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classes.php
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classes.php
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<?php
/*
* Crypto Currency Address Codec Library
* For use with Bitcoin and Zetacoin compatable crypto currency using the secp256k1 ECC curve
*/
class AddressCodec{
/***
* returns the Uncompressed DER encoded public key.
*
* @return String Hex
*/
public static function Hex(Array $point){
$derPubKey = '04' . $point['x'] . $point['y'];
return $derPubKey;
}
/***
* returns the public key coordinates as an array.
* Input can be compressed or uncompressed DER Encoded Pubkey
*
* @return array
*/
public static function Point($derPubKey){
if(substr($derPubKey, 0, 2) == '04' && strlen($derPubKey) == 130){
//uncompressed der encoded public key
$x = substr($derPubKey, 2, 64);
$y = substr($derPubKey, 66, 64);
return array('x' => $x, 'y' => $y);
}
// Oops This is actually a compressed DER Public Key, send it to the correct function
elseif((substr($derPubKey, 0, 2) == '02' || substr($derPubKey, 0, 2) == '03') && strlen($derPubKey) == 66){
return self::Decompress($derPubKey);
}
else
{
throw new \Exception('Invalid derPubKey format : ' . $compressedDerPubKey);
}
}
/***
* returns the public key coordinates as an array.
* Input can be compressed or uncompressed DER Encoded Pubkey
*
* @param $derPubKey
* @return array
* @throws \Exception
*/
public static function Decompress($compressedDerPubKey) {
if((substr($compressedDerPubKey, 0, 2) == '02' || substr($compressedDerPubKey, 0, 2) == '03') && strlen($compressedDerPubKey) == 66){
//compressed der encoded public key
$x = substr($compressedDerPubKey, 2, 64);
// secp256k1
$secp256k1 = new SECp256k1();
$a = $secp256k1->a;
$b = $secp256k1->b;
$p = $secp256k1->p;
// This is where the magic happens
$y = PointMathGMP::calculateYWithX($x, $a, $b, $p, substr($compressedDerPubKey, 0, 2));
return array('x' => $x, 'y' => $y);
}
// OOps.. This is actually a non-compressed DER Public Key, send it to the correct function
elseif(substr($compressedDerPubKey, 0, 2) == '04' && strlen($compressedDerPubKey) == 130){
return self::Point($compressedDerPubKey);
}
else{
throw new \Exception('Invalid compressedDerPubKey format : ' . $compressedDerPubKey);
}
}
/***
* returns the compressed DER encoded public key.
*
* @return String Hex
*/
public static function Compress($pubKey){
if(gmp_strval(gmp_mod(gmp_init($pubKey['y'], 16), gmp_init(2, 10))) == 0)
$compressedDerPubKey = '02' . $pubKey['x']; //if $pubKey['y'] is even
else
$compressedDerPubKey = '03' . $pubKey['x']; //if $pubKey['y'] is odd
return $compressedDerPubKey;
}
/***
* returns the HASH160 version of the Publick Key
* .
*
* @param string $derPubKey
* @throws \Exception
* @return String Hash160
*/
public static function Hash($derPubKey){
$sha256 = hash('sha256', hex2bin($derPubKey));
$ripem160 = hash('ripemd160', hex2bin($sha256));
return $ripem160;
}
/***
* returns the Bitcoin address version of the Publick Key
* .
*
* @param string $hex
* @throws \Exception
* @return String Base58
*/
public static function Encode($hex, $prefix = "00") {
// The magical prefix
$hex_with_prefix = $prefix . $hex;
//checksum
$sha256 = hash('sha256', hex2bin($hex_with_prefix));
$checksum = hash('sha256', hex2bin($sha256));
// Encode
$address = $hex_with_prefix . substr($checksum, 0, 8);
$address = Base58::Encode($address);
return $address;
}
public static function Decode($address) {
$hex_with_prefix_and_check = Base58::Decode($address);
$prefix = substr($hex_with_prefix_and_check, 0, 2);
$checksum = substr($hex_with_prefix_and_check, -8);
$hex = substr($hex_with_prefix_and_check, 2, -8);
return $hex;
}
/***
* returns the private key under the Wallet Import Format
*
* @return String Base58
* @throws \Exception
*/
public static function WIF($private_key, $prefix = '80', $compressed = true,$is_reverse=true){
if ($compressed) {$private_key = $private_key . '01';}
if ($is_reverse) return strrev(self::Encode($private_key, $prefix));
else return strval(self::Encode($private_key, $prefix));
}
public static function DeWIF($wif, $compressed = true,$is_reverse=true){
if ($is_reverse) $base58 = strrev($wif);
else $base58=strval($wif);
$hex = self::Decode($base58);
if ($compressed) {$hex = substr($hex, 0, -2);}
return $hex;
}
}
/*
* Crypto Currency Address Validation Library
* For use with Bitcoin and Zetacoin compatable crypto currency using the secp256k1 ECC curve
*/
class AddressValidation {
/***
* Tests if the address is valid or not.
