RSACrypt::getRSADP() - Code Metrics - Inspection of "Merge branch 'v1.1'" - web-token/jwt-framework - Measure and Improve Code Quality continuously with Scrutinizer

Failed Conditions

Push — master ( d40a11...28d61e )

by Florent

created 2018-02-16 11:44 UTC

RSACrypt::getRSADP() A

↳ Parent: RSACrypt

Complexity

Conditions	3
Paths	2

Size

Total Lines	8
Code Lines	4

Duplication

Lines	0
Ratio	0 %

Importance

Changes

Metric	Value
dl	0
loc	8
rs	9.4285
c	0
b	0
f	0
cc	3
eloc	4
nc	2
nop	2

<?php

declare(strict_types=1);

/*
 * The MIT License (MIT)
 *
 * Copyright (c) 2014-2018 Spomky-Labs
 *
 * This software may be modified and distributed under the terms
 * of the MIT license.  See the LICENSE file for details.
 */

namespace Jose\Component\Encryption\Util;

use Jose\Component\Core\Util\BigInteger;
use Jose\Component\Core\Util\Hash;
use Jose\Component\Core\Util\RSAKey;

/**
 * @internal
 */
class RSACrypt
{
    /**
     * Optimal Asymmetric Encryption Padding (OAEP).
     */
    public const ENCRYPTION_OAEP = 1;

    /**
     * Use PKCS#1 padding.
     */
    public const ENCRYPTION_PKCS1 = 2;

    /**
     * @param RSAKey      $key
     * @param string      $data
     * @param int         $mode
     * @param null|string $hash
     *
     * @return string
     */
    public static function encrypt(RSAKey $key, string $data, int $mode, ?string $hash = null): string
    {
        switch ($mode) {
            case self::ENCRYPTION_OAEP:
                return self::encryptWithRSAOAEP($key, $data, $hash);
            case self::ENCRYPTION_PKCS1:
                return self::encryptWithRSA15($key, $data);
            default:
                throw new \InvalidArgumentException('Unsupported mode.');
        }
    }

    /**
     * @param RSAKey      $key
     * @param string      $plaintext
     * @param int         $mode
     * @param null|string $hash
     *
     * @return string
     */
    public static function decrypt(RSAKey $key, string $plaintext, int $mode, ?string $hash = null): string
    {
        switch ($mode) {
            case self::ENCRYPTION_OAEP:
                return self::decryptWithRSAOAEP($key, $plaintext, $hash);
            case self::ENCRYPTION_PKCS1:
                return self::decryptWithRSA15($key, $plaintext);
            default:
                throw new \InvalidArgumentException('Unsupported mode.');
        }
    }

    /**
     * @param RSAKey $key
     * @param string $data
     *
     * @return string
     */
    public static function encryptWithRSA15(RSAKey $key, string $data): string
    {
        $mLen = mb_strlen($data, '8bit');

        if ($mLen > $key->getModulusLength() - 11) {
            throw new \InvalidArgumentException('Message too long');
        }

        $psLen = $key->getModulusLength() - $mLen - 3;
        $ps = '';
        while (mb_strlen($ps, '8bit') !== $psLen) {
            $temp = random_bytes($psLen - mb_strlen($ps, '8bit'));
            $temp = str_replace("\x00", '', $temp);
            $ps .= $temp;
        }
        $type = 2;
        $data = chr(0).chr($type).$ps.chr(0).$data;

        $data = BigInteger::createFromBinaryString($data);
        $c = self::getRSAEP($key, $data);
        $c = self::convertIntegerToOctetString($c, $key->getModulusLength());

        return $c;
    }

    /**
     * @param RSAKey $key
     * @param string $c
     *
     * @return string
     */
    public static function decryptWithRSA15(RSAKey $key, string $c): string
    {
        if (mb_strlen($c, '8bit') !== $key->getModulusLength()) {
            throw new \InvalidArgumentException('Unable to decrypt');
        }

        $c = BigInteger::createFromBinaryString($c);
        $m = self::getRSADP($key, $c);
        $em = self::convertIntegerToOctetString($m, $key->getModulusLength());

        if (0 != ord($em[0]) || ord($em[1]) > 2) {
            throw new \InvalidArgumentException('Unable to decrypt');
        }

