b*w+x;
+    if(++j >= cs) {
+      this.dMultiply(d);
+      this.dAddOffset(w,0);
+      j = 0;
+      w = 0;
+    }
+  }
+  if(j > 0) {
+    this.dMultiply(Math.pow(b,j));
+    this.dAddOffset(w,0);
+  }
+  if(mi) BigInteger.ZERO.subTo(this,this);
+}
+
+// (protected) alternate constructor
+function bnpFromNumber(a,b,c) {
+  if("number" == typeof b) {
+    // new BigInteger(int,int,RNG)
+    if(a < 2) this.fromInt(1);
+    else {
+      this.fromNumber(a,c);
+      if(!this.testBit(a-1))	// force MSB set
+        this.bitwiseTo(BigInteger.ONE.shiftLeft(a-1),op_or,this);
+      if(this.isEven()) this.dAddOffset(1,0); // force odd
+      while(!this.isProbablePrime(b)) {
+        this.dAddOffset(2,0);
+        if(this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a-1),this);
+      }
+    }
+  }
+  else {
+    // new BigInteger(int,RNG)
+    var x = new Array(), t = a&7;
+    x.length = (a>>3)+1;
+    b.nextBytes(x);
+    if(t > 0) x[0] &= ((1<<t)-1); else x[0] = 0;
+    this.fromString(x,256);
+  }
+}
+
+// (public) convert to bigendian byte array
+function bnToByteArray() {
+  var i = this.t, r = new Array();
+  r[0] = this.s;
+  var p = this.DB-(i*this.DB)%8, d, k = 0;
+  if(i-- > 0) {
+    if(p < this.DB && (d = this[i]>>p) != (this.s&this.DM)>>p)
+      r[k++] = d|(this.s<<(this.DB-p));
+    while(i >= 0) {
+      if(p < 8) {
+        d = (this[i]&((1<<p)-1))<<(8-p);
+        d |= this[--i]>>(p+=this.DB-8);
+      }
+      else {
+        d = (this[i]>>(p-=8))&0xff;
+        if(p <= 0) { p += this.DB; --i; }
+      }
+      if((d&0x80) != 0) d |= -256;
+      if(k == 0 && (this.s&0x80) != (d&0x80)) ++k;
+      if(k > 0 || d != this.s) r[k++] = d;
+    }
+  }
+  return r;
+}
+
+function bnEquals(a) { return(this.compareTo(a)==0); }
+function bnMin(a) { return(this.compareTo(a)<0)?this:a; }
+function bnMax(a) { return(this.compareTo(a)>0)?this:a; }
+
+// (protected) r = this op a (bitwise)
+function bnpBitwiseTo(a,op,r) {
+  var i, f, m = Math.min(a.t,this.t);
+  for(i = 0; i < m; ++i) r[i] = op(this[i],a[i]);
+  if(a.t < this.t) {
+    f = a.s&this.DM;
+    for(i = m; i < this.t; ++i) r[i] = op(this[i],f);
+    r.t = this.t;
+  }
+  else {
+    f = this.s&this.DM;
+    for(i = m; i < a.t; ++i) r[i] = op(f,a[i]);
+    r.t = a.t;
+  }
+  r.s = op(this.s,a.s);
+  r.clamp();
+}
+
+// (public) this & a
+function op_and(x,y) { return x&y; }
+function bnAnd(a) { var r = nbi(); this.bitwiseTo(a,op_and,r); return r; }
+
+// (public) this | a
+function op_or(x,y) { return x|y; }
+function bnOr(a) { var r = nbi(); this.bitwiseTo(a,op_or,r); return r; }
+
+// (public) this ^ a
+function op_xor(x,y) { return x^y; }
+function bnXor(a) { var r = nbi(); this.bitwiseTo(a,op_xor,r); return r; }
+
+// (public) this & ~a
+function op_andnot(x,y) { return x&~y; }
+function bnAndNot(a) { var r = nbi(); this.bitwiseTo(a,op_andnot,r); return r; }
+
+// (public) ~this
+function bnNot() {
+  var r = nbi();
+  for(var i = 0; i < this.t; ++i) r[i] = this.DM&~this[i];
+  r.t = this.t;
+  r.s = ~this.s;
+  return r;
+}
+
+// (public) this << n
+function bnShiftLeft(n) {
+  var r = nbi();
+  if(n < 0) this.rShiftTo(-n,r); else this.lShiftTo(n,r);
+  return r;
+}
+
+// (public) this >> n
+function bnShiftRight(n) {
+  var r = nbi();
+  if(n < 0) this.lShiftTo(-n,r); else this.rShiftTo(n,r);
+  return r;
+}
+
+// return index of lowest 1-bit in x, x < 2^31
+function lbit(x) {
+  if(x == 0) return -1;
+  var r = 0;
+  if((x&0xffff) == 0) { x >>= 16; r += 16; }
+  if((x&0xff) == 0) { x >>= 8; r += 8; }