*
* @param String Base58 $address
* @return bool
*/
public static function validateAddress($address){
$address = hex2bin(Base58::Decode($address));
if(strlen($address) != 25)
return false;
$checksum = substr($address, 21, 4);
$rawAddress = substr($address, 0, 21);
$sha256 = hash('sha256', $rawAddress);
$sha256 = hash('sha256', hex2bin($sha256));
if(substr(hex2bin($sha256), 0, 4) == $checksum)
return true;
else
return false;
}
/***
* Tests if the Wif key (Wallet Import Format) is valid or not.
*
* @param String Base58 $wif
* @return bool
*/
public static function validateWifKey($wif){
$key = Base58::Decode($wif, false);
$length = strlen($key);
$firstSha256 = hash('sha256', hex2bin(substr($key, 0, $length - 8)));
$secondSha256 = hash('sha256', hex2bin($firstSha256));
if(substr($secondSha256, 0, 8) == substr($key, $length - 8, 8))
return true;
else
return false;
}
}
/*
* Object Oriented implimentation to Base58.
* For use with Bitcoin and Zetacoin compatable crypto currency using the secp256k1 ECC curve
*/
class Base58 {
/***
* Permutation table used for Base58 encoding and decoding.
*
* @param $char
* @param bool $reverse
* @return null
*/
private static function permutation_lookup($char, $reverse = false){
$table = array('1','2','3','4','5','6','7','8','9','A','B','C','D',
'E','F','G','H','J','K','L','M','N','P','Q','R','S','T','U','V','W',
'X','Y','Z','a','b','c','d','e','f','g','h','i','j','k','m','n','o',
'p','q','r','s','t','u','v','w','x','y','z'
);
if($reverse)
{
$reversedTable = array();
foreach($table as $key => $element)
{
$reversedTable[$element] = $key;
}
if(isset($reversedTable[$char]))
return $reversedTable[$char];
else
return null;
}
if(isset($table[$char]))
return $table[$char];
else
return null;
}
/***
* encode a hexadecimal string in Base58.
*
* @param String Hex $data
* @param bool $littleEndian
* @return String Base58
* @throws \Exception
*/
public static function Encode($data, $littleEndian = true){
$res = '';
$dataIntVal = gmp_init($data, 16);
while(gmp_cmp($dataIntVal, gmp_init(0, 10)) > 0)
{
$qr = gmp_div_qr($dataIntVal, gmp_init(58, 10));
$dataIntVal = $qr[0];
$reminder = gmp_strval($qr[1]);
if(!self::permutation_lookup($reminder))
{
throw new \Exception('Something went wrong during base58 encoding');
}
$res .= self::permutation_lookup($reminder);
}
//get number of leading zeros
$leading = '';
$i=0;
while(substr($data, $i, 1) == '0')
{
if($i!= 0 && $i%2)
{
$leading .= '1';
}
$i++;
}
if($littleEndian)
return strrev($res . $leading);
else
return $res.$leading;
}
/***
* Decode a Base58 encoded string and returns it's value as a hexadecimal string
*
* @param $encodedData
* @param bool $littleEndian
* @return String Hex
*/
public static function Decode($encodedData, $littleEndian = true){
$res = gmp_init(0, 10);
$length = strlen($encodedData);
if($littleEndian)
{
$encodedData = strrev($encodedData);
}
for($i = $length - 1; $i >= 0; $i--)
{
$res = gmp_add(
gmp_mul(