        $ps = mb_substr($em, 2, mb_strpos($em, chr(0), 2, '8bit') - 2, '8bit');
        $m = mb_substr($em, mb_strlen($ps, '8bit') + 3, null, '8bit');

        if (mb_strlen($ps, '8bit') < 8) {
            throw new \InvalidArgumentException('Unable to decrypt');
        }

        return $m;
    }

    /**
     * Encryption.
     *
     * @param RSAKey $key
     * @param string $plaintext
     * @param string $hash_algorithm
     *
     * @return string
     */
    public static function encryptWithRSAOAEP(RSAKey $key, string $plaintext, string $hash_algorithm): string
    {
        /** @var Hash $hash */
        $hash = Hash::$hash_algorithm();
        $length = $key->getModulusLength() - 2 * $hash->getLength() - 2;
        if (0 >= $length) {
            throw new \RuntimeException();
        }
        $plaintext = str_split($plaintext, $length);
        $ciphertext = '';
        foreach ($plaintext as $m) {
            $ciphertext .= self::encryptRSAESOAEP($key, $m, $hash);
        }

        return $ciphertext;
    }

    /**
     * Decryption.
     *
     * @param RSAKey $key
     * @param string $ciphertext
     * @param string $hash_algorithm
     *
     * @return string
     */
    public static function decryptWithRSAOAEP(RSAKey $key, string $ciphertext, string $hash_algorithm): string
    {
        if (0 >= $key->getModulusLength()) {
            throw new \RuntimeException();
        }
        $hash = Hash::$hash_algorithm();
        $ciphertext = str_split($ciphertext, $key->getModulusLength());
        $ciphertext[count($ciphertext) - 1] = str_pad($ciphertext[count($ciphertext) - 1], $key->getModulusLength(), chr(0), STR_PAD_LEFT);
        $plaintext = '';
        foreach ($ciphertext as $c) {
            $temp = self::getRSAESOAEP($key, $c, $hash);
            $plaintext .= $temp;
        }

        return $plaintext;
    }

    /**
     * @param BigInteger $x
     * @param int        $xLen
     *
     * @return string
     */
    private static function convertIntegerToOctetString(BigInteger $x, int $xLen): string
    {
        $x = $x->toBytes();
        if (mb_strlen($x, '8bit') > $xLen) {
            throw new \RuntimeException('Invalid length.');
        }

        return str_pad($x, $xLen, chr(0), STR_PAD_LEFT);
    }

    /**
     * Octet-String-to-Integer primitive.
     *
     * @param string $x
     *
     * @return BigInteger
     */
    private static function convertOctetStringToInteger(string $x): BigInteger
    {
        return BigInteger::createFromBinaryString($x);
    }

    /**
     * RSA EP.
     *
     * @param RSAKey     $key
     * @param BigInteger $m
     *
     * @return BigInteger
     */
    private static function getRSAEP(RSAKey $key, BigInteger $m): BigInteger
    {
        if ($m->compare(BigInteger::createFromDecimal(0)) < 0 || $m->compare($key->getModulus()) > 0) {
function acceptsInteger($int) { }

$x = '123'; // string "123"

// Instead of
acceptsInteger($x);

// we recommend to use
acceptsInteger((integer) $x);
            throw new \RuntimeException();
        }

        return RSAKey::exponentiate($key, $m);
function acceptsInteger($int) { }

$x = '123'; // string "123"

// Instead of
acceptsInteger($x);

// we recommend to use
acceptsInteger((integer) $x);
    }

    /**
     * RSA DP.
     *
     * @param RSAKey     $key
     * @param BigInteger $c
     *
     * @return BigInteger
     */
    private static function getRSADP(RSAKey $key, BigInteger $c): BigInteger
    {
        if ($c->compare(BigInteger::createFromDecimal(0)) < 0 || $c->compare($key->getModulus()) > 0) {
function acceptsInteger($int) { }

$x = '123'; // string "123"

// Instead of
acceptsInteger($x);

// we recommend to use
acceptsInteger((integer) $x);
            throw new \RuntimeException();
        }

        return RSAKey::exponentiate($key, $c);
function acceptsInteger($int) { }

$x = '123'; // string "123"

// Instead of
acceptsInteger($x);

