PHP RSA Verschlüsselung
Ich habe schon mal einen ähnlichen Thread erstellt, bin aber vermutlich falsch an das Problem herangegangen. Ich bin jetzt kein Javascript Talent, brauche aber diesen Javascript Code in PHP. (Es geht darum, dass ich einen Login auf der Seite http://steampowered.com mit PHP simulieren will)
Es reicht aber nicht aus die Daten einfach mit einen POST Request an die Seite zu senden. Das Passwort muss davor noch mit einen RSA Verfahren verschlüsselt werden.
Es geht wie oben schon genannt darum einen Text mit dem RSA Verfahren zu verschlüsseln.
Man bekommt aus einer Datei den publickey_exponent und den publickey_modulus. Mit diesen zwei Zahlen wird dann der Text verschlüsselt. Ich habe schon ein paar Ansätze, aber keins davon funktioniert.
Javascript:
In dieser Datei sind die Funktionen die für den Login verwendet werden. Wenn man sich anmeldet wird als erstes die Funktion DoLogin() aufgerufen. Diese holt aus einer Datei den PublicKey modulus und exponent. Danach wird das Passwort mit diesen 2 Zahlen verschlüsselt und an die Datei gesendet, die überprüft ob der Login richtig ist.
Hier ist der Quellcode der Datei mit den Funktionen:
Die Datei /getrsakey sieht in etwa so aus:
Das ist die RSA Klasse
Die RSA Klasse verwendet zum Teil die Klasse BigInteger:
Ich habe schon diverse Sachen mit 3rdparty libs probiert, die aber alle nicht funktioniert haben. Hier ist mein letzter Versuch. Ich benutze hier in diesen Beispiel "phpseclib" Was mache ich falsch?
Wie würdet ihr die Methode RSA.encrypt() in PHP schreiben?
Ich habe schon mal einen ähnlichen Thread erstellt, bin aber vermutlich falsch an das Problem herangegangen. Ich bin jetzt kein Javascript Talent, brauche aber diesen Javascript Code in PHP. (Es geht darum, dass ich einen Login auf der Seite http://steampowered.com mit PHP simulieren will)
Es reicht aber nicht aus die Daten einfach mit einen POST Request an die Seite zu senden. Das Passwort muss davor noch mit einen RSA Verfahren verschlüsselt werden.
Es geht wie oben schon genannt darum einen Text mit dem RSA Verfahren zu verschlüsseln.
Man bekommt aus einer Datei den publickey_exponent und den publickey_modulus. Mit diesen zwei Zahlen wird dann der Text verschlüsselt. Ich habe schon ein paar Ansätze, aber keins davon funktioniert.
Javascript:
In dieser Datei sind die Funktionen die für den Login verwendet werden. Wenn man sich anmeldet wird als erstes die Funktion DoLogin() aufgerufen. Diese holt aus einer Datei den PublicKey modulus und exponent. Danach wird das Passwort mit diesen 2 Zahlen verschlüsselt und an die Datei gesendet, die überprüft ob der Login richtig ist.
