如何使用公共/私有RSA密钥对某些数据进行签名？

Question

我有一个RSA公钥/私钥xml文件。我想用它来签署一些数据，下面是我如何使用这个类：

$processor = new RSAProcessor("certificate.xml", RSAKeyType:: XMLFile);
$data =  $processor->sign($data); 
print(base64_encode($data));

但我得到了错误：WARNING: str_repeat(): Second argument has to be greater than or equal to 0 in RSA.php on line 81。怎么修呢？我想php7.2有些东西已经过时了吧？非常感谢您的帮助，为了避免这个错误，我应该在我的课堂上做些什么改变？

Rsa类：

define("BCCOMP_LARGER", 1);
class RSA {
 static function rsa_encrypt($message, $public_key, $modulus, $keylength) {
  $padded = RSA::add_PKCS1_padding($message, true, $keylength / 8);
  $number = RSA::binary_to_number($padded);
  $encrypted = RSA::pow_mod($number, $public_key, $modulus);
  $result = RSA::number_to_binary($encrypted, $keylength / 8);
  return $result;
 }
 static function rsa_decrypt($message, $private_key, $modulus, $keylength) {
  $number = RSA::binary_to_number($message);
  $decrypted = RSA::pow_mod($number, $private_key, $modulus);
  $result = RSA::number_to_binary($decrypted, $keylength / 8);
  return RSA::remove_PKCS1_padding($result, $keylength / 8);
 }
 static function rsa_sign($message, $private_key, $modulus, $keylength) {
  $padded = RSA::add_PKCS1_padding($message, false, $keylength / 8);
  $number = RSA::binary_to_number($padded);
  $signed = RSA::pow_mod($number, $private_key, $modulus);
  $result = RSA::number_to_binary($signed, $keylength / 8);
  return $result;
 }
 static function rsa_verify($message, $public_key, $modulus, $keylength) {
  return RSA::rsa_decrypt($message, $public_key, $modulus, $keylength);
 }
 static function rsa_kyp_verify($message, $public_key, $modulus, $keylength) {
  $number = RSA::binary_to_number($message);
  $decrypted = RSA::pow_mod($number, $public_key, $modulus);
  $result = RSA::number_to_binary($decrypted, $keylength / 8);
  return RSA::remove_KYP_padding($result, $keylength / 8);
 }
 static function pow_mod($p, $q, $r) {
  $factors = array();
  $div = $q;
  $power_of_two = 0;
while(bccomp($div, "0") == BCCOMP_LARGER)  {
   $rem = bcmod($div, 2);
   $div = bcdiv($div, 2);
   if($rem) array_push($factors, $power_of_two);
   $power_of_two++;
  }
  $partial_results = array();
  $part_res = $p;
  $idx = 0;
  foreach($factors as $factor)  {
   while($idx < $factor)
   {
    $part_res = bcpow($part_res, "2");
    $part_res = bcmod($part_res, $r);
    $idx++;
   }
   array_push($partial_results, $part_res);
  }
  $result = "1";
  foreach($partial_results as $part_res)
  {
   $result = bcmul($result, $part_res);
   $result = bcmod($result, $r);
  }
  return $result;
 }
 static  function add_PKCS1_padding($data, $isPublicKey, $blocksize)
 {
  $pad_length = $blocksize - 3 - strlen($data);
  if($isPublicKey)
  {
   $block_type = "\x02";
   $padding = "";
   for($i = 0; $i < $pad_length; $i++)
   {
    $rnd = mt_rand(1, 255);
    $padding .= chr($rnd);
   }
  }
  else
  {
   $block_type = "\x01";
   $padding = str_repeat("\xFF", $pad_length);
  }
  return "\x00" . $block_type . $padding . "\x00" . $data;
 }
  static function remove_PKCS1_padding($data, $blocksize)
 {
  assert(strlen($data) == $blocksize);
  $data = substr($data, 1);
  if($data{0} == '\0')
  die("Block type 0 not implemented.");
  assert(($data{0} == "\x01") || ($data{0} == "\x02"));
  $offset = strpos($data, "\0", 1);
  return substr($data, $offset + 1);
 }
  static function remove_KYP_padding($data, $blocksize)
 {
  assert(strlen($data) == $blocksize);
  $offset = strpos($data, "\0");
  return substr($data, 0, $offset);
 }
 static function binary_to_number($data)
 {
  $base = "256";
  $radix = "1";
  $result = "0";
  for($i = strlen($data) - 1; $i >= 0; $i--)
  {
   $digit = ord($data{$i});
   $part_res = bcmul($digit, $radix);
   $result = bcadd($result, $part_res);
   $radix = bcmul($radix, $base);
  }
  return $result;
  }
 static  function number_to_binary($number, $blocksize)
 {
  $base = "256";
  $result = "";
  $div = $number;
  while($div > 0)
  {
   $mod = bcmod($div, $base);
   $div = bcdiv($div, $base);
   $result = chr($mod) . $result;
  }
  return str_pad($result, $blocksize, "\x00", STR_PAD_LEFT);
 }
}