// we recommend to use
acceptsInteger((integer) $x);
    }

    /**
     * MGF1.
     *
     * @param string $mgfSeed
     * @param int    $maskLen
     * @param Hash   $mgfHash
     *
     * @return string
     */
    private static function getMGF1(string $mgfSeed, int $maskLen, Hash $mgfHash): string
    {
        $t = '';
        $count = ceil($maskLen / $mgfHash->getLength());
        for ($i = 0; $i < $count; $i++) {
            $c = pack('N', $i);
            $t .= $mgfHash->hash($mgfSeed.$c);
        }

        return mb_substr($t, 0, $maskLen, '8bit');
    }

    /**
     * RSAES-OAEP-ENCRYPT.
     *
     * @param RSAKey $key
     * @param string $m
     * @param Hash   $hash
     *
     * @return string
     */
    private static function encryptRSAESOAEP(RSAKey $key, string $m, Hash $hash): string
    {
        $mLen = mb_strlen($m, '8bit');
        $lHash = $hash->hash('');
        $ps = str_repeat(chr(0), $key->getModulusLength() - $mLen - 2 * $hash->getLength() - 2);
        $db = $lHash.$ps.chr(1).$m;
        $seed = random_bytes($hash->getLength());
        $dbMask = self::getMGF1($seed, $key->getModulusLength() - $hash->getLength() - 1, $hash/*MGF*/);
        $maskedDB = strval($db ^ $dbMask);
        $seedMask = self::getMGF1($maskedDB, $hash->getLength(), $hash/*MGF*/);
        $maskedSeed = $seed ^ $seedMask;
        $em = chr(0).$maskedSeed.$maskedDB;

        $m = self::convertOctetStringToInteger($em);
        $c = self::getRSAEP($key, $m);
        $c = self::convertIntegerToOctetString($c, $key->getModulusLength());

        return $c;
    }

    /**
     * RSAES-OAEP-DECRYPT.
     *
     * @param RSAKey $key
     * @param string $c
     * @param Hash   $hash
     *
     * @return string
     */
    private static function getRSAESOAEP(RSAKey $key, string $c, Hash $hash): string
    {
        $c = self::convertOctetStringToInteger($c);
        $m = self::getRSADP($key, $c);
        $em = self::convertIntegerToOctetString($m, $key->getModulusLength());
        $lHash = $hash->hash('');
        $maskedSeed = mb_substr($em, 1, $hash->getLength(), '8bit');
        $maskedDB = mb_substr($em, $hash->getLength() + 1, null, '8bit');
        $seedMask = self::getMGF1($maskedDB, $hash->getLength(), $hash/*MGF*/);
        $seed = strval($maskedSeed ^ $seedMask);
        $dbMask = self::getMGF1($seed, $key->getModulusLength() - $hash->getLength() - 1, $hash/*MGF*/);
        $db = $maskedDB ^ $dbMask;
        $lHash2 = mb_substr($db, 0, $hash->getLength(), '8bit');
        $m = mb_substr($db, $hash->getLength(), null, '8bit');
        if (!hash_equals($lHash, $lHash2)) {
            throw new \RuntimeException();
        }
        $m = ltrim($m, chr(0));
        if (1 !== ord($m[0])) {
            throw new \RuntimeException();
        }