Hier ist der Quellcode der Datei mit den Funktionen:
PHP-Code:
//Used to add a unique get var to all ajax calls, so IE doesn't do stupid caching
var iAjaxCalls = 0;
var iIncorrectLoginFailures = 0;
function HighlightFailure( msg )
{
var errorDisplay = $('error_display');
if ( errorDisplay )
{
errorDisplay.update( msg );
errorDisplay.show();
errorDisplay.style.color = '#ffffff';
try {
new Effect.Morph( 'error_display', { style: 'color: #d0434b' } );
}
catch(err) { }
}
}
//Refresh the catpcha image
function RefreshCaptcha()
{
++iAjaxCalls;
new Ajax.Request('https://steamcommunity.com/actions/RefreshCaptcha/',
{
method:'get',
parameters: { count : iAjaxCalls },
onSuccess: function(transport){
if ( transport.responseText ){
try {
var result = transport.responseText.evalJSON(true);
} catch ( e ) {
//alert(e);
return;
}
gid = result.gid;
UpdateCaptcha( gid );
}
}
});
}
function UpdateCaptcha( gid )
{
if ( gid != -1 )
{
$('captcha_entry').show();
$('captchaImg').src = 'https://steamcommunity.com/public/captcha.php?gid='+gid;
$('input_captcha').value='';
}
$('captchagid').value = gid;
}
var g_bLoginInFlight = false;
var g_bInEmailAuthProcess = false;
var g_bInTwoFactorAuthProcess = false;
var g_bEmailAuthSuccessful = false;
var g_bLoginTransferInProgress = false;
var g_bEmailAuthSuccessfulWantToLeave = false;
var g_bTwoFactorAuthSuccessful = false;
var g_bTwoFactorAuthSuccessfulWantToLeave = false;
var g_sOAuthRedirectURI = 'steammobile://mobileloginsucceeded';
var g_sAuthCode = "";
function DoLogin()
{
var form = document.forms['logon'];
var username = form.elements['username'].value;
username = username.replace( /[^\x00-\x7F]/g, '' ); // remove non-standard-ASCII characters
var password = form.elements['password'].value;
password = password.replace( /[^\x00-\x7F]/g, '' ); // remove non-standard-ASCII characters
if ( g_bLoginInFlight || password.length == 0 || username.length == 0 )
return;
g_bLoginInFlight = true;
$('login_btn_signin').hide();
$('login_btn_wait').show();
new Ajax.Request( 'https://steamcommunity.com/login/getrsakey/',
{
method: 'post',
parameters: {
username: username,
donotcache: ( new Date().getTime() )
},
onSuccess: OnRSAKeyResponse,
onException: function( req, e ) {
throw e;
}
}
);
}
function getAuthCode( results )
{
var authCode = g_sAuthCode;
g_sAuthCode = '';
return authCode;
}
function OnRSAKeyResponse( transport )
{
var results = transport.responseJSON;
if ( results.publickey_mod && results.publickey_exp && results.timestamp )
{
var form = document.forms['logon'];
var pubKey = RSA.getPublicKey( results.publickey_mod, results.publickey_exp );
var username = form.elements['username'].value;
username = username.replace( /[^\x00-\x7F]/g, '' ); // remove non-standard-ASCII characters
var password = form.elements['password'].value;
password = password.replace( /[^\x00-\x7F]/g, '' ); // remove non-standard-ASCII characters
var encryptedPassword = RSA.encrypt( password, pubKey );
new Ajax.Request( 'https://steamcommunity.com/login/dologin/',
{
method: 'post',
parameters: {
password: encryptedPassword,
username: username,
twofactorcode: getAuthCode( results ),
emailauth: form.elements['emailauth'].value,
loginfriendlyname: form.elements['loginfriendlyname'].value,
captchagid: form.elements['captchagid'].value,
captcha_text: form.elements['captcha_text'].value,
emailsteamid: form.elements['emailsteamid'].value,
rsatimestamp: results.timestamp,
remember_login: ( form.elements['remember_login'] && form.elements['remember_login'].checked ) ? 'true' : 'false',
donotcache: ( new Date().getTime() )
},
onSuccess: OnLoginResponse,
onException: function( req, e ) {
throw e;
}
}
);
}
else
{
if ( results.message )
{
HighlightFailure( results.message );
}
$('login_btn_signin').show();
$('login_btn_wait').hide();
g_bLoginInFlight = false;
}
}
function OnLoginResponse( transport )
{
var results = transport.responseJSON;
g_bLoginInFlight = false;
var bRetry = true;
if ( results.login_complete )
{
var bRunningTransfer = false;
if ( results.transfer_url && results.transfer_parameters )
{
bRunningTransfer = true;
TransferLogin( results.transfer_url, results.transfer_parameters );