RSAProcessor类：

class RSAProcessor
{
 private $public_key = null;
 private $private_key = null;
 private $modulus = null;
 private $key_length = "1024";
 public function __construct($xmlRsakey=null,$type=null)
 {
         $xmlObj = null;
         if ($xmlRsakey==null) {
             $xmlObj = simplexml_load_file("xmlfile/RSAKey.xml");
          } elseif ($type==RSAKeyType::XMLFile) {
             $xmlObj = simplexml_load_file($xmlRsakey);
          } else {
             $xmlObj = simplexml_load_string($xmlRsakey);
          }
         $this->modulus = RSA::binary_to_number(base64_decode($xmlObj->Modulus));
         $this->public_key = RSA::binary_to_number(base64_decode($xmlObj->Exponent));
         $this->private_key = RSA::binary_to_number(base64_decode($xmlObj->D));
         $this->key_length = strlen(base64_decode($xmlObj->Modulus))*8;
 }
 public function getPublicKey() {
  return $this->public_key;
 }
 public function getPrivateKey() {
  return $this->private_key;
 }
 public function getKeyLength() {
  return $this->key_length;
 }
 public function getModulus() {
  return $this->modulus;
 }
 public function encrypt($data) {
  return base64_encode(RSA::rsa_encrypt($data,$this->public_key,$this->modulus,$this->key_length));
 }
  public function dencrypt($data) {
  return RSA::rsa_decrypt($data,$this->private_key,$this->modulus,$this->key_length);
 }
  public function sign($data) {
  return RSA::rsa_sign($data,$this->private_key,$this->modulus,$this->key_length);
 }
  public function verify($data) {
  return RSA::rsa_verify($data,$this->public_key,$this->modulus,$this->key_length);
 }
}


class RSAKeyType{
 const XMLFile = 0;
 const XMLString = 1;
}

certificate.xml：

<RSAKeyValue>
<Modulus>tCZiqDS5BVQQZDBUYbyeoP4rENN4mX5FZJjjMNfGbyzfzH45RY2/YsMaY0yI1jMCOpukvkUyl153tcn0LXhMCDdsEhhZPoKbPUGMniKtFGjs18rv/b5FFUUW1utgwoL8+WJqjOqhQGgvbja63X9+WMFP0nM3d8yudn9C/X55KyM=</Modulus>
    <Exponent>AQAB</Exponent>
    <P>5HXvmU4IfqUG2jFLSqi/BMEQ3x1NsUDvx3zN5O1p9yLLspJ4sqAt4RUkxzcGodYgBSdXsR9IGcPwjQfbx3a7nQ==</P>
    <Q>yd2hDCF/5Zqtz9DXjY1NRYGvBjTS4AQn83ERR46Y5eBSnLjpVjv6gPfARuhsUP44nikrQPvwPnjxQcOhJaOlvw==</Q>
    <DP>ztuqUplBP8qU5cN0dOlN7DQT3rFdw30Unv/2Pa5qIAc1gT72YmZ+pCrM3kSIkMicvY3d7NZyJkIv8MKI0ZZEUQ==</DP>
    <DQ>QFLJ5YarLWubZPQEK4vSCornTY/5ff51CIKH4ghTOjS/vkbBu4PDL+NCNpYLJcfMHMG7kap2BEIfhjgjGk5KGw==</DQ>
    <InverseQ>WE6TqpcexQJwt9Mnp1FbeLtarBcFkXVdBauouFKHcbHCfQjA3IjUrGTxgSO74O/4QSKqaF2gnlL6GI7gKuGbzQ==</InverseQ>  <D>czYtWDfHsFGv3fNOs+cGaB3E+xDTiw7HYGuquJz2qjk/s69x/zqFEKuIH8Ndq+eZYFQUCx+EGGxxENDkmYPa0z8wbfFI6JEHpxaLmQfpkkbSL1BJIp9Z5BNM2gy6jJqgbWwQPcN/4jpiMefHZWAqhMKqenUu1KIq1ZX6Bz5xKYk=</D>
</RSAKeyValue>