        return mb_substr($m, 1, null, '8bit');
    }
}


1			<?php
2
3			declare(strict_types=1);
4
5			/*
6			* The MIT License (MIT)
7			*
8			* Copyright (c) 2014-2018 Spomky-Labs
9			*
10			* This software may be modified and distributed under the terms
11			* of the MIT license. See the LICENSE file for details.
12			*/
13
14			namespace Jose\Component\Encryption\Util;
15
16			use Jose\Component\Core\Util\BigInteger;
17			use Jose\Component\Core\Util\Hash;
18			use Jose\Component\Core\Util\RSAKey;
19
20			/**
21			* @internal
22			*/
23			class RSACrypt
24			{
25			/**
26			* Optimal Asymmetric Encryption Padding (OAEP).
27			*/
28			public const ENCRYPTION_OAEP = 1;
29
30			/**
31			* Use PKCS#1 padding.
32			*/
33			public const ENCRYPTION_PKCS1 = 2;
34
35			/**
36			* @param RSAKey $key
37			* @param string $data
38			* @param int $mode
39			* @param null\|string $hash
40			*
41			* @return string
42			*/
43			public static function encrypt(RSAKey $key, string $data, int $mode, ?string $hash = null): string
44			{
45			switch ($mode) {
46			case self::ENCRYPTION_OAEP:
47			return self::encryptWithRSAOAEP($key, $data, $hash);
48			case self::ENCRYPTION_PKCS1:
49			return self::encryptWithRSA15($key, $data);
50			default:
51			throw new \InvalidArgumentException('Unsupported mode.');
52			}
53			}
54
55			/**
56			* @param RSAKey $key
57			* @param string $plaintext
58			* @param int $mode
59			* @param null\|string $hash
60			*
61			* @return string
62			*/
63			public static function decrypt(RSAKey $key, string $plaintext, int $mode, ?string $hash = null): string
64			{
65			switch ($mode) {
66			case self::ENCRYPTION_OAEP:
67			return self::decryptWithRSAOAEP($key, $plaintext, $hash);
68			case self::ENCRYPTION_PKCS1:
69			return self::decryptWithRSA15($key, $plaintext);
70			default:
71			throw new \InvalidArgumentException('Unsupported mode.');
72			}
73			}
74
75			/**
76			* @param RSAKey $key
77			* @param string $data
78			*
79			* @return string
80			*/
81			public static function encryptWithRSA15(RSAKey $key, string $data): string
82			{
83			$mLen = mb_strlen($data, '8bit');
84
85			if ($mLen > $key->getModulusLength() - 11) {
86			throw new \InvalidArgumentException('Message too long');
87			}
88
89			$psLen = $key->getModulusLength() - $mLen - 3;
90			$ps = '';
91			while (mb_strlen($ps, '8bit') !== $psLen) {
92			$temp = random_bytes($psLen - mb_strlen($ps, '8bit'));
93			$temp = str_replace("\x00", '', $temp);
94			$ps .= $temp;
95			}
96			$type = 2;
97			$data = chr(0).chr($type).$ps.chr(0).$data;
98
99			$data = BigInteger::createFromBinaryString($data);
100			$c = self::getRSAEP($key, $data);
101			$c = self::convertIntegerToOctetString($c, $key->getModulusLength());
102
103			return $c;
104			}
105
106			/**
107			* @param RSAKey $key
108			* @param string $c
109			*
110			* @return string
111			*/
112			public static function decryptWithRSA15(RSAKey $key, string $c): string
113			{
114			if (mb_strlen($c, '8bit') !== $key->getModulusLength()) {
115			throw new \InvalidArgumentException('Unable to decrypt');
116			}
117
118			$c = BigInteger::createFromBinaryString($c);
119			$m = self::getRSADP($key, $c);
120			$em = self::convertIntegerToOctetString($m, $key->getModulusLength());
121
122			if (0 != ord($em[0]) \|\| ord($em[1]) > 2) {
123			throw new \InvalidArgumentException('Unable to decrypt');
124			}
125
126			$ps = mb_substr($em, 2, mb_strpos($em, chr(0), 2, '8bit') - 2, '8bit');
127			$m = mb_substr($em, mb_strlen($ps, '8bit') + 3, null, '8bit');
128
129			if (mb_strlen($ps, '8bit') < 8) {
130			throw new \InvalidArgumentException('Unable to decrypt');
131			}
132
133			return $m;
134			}
135
136			/**
137			* Encryption.
138			*
139			* @param RSAKey $key
140			* @param string $plaintext
141			* @param string $hash_algorithm
142			*
143			* @return string
144			*/
145			public static function encryptWithRSAOAEP(RSAKey $key, string $plaintext, string $hash_algorithm): string
146			{
147			/** @var Hash $hash */
148			$hash = Hash::$hash_algorithm();
149			$length = $key->getModulusLength() - 2 * $hash->getLength() - 2;
150			if (0 >= $length) {