}
if ( g_bInEmailAuthProcess )
{
g_bEmailAuthSuccessful = true;
SetEmailAuthModalState( 'success' );
}
else if ( g_bInTwoFactorAuthProcess )
{
g_bTwoFactorAuthSuccessful = true;
SetTwoFactorAuthModalState( 'success' );
}
else
{
bRetry = false;
if ( !bRunningTransfer )
LoginComplete();
}
}
else
{
if ( results.requires_twofactor )
{
$('captcha_entry').hide();
if ( !g_bInTwoFactorAuthProcess )
StartTwoFactorAuthProcess();
else
SetTwoFactorAuthModalState( 'incorrectcode' );
}
else if ( results.captcha_needed && results.captcha_gid )
{
UpdateCaptcha( results.captcha_gid );
iIncorrectLoginFailures ++;
}
else if ( results.emailauth_needed )
{
if ( results.emaildomain )
$('emailauth_entercode_emaildomain').update( results.emaildomain );
if ( results.emailsteamid )
$('emailsteamid').value = results.emailsteamid;
if ( !g_bInEmailAuthProcess )
StartEmailAuthProcess();
else
SetEmailAuthModalState( 'incorrectcode' );
}
else if ( results.denied_ipt )
{
$('loginIPTModal').OnModalDismissal = ClearLoginForm;
showModal( 'loginIPTModal' );
}
else
{
iIncorrectLoginFailures ++;
}
if ( results.message )
{
HighlightFailure( results.message );
}
}
if ( bRetry )
{
$('login_btn_signin').show();
$('login_btn_wait').hide();
}
}
function ClearLoginForm()
{
var rgElements = document.forms['logon'].elements;
rgElements['username'].value = '';
rgElements['password'].value = '';
rgElements['emailauth'].value = '';
rgElements['emailsteamid'].value = '';
$('authcode').value = '';
if ( rgElements['captchagid'].value )
RefreshCaptcha();
rgElements['username'].focus();
}
function StartEmailAuthProcess()
{
g_bInEmailAuthProcess = true;
SetEmailAuthModalState( 'entercode' );
$('loginAuthCodeModal').OnModalDismissal = CancelEmailAuthProcess;
showModal ( 'loginAuthCodeModal', true );
}
function CancelEmailAuthProcess()
{
g_bInEmailAuthProcess = false;
// if the user closed the auth window on the last step, just redirect them like we normally would
if ( g_bEmailAuthSuccessful )
LoginComplete();
else
ClearLoginForm();
}
function TransferLogin( url, parameters )
{
if ( g_bLoginTransferInProgress )
return;
g_bLoginTransferInProgress = true;
var iframeElement = document.createElement( 'iframe' );
iframeElement.id = 'transfer_iframe';
var iframe = $( iframeElement );
iframe.hide();
$(document.body).appendChild( iframe );
var doc = iframe.contentWindow.document;
doc.open();
doc.write( '<form method="POST" action="' + url + '" name="transfer_form">' );
for ( var param in parameters )
{
doc.write( '<input type="hidden" name="' + param + '" value="' + parameters[param] + '">' );
}
doc.write( '</form>' );
doc.write( '<script>window.onload = function(){ document.forms["transfer_form"].submit(); }</script>' );
doc.close();
// firefox fires the onload event twice
var cLoadCount = Prototype.Browser.Gecko ? 2 : 1;
Event.observe( iframe, 'load', function( event ) { if ( --cLoadCount == 0 ) OnTransferComplete() } );
Event.observe( iframe, 'error', function( event ) { OnTransferComplete(); } );
// after 10 seconds, give up on waiting for transfer
window.setTimeout( OnTransferComplete, 10000 );
}
function OnTransferComplete()
{
if ( !g_bLoginTransferInProgress )
return;
g_bLoginTransferInProgress = false;
if ( !g_bInEmailAuthProcess && !g_bInTwoFactorAuthProcess )
LoginComplete();
else if ( g_bEmailAuthSuccessfulWantToLeave || g_bTwoFactorAuthSuccessfulWantToLeave)
LoginComplete();
}
function OnEmailAuthSuccessContinue()
{
if ( g_bLoginTransferInProgress )
{
$('auth_buttonsets').childElements().invoke('hide');
if ( $('auth_buttonset_waiting') )
$('auth_buttonset_waiting').show();
g_bEmailAuthSuccessfulWantToLeave = true;
}
else
LoginComplete();
}
function LoginComplete()
{
if ( $('openidForm') )
{
$('openidForm').submit();
}
else
{
{
window.location = document.forms['logon'].elements['redir'].value;
}
}
}
function SubmitAuthCode( defaultFriendlyNameText )
{
var friendlyname = $('friendlyname').value;
$('auth_details_computer_name').style.color='#85847f';
if ( friendlyname == defaultFriendlyNameText )
{
friendlyname = '';
}
$('auth_buttonsets').childElements().invoke('hide');
if ( $('auth_buttonset_waiting') )
$('auth_buttonset_waiting').show();