$res,
gmp_init(58, 10)
),
self::permutation_lookup(substr($encodedData, $i, 1), true)
);
}
$res = gmp_strval($res, 16);
$i = $length - 1;
while(substr($encodedData, $i, 1) == '1')
{
$res = '00' . $res;
$i--;
}
if(strlen($res)%2 != 0)
{
$res = '0' . $res;
}
return $res;
}
}
/*
* Object orieted interface to Helpful Point Math Operations
* Using the BCMATH library
*/
class PointMathBCMATH {
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt
* @param $a
* @param $p
* @return Array Point
* @throws \Exception
*/
public static function doublePoint(Array $pt, $a, $p) {
$nPt = array();
// 2*ptY
$pty2 = bcmul(2, $pt['y']);
// ( 2*ptY )^-1
$n_pty2 = self::inverse_mod($pty2, $p);
// 3 * ptX^2
$three_x2 = bcmul(3, bcpow($pt['x'], 2));
// (3 * ptX^2 + a ) * ( 2*ptY )^-1
$slope = bcmod(bcmul(bcadd($three_x2, $a), $n_pty2), $p);
// slope^2 - 2 * ptX
$nPt['x'] = bcmod(bcsub(bcpow($slope, 2), bcmul(2, $pt['x'])), $p);
// slope * (ptX - nPtx) - ptY
$nPt['y'] = bcmod(bcsub(bcmul($slope, bcsub($pt['x'], $nPt['x'])), $pt['y']), $p);
if (bccomp(0, $nPt['y']) == 1) {
$nPt['y'] = bcadd($p, $nPt['y']);
}
return $nPt;
}
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt1
* @param Array $pt2
* @param $a
* @param $p
* @return Array Point
* @throws \Exception
*/
public static function addPoints(Array $pt1, Array $pt2, $a, $p) {
$nPt = array();
$gcd = self::bcgcd(bcsub($pt1['x'], $pt2['x']), $p);
if($gcd != '1'){
throw new \Exception('This library doesn\'t yet supports point at infinity.');
}
if (bcmod(bccomp($pt1['x'], $pt2['x']), $p) == 0) {
if (bcmod(bcadd($pt1['y'], $pt2['y']), $p) == 0) {
throw new \Exception('This library doesn\'t yet supports point at infinity.');
} else {
return self::doublePoint($pt1, $a, $p);
}
}
// (pt1Y - pt2Y) * ( pt1X - pt2X )^-1
$slope = bcmod(bcmul(bcsub($pt2['y'], $pt1['y']), self::inverse_mod(bcsub($pt2['x'], $pt1['x']), $p)), $p);
// slope^2 - ptX1 - ptX2
$nPt['x'] = bcmod(bcsub(bcsub(bcpow($slope, 2), $pt1['x']), $pt2['x']), $p);
// slope * (ptX1 - nPtX) - ptY1
$nPt['y'] = bcmod(bcsub(bcmul($slope, bcsub($pt1['x'], $nPt['x'])), $pt1['y']), $p);
if (bccomp(0, $nPt['y']) == 1) {
$nPt['y'] = bcadd($p, $nPt['y']);
}
return $nPt;
}
/***
* Returns inverse mod.
*
* @param $a
* @param $m
* @return bbc math number
*/
private static function inverse_mod($a, $m) {
while (bccomp($a, 0) == -1) {
$a = bcadd($m, $a);
}
while (bccomp($m, $a) == -1) {
$a = bcmod($a, $m);
}
$c = $a;
$d = $m;
$uc = 1;
$vc = 0;
$ud = 0;
$vd = 1;
while (bccomp($c, 0) != 0) {
$temp1 = $c;
$q = bcdiv($d, $c, 0);
$c = bcmod($d, $c);
$d = $temp1;
$temp2 = $uc;
$temp3 = $vc;
$uc = bcsub($ud, bcmul($q, $uc));
$vc = bcsub($vd, bcmul($q, $vc));
$ud = $temp2;
$vd = $temp3;
}
$result = '';
if (bccomp($d, 1) == 0) {
if (bccomp($ud, 0) == 1)
$result = $ud;
else
$result = bcadd($ud, $m);
}else {
throw new ErrorException("ERROR: $a and $m are NOT relatively prime.");
}
return $result;
}
/***
* Compares Points if Identical.