151			throw new \RuntimeException();
152			}
153			$plaintext = str_split($plaintext, $length);
154			$ciphertext = '';
155			foreach ($plaintext as $m) {
156			$ciphertext .= self::encryptRSAESOAEP($key, $m, $hash);
157			}
158
159			return $ciphertext;
160			}
161
162			/**
163			* Decryption.
164			*
165			* @param RSAKey $key
166			* @param string $ciphertext
167			* @param string $hash_algorithm
168			*
169			* @return string
170			*/
171			public static function decryptWithRSAOAEP(RSAKey $key, string $ciphertext, string $hash_algorithm): string
172			{
173			if (0 >= $key->getModulusLength()) {
174			throw new \RuntimeException();
175			}
176			$hash = Hash::$hash_algorithm();
177			$ciphertext = str_split($ciphertext, $key->getModulusLength());
178			$ciphertext[count($ciphertext) - 1] = str_pad($ciphertext[count($ciphertext) - 1], $key->getModulusLength(), chr(0), STR_PAD_LEFT);
179			$plaintext = '';
180			foreach ($ciphertext as $c) {
181			$temp = self::getRSAESOAEP($key, $c, $hash);
182			$plaintext .= $temp;
183			}
184
185			return $plaintext;
186			}
187
188			/**
189			* @param BigInteger $x
190			* @param int $xLen
191			*
192			* @return string
193			*/
194			private static function convertIntegerToOctetString(BigInteger $x, int $xLen): string
195			{
196			$x = $x->toBytes();
197			if (mb_strlen($x, '8bit') > $xLen) {
198			throw new \RuntimeException('Invalid length.');
199			}
200
201			return str_pad($x, $xLen, chr(0), STR_PAD_LEFT);
202			}
203
204			/**
205			* Octet-String-to-Integer primitive.
206			*
207			* @param string $x
208			*
209			* @return BigInteger
210			*/
211			private static function convertOctetStringToInteger(string $x): BigInteger
212			{
213			return BigInteger::createFromBinaryString($x);
214			}
215
216			/**
217			* RSA EP.
218			*
219			* @param RSAKey $key
220			* @param BigInteger $m
221			*
222			* @return BigInteger
223			*/
224			private static function getRSAEP(RSAKey $key, BigInteger $m): BigInteger
225			{
226			if ($m->compare(BigInteger::createFromDecimal(0)) < 0 \|\| $m->compare($key->getModulus()) > 0) {
			0 ignored issues – show Documentation introduced 2017-11-13 20:39 UTC by Report Bug Copy Issue Report `$key->getModulus()` is of type `object<Jose\Component\Core\Util\BigInteger>`, but the function expects a `object<self>`. It seems like the type of the argument is not accepted by the function/method which you are calling. In some cases, in particular if PHP’s automatic type-juggling kicks in this might be fine. In other cases, however this might be a bug. We suggest to add an explicit type cast like in the following example: function acceptsInteger($int) { } $x = '123'; // string "123" // Instead of acceptsInteger($x); // we recommend to use acceptsInteger((integer) $x); Loading history...
227			throw new \RuntimeException();
228			}
229
230			return RSAKey::exponentiate($key, $m);
			0 ignored issues – show Documentation introduced 2017-11-25 22:04 UTC by Report Bug Copy Issue Report `$key` is of type `object<Jose\Component\Core\Util\RSAKey>`, but the function expects a `object<self>`. It seems like the type of the argument is not accepted by the function/method which you are calling. In some cases, in particular if PHP’s automatic type-juggling kicks in this might be fine. In other cases, however this might be a bug. We suggest to add an explicit type cast like in the following example: function acceptsInteger($int) { } $x = '123'; // string "123" // Instead of acceptsInteger($x); // we recommend to use acceptsInteger((integer) $x); Loading history...
231			}
232
233			/**
234			* RSA DP.
235			*
236			* @param RSAKey $key
237			* @param BigInteger $c
238			*
239			* @return BigInteger
240			*/
241			private static function getRSADP(RSAKey $key, BigInteger $c): BigInteger
242			{
243			if ($c->compare(BigInteger::createFromDecimal(0)) < 0 \|\| $c->compare($key->getModulus()) > 0) {