document.forms['logon'].elements['loginfriendlyname'].value = friendlyname;
document.forms['logon'].elements['emailauth'].value = $('authcode').value;
DoLogin();
}
function SetEmailAuthModalState( step )
{
$('auth_messages').childElements().invoke('hide');
$('auth_message_' + step ).show();
$('auth_details_messages').childElements().invoke('hide');
if ( $('auth_details_' + step ) )
$('auth_details_' + step ).show();
$('auth_buttonsets').childElements().invoke('hide');
if ( $('auth_buttonset_' + step ) )
$('auth_buttonset_' + step ).show();
$('authcode_help_supportlink').hide();
var icon='key';
var bShowAuthcodeEntry = true;
if ( step == 'entercode' )
{
icon = 'key';
}
else if ( step == 'checkspam' )
{
icon = 'trash';
}
else if ( step == 'success' )
{
icon = 'unlock';
bShowAuthcodeEntry = false;
$('success_continue_btn').focus();
}
else if ( step == 'incorrectcode' )
{
icon = 'lock';
}
else if ( step == 'help' )
{
icon = 'steam';
bShowAuthcodeEntry = false;
$('authcode_help_supportlink').show();
}
if ( bShowAuthcodeEntry )
{
$('authcode_entry').show();
$('auth_details_computer_name').show();
}
else
{
$('authcode_entry').hide();
$('auth_details_computer_name').hide();
}
$('auth_icon').className = 'auth_icon auth_icon_' + icon;
}
function OnAuthcodeFocus( defaultText )
{
if ( $('authcode').value == defaultText )
{
$('authcode').value = '';
$('authcode').removeClassName( 'defaulttext' );
}
}
function OnAuthcodeBlur( defaultText )
{
if ( $('authcode').value == '' )
{
$('authcode').value = defaultText;
$('authcode').addClassName( 'defaulttext' );
}
}
function OnFriendlyNameFocus( defaultText )
{
if ( $('friendlyname').value == defaultText )
{
$('friendlyname').value = '';
$('friendlyname').removeClassName( 'defaulttext' );
}
}
function OnFriendlyNameBlur( defaultText )
{
if ( $('friendlyname').value == '' )
{
$('friendlyname').value = defaultText;
$('friendlyname').addClassName( 'defaulttext' );
}
}
function StartTwoFactorAuthProcess()
{
g_bInTwoFactorAuthProcess = true;
SetTwoFactorAuthModalState( 'entercode' );
$('loginTwoFactorCodeModal').OnModalDismissal = CancelTwoFactorAuthProcess;
}
function CancelTwoFactorAuthProcess()
{
g_bInTwoFactorAuthProcess = false;
if ( g_bEmailAuthSuccessful )
LoginComplete();
else
ClearLoginForm();
}
function OnTwoFactorAuthSuccessContinue()
{
if ( g_bLoginTransferInProgress )
{
$('login_twofactorauth_buttonsets').childElements().invoke('hide');
if ( $('login_twofactorauth_buttonset_waiting') )
$('login_twofactorauth_buttonset_waiting').show();
g_bTwoFactorAuthSuccessfulWantToLeave = true;
}
else
LoginComplete();
}
function SetTwoFactorAuthModalState( step )
{
if ( step == 'success' )
{
g_bInTwoFactorAuthProcess = false;
}
$('login_twofactorauth_messages').childElements().invoke('hide');
if ( $('login_twofactorauth_message_' + step ) )
$('login_twofactorauth_message_' + step ).show();
$('login_twofactorauth_details_messages').childElements().invoke('hide');
if ( $('login_twofactorauth_details_' + step ) )
$('login_twofactorauth_details_' + step ).show();
$('login_twofactorauth_buttonsets').childElements().invoke('hide');
if ( $('login_twofactorauth_buttonset_' + step ) )
$('login_twofactorauth_buttonset_' + step ).show();
$('login_twofactor_authcode_help_supportlink').hide();
var icon = 'key';
if ( step == 'entercode' )
{
showModal( 'loginTwoFactorCodeModal', true );
$('twofactorcode_entry').focus();
}
else if ( step == 'incorrectcode' )
{
icon = 'lock';
$('twofactorcode_entry').focus();
}
else if ( step == 'help' )
{
icon = 'steam';
$('login_twofactor_authcode_entry').hide();
$('login_twofactor_authcode_help_supportlink').show();
}
if ( ! g_bInTwoFactorAuthProcess )
{
$('loginTwoFactorCodeModal').hide();
}
$('login_twofactorauth_icon').className = 'auth_icon auth_icon_' + icon;
}
function SubmitTwoFactorCode( )
{
g_sAuthCode = $('twofactorcode_entry').value;
$('login_twofactorauth_messages').childElements().invoke('hide');
$('login_twofactorauth_details_messages').childElements().invoke('hide');
$('login_twofactorauth_buttonsets').childElements().invoke('hide');
if ( $('login_twofactorauth_buttonset_waiting') )
{