*
* @param $pt1 Array(BC, BC)
* @param $pt2 Array(BC, BC)
* @return Array(BC, BC)
*/
private static function comparePoint($pt1, $pt2){
if (bccomp($pt1['x'], $pt2['x']) == 0 && bccomp($pt1['y'], $pt2['y']) == 0) {
return 0;
} else {
return 1;
}
}
// The Greatest Common Denominator of two large numbers, using BCMath functions.
private static function bcgcd($value1, $value2) {
if ($value1 < $value2)
// Swap $value1 and $value2
{
$temp = $value1;
$value1 = $value2;
$value2 = $temp;
}
// We use the Euclid's algorithm
// for finding the Greatest Common Denominator (GCD)
$mod = 1;
while ($mod != 0)
{
$mod = bcmod ($value1, $value2);
$value1 = $value2;
$value2 = $mod;
}
return $value1;
}
/***
* Returns Negated Point (Y).
*
* @param $point Array(BC, BC)
* @return Array(BC, BC)
*/
public static function negatePoint($point) {
return array('x' => $point['x'], 'y' => bcsub(0, $point['y']));
}
// These 2 function don't really belong here.
// Checks is the given number (DEC String) is even
public static function isEvenNumber($number) {
return (((int)$number[strlen($number)-1]) & 1) == 0;
}
}
/*
* Object orieted interface to Helpful Point Math Operations
* Using the GMP library
*/
class PointMathGMP {
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt
* @return Array Point
* @throws \Exception
*/
public static function doublePoint(Array $pt, $a, $p){
$gcd = gmp_strval(gmp_gcd(gmp_mod(gmp_mul(gmp_init(2, 10), $pt['y']), $p),$p));
if($gcd != '1')
{
throw new \Exception('This library doesn\'t yet supports point at infinity. See https://github.com/BitcoinPHP/BitcoinECDSA.php/issues/9');
}
// SLOPE = (3 * ptX^2 + a )/( 2*ptY )
// Equals (3 * ptX^2 + a ) * ( 2*ptY )^-1
$slope = gmp_mod(
gmp_mul(
gmp_invert(
gmp_mod(
gmp_mul(
gmp_init(2, 10),
$pt['y']
),
$p
),
$p
),
gmp_add(
gmp_mul(
gmp_init(3, 10),
gmp_pow($pt['x'], 2)
),
$a
)
),
$p
);
// nPtX = slope^2 - 2 * ptX
// Equals slope^2 - ptX - ptX
$nPt = array();
$nPt['x'] = gmp_mod(
gmp_sub(
gmp_sub(
gmp_pow($slope, 2),
$pt['x']
),
$pt['x']
),
$p
);
// nPtY = slope * (ptX - nPtx) - ptY
$nPt['y'] = gmp_mod(
gmp_sub(
gmp_mul(
$slope,
gmp_sub(
$pt['x'],
$nPt['x']
)
),
$pt['y']
),
$p
);
return $nPt;
}
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt1
* @param Array $pt2
* @return Array Point
* @throws \Exception
*/
public static function addPoints(Array $pt1, Array $pt2, $a, $p){
if(gmp_cmp($pt1['x'], $pt2['x']) == 0 && gmp_cmp($pt1['y'], $pt2['y']) == 0) //if identical
{
return self::doublePoint($pt1, $a, $p);
}
$gcd = gmp_strval(gmp_gcd(gmp_sub($pt1['x'], $pt2['x']), $p));
if($gcd != '1')
{
throw new \Exception('This library doesn\'t yet supports point at infinity. See https://github.com/BitcoinPHP/BitcoinECDSA.php/issues/9');
}
// SLOPE = (pt1Y - pt2Y)/( pt1X - pt2X )
// Equals (pt1Y - pt2Y) * ( pt1X - pt2X )^-1
$slope = gmp_mod(
gmp_mul(
gmp_sub(
$pt1['y'],
$pt2['y']
),
gmp_invert(
gmp_sub(
$pt1['x'],
$pt2['x']
),
$p
)
),
$p
);
// nPtX = slope^2 - ptX1 - ptX2
$nPt = array();
$nPt['x'] = gmp_mod(
gmp_sub(
gmp_sub(
gmp_pow($slope, 2),
$pt1['x']
),
$pt2['x']
),
$p
);
// nPtX = slope * (ptX1 - nPtX) - ptY1
$nPt['y'] = gmp_mod(
gmp_sub(
gmp_mul(
$slope,
gmp_sub(
$pt1['x'],
$nPt['x']
)
),
$pt1['y']
),
$p
);
return $nPt;
}
/***
* Computes the result of a point multiplication and returns the resulting point as an Array.