+  if((x&0xf) == 0) { x >>= 4; r += 4; }
+  if((x&3) == 0) { x >>= 2; r += 2; }
+  if((x&1) == 0) ++r;
+  return r;
+}
+
+// (public) returns index of lowest 1-bit (or -1 if none)
+function bnGetLowestSetBit() {
+  for(var i = 0; i < this.t; ++i)
+    if(this[i] != 0) return i*this.DB+lbit(this[i]);
+  if(this.s < 0) return this.t*this.DB;
+  return -1;
+}
+
+// return number of 1 bits in x
+function cbit(x) {
+  var r = 0;
+  while(x != 0) { x &= x-1; ++r; }
+  return r;
+}
+
+// (public) return number of set bits
+function bnBitCount() {
+  var r = 0, x = this.s&this.DM;
+  for(var i = 0; i < this.t; ++i) r += cbit(this[i]^x);
+  return r;
+}
+
+// (public) true iff nth bit is set
+function bnTestBit(n) {
+  var j = Math.floor(n/this.DB);
+  if(j >= this.t) return(this.s!=0);
+  return((this[j]&(1<<(n%this.DB)))!=0);
+}
+
+// (protected) this op (1<<n)
+function bnpChangeBit(n,op) {
+  var r = BigInteger.ONE.shiftLeft(n);
+  this.bitwiseTo(r,op,r);
+  return r;
+}
+
+// (public) this | (1<<n)
+function bnSetBit(n) { return this.changeBit(n,op_or); }
+
+// (public) this & ~(1<<n)
+function bnClearBit(n) { return this.changeBit(n,op_andnot); }
+
+// (public) this ^ (1<<n)
+function bnFlipBit(n) { return this.changeBit(n,op_xor); }
+
+// (protected) r = this + a
+function bnpAddTo(a,r) {
+  var i = 0, c = 0, m = Math.min(a.t,this.t);
+  while(i < m) {
+    c += this[i]+a[i];
+    r[i++] = c&this.DM;
+    c >>= this.DB;
+  }
+  if(a.t < this.t) {
+    c += a.s;
+    while(i < this.t) {
+      c += this[i];
+      r[i++] = c&this.DM;
+      c >>= this.DB;
+    }
+    c += this.s;
+  }
+  else {
+    c += this.s;
+    while(i < a.t) {
+      c += a[i];
+      r[i++] = c&this.DM;
+      c >>= this.DB;
+    }
+    c += a.s;
+  }
+  r.s = (c<0)?-1:0;
+  if(c > 0) r[i++] = c;
+  else if(c < -1) r[i++] = this.DV+c;
+  r.t = i;
+  r.clamp();
+}
+
+// (public) this + a
+function bnAdd(a) { var r = nbi(); this.addTo(a,r); return r; }
+
+// (public) this - a
+function bnSubtract(a) { var r = nbi(); this.subTo(a,r); return r; }
+
+// (public) this * a
+function bnMultiply(a) { var r = nbi(); this.multiplyTo(a,r); return r; }
+
+// (public) this^2
+function bnSquare() { var r = nbi(); this.squareTo(r); return r; }
+
+// (public) this / a
+function bnDivide(a) { var r = nbi(); this.divRemTo(a,r,null); return r; }
+
+// (public) this % a
+function bnRemainder(a) { var r = nbi(); this.divRemTo(a,null,r); return r; }
+
+// (public) [this/a,this%a]
+function bnDivideAndRemainder(a) {
+  var q = nbi(), r = nbi();
+  this.divRemTo(a,q,r);
+  return new Array(q,r);
+}
+
+// (protected) this *= n, this >= 0, 1 < n < DV
+function bnpDMultiply(n) {
+  this[this.t] = this.am(0,n-1,this,0,0,this.t);
+  ++this.t;
+  this.clamp();
+}
+
+// (protected) this += n << w words, this >= 0
+function bnpDAddOffset(n,w) {
+  if(n == 0) return;
+  while(this.t <= w) this[this.t++] = 0;
+  this[w] += n;
+  while(this[w] >= this.DV) {
+    this[w] -= this.DV;
+    if(++w >= this.t) this[this.t++] = 0;
+    ++this[w];
+  }
+}
+
+// A "null" reducer
+function NullExp() {}
+function nNop(x) { return x; }
+function nMulTo(x,y,r) { x.multiplyTo(y,r); }
+function nSqrTo(x,r) { x.squareTo(r); }
+
+NullExp.prototype.convert = nNop;
+NullExp.prototype.revert = nNop;
+NullExp.prototype.mulTo = nMulTo;
+NullExp.prototype.sqrTo = nSqrTo;
+
+// (public) this^e
+function bnPow(e) { return this.exp(e,new NullExp()); }
+
+// (protected) r = lower n words of "this * a", a.t <= n
+// "this" should be the larger one if appropriate.