非常感谢您的帮助，为了避免这个错误，我应该在我的课堂上做些什么改变？

Answer 1

在我的本地环境中，代码运行平稳，而且在http://phpfiddle.org/ (PHP7.0.33)上运行也很顺利！但是，对于后者，键必须作为字符串传递，因为在线没有可用的文件系统：

$privateKey = "<RSAKeyValue>...</RSAKeyValue>";
$processor = new RSAProcessor($privateKey, RSAKeyType::XMLString);

另一方面，相同的代码在http://sandbox.onlinephpfunctions.com/ (PHP7.01-PHP7.3.5)上失败，错误消息与您的相同。原因是禁用了simplexml_load_string()方法。因此，键无法加载，并且成员变量$modulus、$key_length、$private_key和RSAProcessor-class的$public_key获得了值0。因此，使用$blocksize=$keylength/8调用的方法$blocksize=$keylength/8确定$pad_length=$blocksize-3-strlen($data)的负值，该值透明地导致错误消息str_repeat()：当调用str_repeat("\xFF", $pad_length)时，第二个参数必须大于或等于0。

如果我在本地环境中禁用了方法simplexml_load_file，我就可以准确地再现这种行为。由于代码在原则上是有效的，所以可以假设您的系统中也禁用了方法，特别是simplexml_load_file。

可以通过从disable_functions-list中删除禁用的方法来启用这些方法。

更新：

正如注释中已经提到的，RSA得到了绝大多数库的支持，例如phpseclib、这里，它们也支持代码中使用的关键格式这里。

通常，对于PKCS#1，不是数据本身，而是使用前面的摘要信息( DigestInfo值的DER编码)的散列根据RFC 8017进行签名，请参见这里，这就是为什么还必须指定摘要的原因。假设您的数据(即传递给您的$data RSAProcessor#sign-method)遵循此约定，即：

$dataToSign = 'The quick brown fox jumps over the lazy dog'; 
$data = hex2bin('3031300d060960864801650304020105000420' . hash('SHA256', $dataToSign, false));

使用phpseclib库(以SHA256作为摘要)的以下代码将生成相同的签名：

include('RSA.php');
include('BigInteger.php');

$rsa = new Crypt_RSA();

$privateKey = "<RSAKeyValue>...</RSAKeyValue>";
$dataToSign = 'The quick brown fox jumps over the lazy dog';

$rsa->setPrivateKeyFormat(CRYPT_RSA_PRIVATE_FORMAT_XML);  // private key format
$rsa->loadKey($privateKey);

$rsa->setHash('sha256');                                  // digest for signing
$rsa->setSignatureMode(CRYPT_RSA_SIGNATURE_PKCS1);        // RSASSA-PKCS1-v1_5-padding
$signature = $rsa->sign($dataToSign);

echo 'Signature (hex):    ' . bin2hex($signature) . "\n";
echo 'Signature (base64): ' . base64_encode($signature) . "\n";

然后，这两个代码提供以下签名(作为十六进制字符串)：

6f00eb1126470e097991aaa1e3e94b49a7b8de6c9b2bf683382f96563479b87067be20635ccc1d36fedff9d60f682fdefcb108f5351dc672ebb442e49231d0306b302b258f6b21fb724b59ad765151f6c724de214d41afa0e1b08228b070c537020df8acf9cad5f2fdde63bc698875527a52e49155bd5e2fd761f541844e92bb

更新2:

对于SHA1，您的代码的ID加散列可以确定如下：

$data = hex2bin('3021300906052b0e03021a05000414' . hash('SHA1', $dataToSign, false));

或

$data = hex2bin('3021300906052b0e03021a05000414' . SHA1($dataToSign, false));

可以使用hash-function或sha1-function。在这两种情况下，最后一个参数$raw_output控制返回是二进制(TRUE)还是十六进制字符串(FALSE)。由于与ID的连接，我以十六进制字符串的形式返回散列，进行连接，最后使用hex2bin显式转换为二进制表示。摘要ID也可以找到这里，第47页。

在phpseclib代码中

$rsa->setHash('sha1');

一定要用。