*
* @param String Hex $k
* @param Array $pG (GMP, GMP)
* @param $base (INT)
* @throws \Exception
* @return Array Point (GMP, GMP)
*/
public static function mulPoint($k, Array $pG, $a, $b, $p, $base = null){
//in order to calculate k*G
if($base == 16 || $base == null || is_resource($base))
$k = gmp_init($k, 16);
if($base == 10)
$k = gmp_init($k, 10);
$kBin = gmp_strval($k, 2);
$lastPoint = $pG;
for($i = 1; $i < strlen($kBin); $i++)
{
if(substr($kBin, $i, 1) == 1 )
{
$dPt = self::doublePoint($lastPoint, $a, $p);
$lastPoint = self::addPoints($dPt, $pG, $a, $p);
}
else
{
$lastPoint = self::doublePoint($lastPoint, $a, $p);
}
}
if(!self::validatePoint(gmp_strval($lastPoint['x'], 16), gmp_strval($lastPoint['y'], 16), $a, $b, $p)){
throw new \Exception('The resulting point is not on the curve.');
}
return $lastPoint;
}
/***
* Calculates the square root of $a mod p and returns the 2 solutions as an array.
*
* @param $a
* @return array|null
* @throws \Exception
*/
public static function sqrt($a, $p){
if(gmp_legendre($a, $p) != 1)
{
//no result
return null;
}
if(gmp_strval(gmp_mod($p, gmp_init(4, 10)), 10) == 3)
{
$sqrt1 = gmp_powm(
$a,
gmp_div_q(
gmp_add($p, gmp_init(1, 10)),
gmp_init(4, 10)
),
$p
);
// there are always 2 results for a square root
// In an infinite number field you have -2^2 = 2^2 = 4
// In a finite number field you have a^2 = (p-a)^2
$sqrt2 = gmp_mod(gmp_sub($p, $sqrt1), $p);
return array($sqrt1, $sqrt2);
}
else
{
throw new \Exception('P % 4 != 3 , this isn\'t supported yet.');
}
}
/***
* Calculate the Y coordinates for a given X coordinate.
*
* @param $x
* @param null $derEvenOrOddCode
* @return array|null|String
*/
public static function calculateYWithX($x, $a, $b, $p, $derEvenOrOddCode = null){
$x = gmp_init($x, 16);
$y2 = gmp_mod(
gmp_add(
gmp_add(
gmp_powm($x, gmp_init(3, 10), $p),
gmp_mul($a, $x)
),
$b
),
$p
);
$y = self::sqrt($y2, $p);
if(!$y) //if there is no result
{
return null;
}
if(!$derEvenOrOddCode)
{
return $y;
}
else if($derEvenOrOddCode == '02') // even
{
$resY = null;
if(false == gmp_strval(gmp_mod($y[0], gmp_init(2, 10)), 10))
$resY = gmp_strval($y[0], 16);
if(false == gmp_strval(gmp_mod($y[1], gmp_init(2, 10)), 10))
$resY = gmp_strval($y[1], 16);
if($resY)
{
while(strlen($resY) < 64)
{
$resY = '0' . $resY;
}
}
return $resY;
}
else if($derEvenOrOddCode == '03') // odd
{
$resY = null;
if(true == gmp_strval(gmp_mod($y[0], gmp_init(2, 10)), 10))
$resY = gmp_strval($y[0], 16);
if(true == gmp_strval(gmp_mod($y[1], gmp_init(2, 10)), 10))
$resY = gmp_strval($y[1], 16);
if($resY)
{
while(strlen($resY) < 64)
{
$resY = '0' . $resY;
}
}
return $resY;
}
return null;
}
/***
* Returns true if the point is on the curve and false if it isn't.
*
* @param $x
* @param $y
* @return bool
*/
public static function validatePoint($x, $y, $a, $b, $p){
$x = gmp_init($x, 16);
$y2 = gmp_mod(
gmp_add(
gmp_add(
gmp_powm($x, gmp_init(3, 10), $p),
gmp_mul($a, $x)
),
$b
),
$p
);
$y = gmp_mod(gmp_pow(gmp_init($y, 16), 2), $p);
if(gmp_cmp($y2, $y) == 0)
return true;
else
return false;
}
/***
* Returns Negated Point (Y).