+function bnpMultiplyLowerTo(a,n,r) {
+  var i = Math.min(this.t+a.t,n);
+  r.s = 0; // assumes a,this >= 0
+  r.t = i;
+  while(i > 0) r[--i] = 0;
+  var j;
+  for(j = r.t-this.t; i < j; ++i) r[i+this.t] = this.am(0,a[i],r,i,0,this.t);
+  for(j = Math.min(a.t,n); i < j; ++i) this.am(0,a[i],r,i,0,n-i);
+  r.clamp();
+}
+
+// (protected) r = "this * a" without lower n words, n > 0
+// "this" should be the larger one if appropriate.
+function bnpMultiplyUpperTo(a,n,r) {
+  --n;
+  var i = r.t = this.t+a.t-n;
+  r.s = 0; // assumes a,this >= 0
+  while(--i >= 0) r[i] = 0;
+  for(i = Math.max(n-this.t,0); i < a.t; ++i)
+    r[this.t+i-n] = this.am(n-i,a[i],r,0,0,this.t+i-n);
+  r.clamp();
+  r.drShiftTo(1,r);
+}
+
+// Barrett modular reduction
+function Barrett(m) {
+  // setup Barrett
+  this.r2 = nbi();
+  this.q3 = nbi();
+  BigInteger.ONE.dlShiftTo(2*m.t,this.r2);
+  this.mu = this.r2.divide(m);
+  this.m = m;
+}
+
+function barrettConvert(x) {
+  if(x.s < 0 || x.t > 2*this.m.t) return x.mod(this.m);
+  else if(x.compareTo(this.m) < 0) return x;
+  else { var r = nbi(); x.copyTo(r); this.reduce(r); return r; }
+}
+
+function barrettRevert(x) { return x; }
+
+// x = x mod m (HAC 14.42)
+function barrettReduce(x) {
+  x.drShiftTo(this.m.t-1,this.r2);
+  if(x.t > this.m.t+1) { x.t = this.m.t+1; x.clamp(); }
+  this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);
+  this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);
+  while(x.compareTo(this.r2) < 0) x.dAddOffset(1,this.m.t+1);
+  x.subTo(this.r2,x);
+  while(x.compareTo(this.m) >= 0) x.subTo(this.m,x);
+}
+
+// r = x^2 mod m; x != r
+function barrettSqrTo(x,r) { x.squareTo(r); this.reduce(r); }
+
+// r = x*y mod m; x,y != r
+function barrettMulTo(x,y,r) { x.multiplyTo(y,r); this.reduce(r); }
+
+Barrett.prototype.convert = barrettConvert;
+Barrett.prototype.revert = barrettRevert;
+Barrett.prototype.reduce = barrettReduce;
+Barrett.prototype.mulTo = barrettMulTo;
+Barrett.prototype.sqrTo = barrettSqrTo;
+
+// (public) this^e % m (HAC 14.85)
+function bnModPow(e,m) {
+  var i = e.bitLength(), k, r = nbv(1), z;
+  if(i <= 0) return r;
+  else if(i < 18) k = 1;
+  else if(i < 48) k = 3;
+  else if(i < 144) k = 4;
+  else if(i < 768) k = 5;
+  else k = 6;
+  if(i < 8)
+    z = new Classic(m);
+  else if(m.isEven())
+    z = new Barrett(m);
+  else
+    z = new Montgomery(m);
+
+  // precomputation
+  var g = new Array(), n = 3, k1 = k-1, km = (1<<k)-1;
+  g[1] = z.convert(this);
+  if(k > 1) {
+    var g2 = nbi();
+    z.sqrTo(g[1],g2);
+    while(n <= km) {
+      g[n] = nbi();
+      z.mulTo(g2,g[n-2],g[n]);
+      n += 2;
+    }
+  }
+
+  var j = e.t-1, w, is1 = true, r2 = nbi(), t;
+  i = nbits(e[j])-1;
+  while(j >= 0) {
+    if(i >= k1) w = (e[j]>>(i-k1))&km;
+    else {
+      w = (e[j]&((1<<(i+1))-1))<<(k1-i);
+      if(j > 0) w |= e[j-1]>>(this.DB+i-k1);
+    }
+
+    n = k;
+    while((w&1) == 0) { w >>= 1; --n; }
+    if((i -= n) < 0) { i += this.DB; --j; }
+    if(is1) {	// ret == 1, don't bother squaring or multiplying it
+      g[w].copyTo(r);
+      is1 = false;
+    }
+    else {
+      while(n > 1) { z.sqrTo(r,r2); z.sqrTo(r2,r); n -= 2; }