			0 ignored issues – show Documentation introduced 2017-11-13 20:39 UTC by Report Bug Copy Issue Report `$key->getModulus()` is of type `object<Jose\Component\Core\Util\BigInteger>`, but the function expects a `object<self>`. It seems like the type of the argument is not accepted by the function/method which you are calling. In some cases, in particular if PHP’s automatic type-juggling kicks in this might be fine. In other cases, however this might be a bug. We suggest to add an explicit type cast like in the following example: function acceptsInteger($int) { } $x = '123'; // string "123" // Instead of acceptsInteger($x); // we recommend to use acceptsInteger((integer) $x); Loading history...
244			throw new \RuntimeException();
245			}
246
247			return RSAKey::exponentiate($key, $c);
			0 ignored issues – show Documentation introduced 2017-11-25 22:04 UTC by Report Bug Copy Issue Report `$key` is of type `object<Jose\Component\Core\Util\RSAKey>`, but the function expects a `object<self>`. It seems like the type of the argument is not accepted by the function/method which you are calling. In some cases, in particular if PHP’s automatic type-juggling kicks in this might be fine. In other cases, however this might be a bug. We suggest to add an explicit type cast like in the following example: function acceptsInteger($int) { } $x = '123'; // string "123" // Instead of acceptsInteger($x); // we recommend to use acceptsInteger((integer) $x); Loading history...
248			}
249
250			/**
251			* MGF1.
252			*
253			* @param string $mgfSeed
254			* @param int $maskLen
255			* @param Hash $mgfHash
256			*
257			* @return string
258			*/
259			private static function getMGF1(string $mgfSeed, int $maskLen, Hash $mgfHash): string
260			{
261			$t = '';
262			$count = ceil($maskLen / $mgfHash->getLength());
263			for ($i = 0; $i < $count; $i++) {
264			$c = pack('N', $i);
265			$t .= $mgfHash->hash($mgfSeed.$c);
266			}
267
268			return mb_substr($t, 0, $maskLen, '8bit');
269			}
270
271			/**
272			* RSAES-OAEP-ENCRYPT.
273			*
274			* @param RSAKey $key
275			* @param string $m
276			* @param Hash $hash
277			*
278			* @return string
279			*/
280			private static function encryptRSAESOAEP(RSAKey $key, string $m, Hash $hash): string
281			{
282			$mLen = mb_strlen($m, '8bit');
283			$lHash = $hash->hash('');
284			$ps = str_repeat(chr(0), $key->getModulusLength() - $mLen - 2 * $hash->getLength() - 2);
285			$db = $lHash.$ps.chr(1).$m;
286			$seed = random_bytes($hash->getLength());
287			$dbMask = self::getMGF1($seed, $key->getModulusLength() - $hash->getLength() - 1, $hash/MGF/);
288			$maskedDB = strval($db ^ $dbMask);
289			$seedMask = self::getMGF1($maskedDB, $hash->getLength(), $hash/MGF/);
290			$maskedSeed = $seed ^ $seedMask;
291			$em = chr(0).$maskedSeed.$maskedDB;
292
293			$m = self::convertOctetStringToInteger($em);
294			$c = self::getRSAEP($key, $m);
295			$c = self::convertIntegerToOctetString($c, $key->getModulusLength());
296
297			return $c;
298			}
299
300			/**
301			* RSAES-OAEP-DECRYPT.
302			*
303			* @param RSAKey $key
304			* @param string $c
305			* @param Hash $hash
306			*
307			* @return string
308			*/
309			private static function getRSAESOAEP(RSAKey $key, string $c, Hash $hash): string
310			{
311			$c = self::convertOctetStringToInteger($c);
312			$m = self::getRSADP($key, $c);
313			$em = self::convertIntegerToOctetString($m, $key->getModulusLength());
314			$lHash = $hash->hash('');
315			$maskedSeed = mb_substr($em, 1, $hash->getLength(), '8bit');
316			$maskedDB = mb_substr($em, $hash->getLength() + 1, null, '8bit');
317			$seedMask = self::getMGF1($maskedDB, $hash->getLength(), $hash/MGF/);
318			$seed = strval($maskedSeed ^ $seedMask);
319			$dbMask = self::getMGF1($seed, $key->getModulusLength() - $hash->getLength() - 1, $hash/MGF/);
320			$db = $maskedDB ^ $dbMask;
321			$lHash2 = mb_substr($db, 0, $hash->getLength(), '8bit');
322			$m = mb_substr($db, $hash->getLength(), null, '8bit');
323			if (!hash_equals($lHash, $lHash2)) {
324			throw new \RuntimeException();
325			}
326			$m = ltrim($m, chr(0));
327			if (1 !== ord($m[0])) {
328			throw new \RuntimeException();
329			}
330
331			return mb_substr($m, 1, null, '8bit');
332			}
333			}
334

web-token / jwt-framework

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RSACrypt::getRSADP() A

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