*
* @param $point Array(GMP, GMP)
* @return Array(GMP, GMP)
*/
public static function negatePoint($point) {
return array('x' => $point['x'], 'y' => gmp_neg($point['y']));
}
// These 2 function don't really belong here.
// Checks is the given number (DEC String) is even
public static function isEvenNumber($number) {
return (((int)$number[strlen($number)-1]) & 1) == 0;
}
// Converts BIN to GMP
public static function bin2gmp($binStr) {
$v = gmp_init('0');
for ($i = 0; $i < strlen($binStr); $i++) {
$v = gmp_add(gmp_mul($v, 256), ord($binStr[$i]));
}
return $v;
}
}
/*
* Private Key
* For Bitcoin/Zetacoin compatable Crypto Currency utilizing the secp256k1 curve
*/
class PrivateKey{
public $k;
public function __construct($private_key = null){
if (empty($private_key)){
$this->generateRandomPrivateKey();
}
else{
$this->setPrivateKey($private_key);
}
}
/***
* Generate a new random private key.
* The extra parameter can be some random data typed down by the user or mouse movements to add randomness.
*
* @param string $extra
* @throws \Exception
*/
public function generateRandomPrivateKey($extra = 'FSQF5356dsdsqdfEFEQ3fq4q6dq4s5d'){
$secp256k1 = new SECp256k1();
$n = $secp256k1->n;
//private key has to be passed as an hexadecimal number
do { //generate a new random private key until to find one that is valid
$bytes = openssl_random_pseudo_bytes(256, $cStrong);
$hex = bin2hex($bytes);
$random = $hex . microtime(true).rand(100000000000, 1000000000000) . $extra;
$this->k = hash('sha256', $random);
if(!$cStrong)
{
throw new \Exception('Your system is not able to generate strong enough random numbers');
}
} while(gmp_cmp(gmp_init($this->k, 16), gmp_sub($n, gmp_init(1, 10))) == 1);
}
/***
* return the private key.
*
* @return String Hex
*/
public function getPrivateKey(){
return $this->k;
}
/***
* set a private key.
*
* @param String Hex $k
* @throws \Exception
*/
public function setPrivateKey($k){
$secp256k1 = new SECp256k1();
$n = $secp256k1->n;
//private key has to be passed as an hexadecimal number
if(gmp_cmp(gmp_init($k, 16), gmp_sub($n, gmp_init(1, 10))) == 1)
{
throw new \Exception('Private Key is not in the 1,n-1 range');
}
$this->k = $k;
}
/***
* returns the X and Y point coordinates of the public key.
*
* @return Array Point
* @throws \Exception
*/
public function getPubKeyPoints(){
$secp256k1 = new SECp256k1();
$G = $secp256k1->G;
$a = $secp256k1->a;
$b = $secp256k1->b;
$p = $secp256k1->p;
$k = $this->k;
if(!isset($this->k))
{
throw new \Exception('No Private Key was defined');
}
$pubKey = PointMathGMP::mulPoint($k,
array('x' => $G['x'], 'y' => $G['y']),
$a,
$b,
$p
);
$pubKey['x'] = gmp_strval($pubKey['x'], 16);
$pubKey['y'] = gmp_strval($pubKey['y'], 16);
while(strlen($pubKey['x']) < 64)
{
$pubKey['x'] = '0' . $pubKey['x'];
}
while(strlen($pubKey['y']) < 64)
{
$pubKey['y'] = '0' . $pubKey['y'];
}
return $pubKey;
}
}
/*
* The SECp256k1 curve
* Fundamental ECC Function for Bitcoin/Zetacoin compatable Crypto Currency
*/
class SECp256k1 {
public $a;
public $b;
public $p;
public $n;
public $G;
public function __construct(){
$this->a = gmp_init('0', 10);
$this->b = gmp_init('7', 10);
$this->p = gmp_init('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F', 16);
$this->n = gmp_init('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141', 16);
$this->G = array('x' => gmp_init('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
'y' => gmp_init('32670510020758816978083085130507043184471273380659243275938904335757337482424'));
}
}
/*
* Crypto Currency Message Signing and Verification