+      if(n > 0) z.sqrTo(r,r2); else { t = r; r = r2; r2 = t; }
+      z.mulTo(r2,g[w],r);
+    }
+
+    while(j >= 0 && (e[j]&(1<<i)) == 0) {
+      z.sqrTo(r,r2); t = r; r = r2; r2 = t;
+      if(--i < 0) { i = this.DB-1; --j; }
+    }
+  }
+  return z.revert(r);
+}
+
+// (public) gcd(this,a) (HAC 14.54)
+function bnGCD(a) {
+  var x = (this.s<0)?this.negate():this.clone();
+  var y = (a.s<0)?a.negate():a.clone();
+  if(x.compareTo(y) < 0) { var t = x; x = y; y = t; }
+  var i = x.getLowestSetBit(), g = y.getLowestSetBit();
+  if(g < 0) return x;
+  if(i < g) g = i;
+  if(g > 0) {
+    x.rShiftTo(g,x);
+    y.rShiftTo(g,y);
+  }
+  while(x.signum() > 0) {
+    if((i = x.getLowestSetBit()) > 0) x.rShiftTo(i,x);
+    if((i = y.getLowestSetBit()) > 0) y.rShiftTo(i,y);
+    if(x.compareTo(y) >= 0) {
+      x.subTo(y,x);
+      x.rShiftTo(1,x);
+    }
+    else {
+      y.subTo(x,y);
+      y.rShiftTo(1,y);
+    }
+  }
+  if(g > 0) y.lShiftTo(g,y);
+  return y;
+}
+
+// (protected) this % n, n < 2^26
+function bnpModInt(n) {
+  if(n <= 0) return 0;
+  var d = this.DV%n, r = (this.s<0)?n-1:0;
+  if(this.t > 0)
+    if(d == 0) r = this[0]%n;
+    else for(var i = this.t-1; i >= 0; --i) r = (d*r+this[i])%n;
+  return r;
+}
+
+// (public) 1/this % m (HAC 14.61)
+function bnModInverse(m) {
+  var ac = m.isEven();
+  if((this.isEven() && ac) || m.signum() == 0) return BigInteger.ZERO;
+  var u = m.clone(), v = this.clone();
+  var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
+  while(u.signum() != 0) {
+    while(u.isEven()) {
+      u.rShiftTo(1,u);
+      if(ac) {
+        if(!a.isEven() || !b.isEven()) { a.addTo(this,a); b.subTo(m,b); }
+        a.rShiftTo(1,a);
+      }
+      else if(!b.isEven()) b.subTo(m,b);
+      b.rShiftTo(1,b);
+    }
+    while(v.isEven()) {
+      v.rShiftTo(1,v);
+      if(ac) {
+        if(!c.isEven() || !d.isEven()) { c.addTo(this,c); d.subTo(m,d); }
+        c.rShiftTo(1,c);
+      }
+      else if(!d.isEven()) d.subTo(m,d);
+      d.rShiftTo(1,d);
+    }
+    if(u.compareTo(v) >= 0) {
+      u.subTo(v,u);
+      if(ac) a.subTo(c,a);
+      b.subTo(d,b);
+    }
+    else {
+      v.subTo(u,v);
+      if(ac) c.subTo(a,c);
+      d.subTo(b,d);
+    }
+  }
+  if(v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
+  if(d.compareTo(m) >= 0) return d.subtract(m);
+  if(d.signum() < 0) d.addTo(m,d); else return d;
+  if(d.signum() < 0) return d.add(m); else return d;
+}
+
+var lowprimes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997];
+var lplim = (1<<26)/lowprimes[lowprimes.length-1];
+
+// (public) test primality with certainty >= 1-.5^t
+function bnIsProbablePrime(t) {
+  var i, x = this.abs();
+  if(x.t == 1 && x[0] <= lowprimes[lowprimes.length-1]) {
+    for(i = 0; i < lowprimes.length; ++i)
+      if(x[0] == lowprimes[i]) return true;
+    return false;
+  }
+  if(x.isEven()) return false;
+  i = 1;
+  while(i < lowprimes.length) {
+    var m = lowprimes[i], j = i+1;
+    while(j < lowprimes.length && m < lplim) m *= lowprimes[j++];
+    m = x.modInt(m);
+    while(i < j) if(m%lowprimes[i++] == 0) return false;
+  }
+  return x.millerRabin(t);
+}
+