$('login_twofactorauth_buttonset_waiting').show();
}
DoLogin();
}
function OnTwoFactorCodeFocus( defaultText )
{
if ( $('twofactorcode_entry').value == defaultText )
{
$('twofactorcode_entry').value = '';
$('twofactorcode_entry').removeClassName( 'defaulttext' );
}
}
function OnTwoFactorCodeBlur( defaultText )
{
}
Code:
{"success":true,"publickey_mod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publickey_exp":"010001","timestamp":"288170250000","token_gid":""}
PHP-Code:
var RSAPublicKey = function($modulus_hex, $encryptionExponent_hex) {
this.modulus = new BigInteger( $modulus_hex, 16);
this.encryptionExponent = new BigInteger( $encryptionExponent_hex, 16);
}
var Base64 = {
base64: "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",
encode: function($input) {
if (!$input) {
return false;
}
var $output = "";
var $chr1, $chr2, $chr3;
var $enc1, $enc2, $enc3, $enc4;
var $i = 0;
do {
$chr1 = $input.charCodeAt($i++);
$chr2 = $input.charCodeAt($i++);
$chr3 = $input.charCodeAt($i++);
$enc1 = $chr1 >> 2;
$enc2 = (($chr1 & 3) << 4) | ($chr2 >> 4);
$enc3 = (($chr2 & 15) << 2) | ($chr3 >> 6);
$enc4 = $chr3 & 63;
if (isNaN($chr2)) $enc3 = $enc4 = 64;
else if (isNaN($chr3)) $enc4 = 64;
$output += this.base64.charAt($enc1) + this.base64.charAt($enc2) + this.base64.charAt($enc3) + this.base64.charAt($enc4);
} while ($i < $input.length);
return $output;
},
decode: function($input) {
if(!$input) return false;
$input = $input.replace(/[^A-Za-z0-9\+\/\=]/g, "");
var $output = "";
var $enc1, $enc2, $enc3, $enc4;
var $i = 0;
do {
$enc1 = this.base64.indexOf($input.charAt($i++));
$enc2 = this.base64.indexOf($input.charAt($i++));
$enc3 = this.base64.indexOf($input.charAt($i++));
$enc4 = this.base64.indexOf($input.charAt($i++));
$output += String.fromCharCode(($enc1 << 2) | ($enc2 >> 4));
if ($enc3 != 64) $output += String.fromCharCode((($enc2 & 15) << 4) | ($enc3 >> 2));
if ($enc4 != 64) $output += String.fromCharCode((($enc3 & 3) << 6) | $enc4);
} while ($i < $input.length);
return $output;
}
};
var Hex = {
hex: "0123456789abcdef",
encode: function($input) {
if(!$input) return false;
var $output = "";
var $k;
var $i = 0;
do {
$k = $input.charCodeAt($i++);
$output += this.hex.charAt(($k >> 4) &0xf) + this.hex.charAt($k & 0xf);
} while ($i < $input.length);
return $output;
},
decode: function($input) {
if(!$input) return false;
$input = $input.replace(/[^0-9abcdef]/g, "");
var $output = "";
var $i = 0;
do {
$output += String.fromCharCode(((this.hex.indexOf($input.charAt($i++)) << 4) & 0xf0) | (this.hex.indexOf($input.charAt($i++)) & 0xf));
} while ($i < $input.length);
return $output;
}
};
var RSA = {
getPublicKey: function( $modulus_hex, $exponent_hex ) {
return new RSAPublicKey( $modulus_hex, $exponent_hex );
},
encrypt: function($data, $pubkey) {
if (!$pubkey) return false;
$data = this.pkcs1pad2($data,($pubkey.modulus.bitLength()+7)>>3);
if(!$data) return false;
$data = $data.modPowInt($pubkey.encryptionExponent, $pubkey.modulus);
if(!$data) return false;
$data = $data.toString(16);
if(($data.length & 1) == 1)
$data = "0" + $data;
return Base64.encode(Hex.decode($data));
},
pkcs1pad2: function($data, $keysize) {
if($keysize < $data.length + 11)
return null;
var $buffer = [];
var $i = $data.length - 1;
while($i >= 0 && $keysize > 0)
$buffer[--$keysize] = $data.charCodeAt($i--);
$buffer[--$keysize] = 0;
while($keysize > 2)
$buffer[--$keysize] = Math.floor(Math.random()*254) + 1;
$buffer[--$keysize] = 2;
$buffer[--$keysize] = 0;
return new BigInteger($buffer);
}
}
PHP-Code:
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
/*
* Copyright (c) 2003-2005 Tom Wu
* All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
* EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
* WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
*
* IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
* INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
* THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
* OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*
* In addition, the following condition applies:
*
* All redistributions must retain an intact copy of this copyright notice
* and disclaimer.