+// (protected) true if probably prime (HAC 4.24, Miller-Rabin)
+function bnpMillerRabin(t) {
+  var n1 = this.subtract(BigInteger.ONE);
+  var k = n1.getLowestSetBit();
+  if(k <= 0) return false;
+  var r = n1.shiftRight(k);
+  t = (t+1)>>1;
+  if(t > lowprimes.length) t = lowprimes.length;
+  var a = nbi();
+  for(var i = 0; i < t; ++i) {
+    //Pick bases at random, instead of starting at 2
+    a.fromInt(lowprimes[Math.floor(Math.random()*lowprimes.length)]);
+    var y = a.modPow(r,this);
+    if(y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
+      var j = 1;
+      while(j++ < k && y.compareTo(n1) != 0) {
+        y = y.modPowInt(2,this);
+        if(y.compareTo(BigInteger.ONE) == 0) return false;
+      }
+      if(y.compareTo(n1) != 0) return false;
+    }
+  }
+  return true;
+}
+
+// protected
+BigInteger.prototype.chunkSize = bnpChunkSize;
+BigInteger.prototype.toRadix = bnpToRadix;
+BigInteger.prototype.fromRadix = bnpFromRadix;
+BigInteger.prototype.fromNumber = bnpFromNumber;
+BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
+BigInteger.prototype.changeBit = bnpChangeBit;
+BigInteger.prototype.addTo = bnpAddTo;
+BigInteger.prototype.dMultiply = bnpDMultiply;
+BigInteger.prototype.dAddOffset = bnpDAddOffset;
+BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
+BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
+BigInteger.prototype.modInt = bnpModInt;
+BigInteger.prototype.millerRabin = bnpMillerRabin;
+
+// public
+BigInteger.prototype.clone = bnClone;
+BigInteger.prototype.intValue = bnIntValue;
+BigInteger.prototype.byteValue = bnByteValue;
+BigInteger.prototype.shortValue = bnShortValue;
+BigInteger.prototype.signum = bnSigNum;
+BigInteger.prototype.toByteArray = bnToByteArray;
+BigInteger.prototype.equals = bnEquals;
+BigInteger.prototype.min = bnMin;
+BigInteger.prototype.max = bnMax;
+BigInteger.prototype.and = bnAnd;
+BigInteger.prototype.or = bnOr;
+BigInteger.prototype.xor = bnXor;
+BigInteger.prototype.andNot = bnAndNot;
+BigInteger.prototype.not = bnNot;
+BigInteger.prototype.shiftLeft = bnShiftLeft;
+BigInteger.prototype.shiftRight = bnShiftRight;
+BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
+BigInteger.prototype.bitCount = bnBitCount;
+BigInteger.prototype.testBit = bnTestBit;
+BigInteger.prototype.setBit = bnSetBit;
+BigInteger.prototype.clearBit = bnClearBit;
+BigInteger.prototype.flipBit = bnFlipBit;
+BigInteger.prototype.add = bnAdd;
+BigInteger.prototype.subtract = bnSubtract;
+BigInteger.prototype.multiply = bnMultiply;
+BigInteger.prototype.divide = bnDivide;
+BigInteger.prototype.remainder = bnRemainder;
+BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
+BigInteger.prototype.modPow = bnModPow;
+BigInteger.prototype.modInverse = bnModInverse;
+BigInteger.prototype.pow = bnPow;
+BigInteger.prototype.gcd = bnGCD;
+BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
+
+// JSBN-specific extension
+BigInteger.prototype.square = bnSquare;
+
+// BigInteger interfaces not implemented in jsbn:
+
+// BigInteger(int signum, byte[] magnitude)
+// double doubleValue()
+// float floatValue()
+// int hashCode()
+// long longValue()
+// static BigInteger valueOf(long val)