*/
// 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 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);
// Copyright (c) 2005 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// (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 / 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) {
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];
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) {
a.fromInt(lowprimes[i]);
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;
// BigInteger interfaces not implemented in jsbn:
// BigInteger(int signum, byte[] magnitude)
// double doubleValue()
// float floatValue()
// int hashCode()
// long longValue()
// static BigInteger valueOf(long val)
PHP-Code:
<?php
if(!class_exists("Crypt_RSA")) {
include("phpseclib/Crypt/RSA.php");
}
if(!class_exists("Math_BigInteger")) {
include("phpseclib/Math/BigInteger.php");
}
$login = "******************";
$password = "****************";
function geturl($url, $ref, $cookie, $postdata, $header, &$info, &$output)
{
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt ($ch, CURLOPT_SSL_VERIFYPEER, 0);
curl_setopt ($ch, CURLOPT_SSL_VERIFYHOST, 0);
if ($ref)
{
curl_setopt($ch, CURLOPT_REFERER, $ref);
}
if ($cookie)
{
curl_setopt($ch, CURLOPT_COOKIE, $cookie);
}
if ($postdata)
{
curl_setopt($ch, CURLOPT_POST, true);
$postStr = "";
foreach ($postdata as $key => $value)
{
if ($postStr)
$postStr .= "&";
$postStr .= $key . "=" . $value;
}
curl_setopt($ch, CURLOPT_POSTFIELDS, $postStr);
}
curl_setopt($ch, CURLOPT_HEADER, $header);
$info = curl_getinfo($ch);
$output = curl_exec($ch);
curl_close($ch);
}
geturl("https://steamcommunity.com/login/getrsakey", null, null, array('username' => $login), 0, $info, $output);
$data = json_decode($output, true);
if ($data['success'] === true)
{
$publickey_exp = $data['publickey_exp'];
$publickey_mod = $data['publickey_mod'];
$RSA = new Crypt_RSA();
$RSA->setEncryptionMode(CRYPT_RSA_ENCRYPTION_PKCS1);
$n = new Math_BigInteger($publickey_mod, 16);
$e = new Math_BigInteger($publickey_exp, 16);
$key = array("modulus"=>$n, "publicExponent"=>$e);
$RSA->loadKey($key, CRYPT_RSA_PUBLIC_FORMAT_RAW);
$encryptedPassword = base64_encode($RSA->encrypt($password, false));
$captchaGid = -1;
$captchaText;
$emailAuth;
$emailSteamId;
$params = array(
'username' => $login,
'password' => $encryptedPassword,
'rsatimestamp' => $data['timestamp'],
'captcha_gid' => $captchaGid,
'captcha_text' => $captchaText,
'emailauth' => $emailAuth,
'emailsteamid' => $emailSteamId
);
geturl("https://steamcommunity.com/login/dologin/", null, null, $params, 0, $info, $output);
$data = json_decode($output, true);
var_dump($data);
if ($data['captcha_needed'])
{
$captchaGid = $data['captcha_gid'];
echo '<img src="https://steamcommunity.com/public/captcha.php?gid=' . $captchaGid . '">';
}
}
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