I have implemented OAEP encryption for the OpenSSL crypto library.
OAEP is the improved padding method for RSA, which is recommended
for new applications in PKCS #1 v2.0 (RFC 2437, October 1998).
OAEP (Optimal Asymmetric Encryption Padding) has better theoretical
foundations than the ad-hoc padding used in PKCS #1 v1.5. It is
secure against Bleichbacher's attack on RSA.
It seems that OpenSSL's x86 assembler implementation of SHA1 is
broken. If the test program aborts with "illegal instruction", use
the C version instead.
diff -u orig/Makefile.ssl ./Makefile.ssl
--- orig/Makefile.ssl Wed Jan 20 00:25:20 1999
+++ ./Makefile.ssl Sat Feb 6 00:01:18 1999
@@ -23,9 +23,9 @@
LIB=$(TOP)/libcrypto.a
LIBSRC= rsa_eay.c rsa_gen.c rsa_lib.c rsa_sign.c rsa_saos.c $(ERRC).c \
- rsa_pk1.c rsa_ssl.c rsa_none.c
+ rsa_pk1.c rsa_ssl.c rsa_none.c rsa_oaep.c
LIBOBJ= rsa_eay.o rsa_gen.o rsa_lib.o rsa_sign.o rsa_saos.o $(ERRC).o \
- rsa_pk1.o rsa_ssl.o rsa_none.o
+ rsa_pk1.o rsa_ssl.o rsa_none.o rsa_oaep.o
SRC= $(LIBSRC)
@@ -127,3 +127,7 @@
rsa_ssl.o: ../../include/bio.h ../../include/bn.h ../../include/buffer.h
rsa_ssl.o: ../../include/e_os.h ../../include/err.h ../../include/rand.h
rsa_ssl.o: ../../include/stack.h ../cryptlib.h ../crypto.h rsa.h
+rsa_oaep.o: ../../include/bio.h ../../include/bn.h ../../include/buffer.h
+rsa_oaep.o: ../../include/e_os.h ../../include/err.h ../../include/rand.h
+rsa_oaep.o: ../../include/stack.h ../cryptlib.h ../crypto.h rsa.h
+rsa_oaep.o: ../../include/sha.h
diff -u orig/rsa.h ./rsa.h
--- orig/rsa.h Fri Feb 5 22:08:26 1999
+++ ./rsa.h Sat Feb 6 02:13:23 1999
@@ -143,6 +143,7 @@
#define RSA_PKCS1_PADDING 1
#define RSA_SSLV23_PADDING 2
#define RSA_NO_PADDING 3
+#define RSA_PKCS1_OAEP_PADDING 4
#define RSA_set_app_data(s,arg) RSA_set_ex_data(s,0,(char *)arg)
#define RSA_get_app_data(s) RSA_get_ex_data(s,0)
@@ -222,6 +223,10 @@
unsigned char *f,int fl);
int RSA_padding_check_PKCS1_type_2(unsigned char *to,int tlen,
unsigned char *f,int fl,int rsa_len);
+int RSA_padding_add_PKCS1_OAEP(unsigned char *to,int tlen,
+ unsigned char *f,int fl,unsigned char *p,int pl);
+int RSA_padding_check_PKCS1_OAEP(unsigned char *to,int tlen,
+ unsigned char *f,int fl,int rsa_len,unsigned char *p,int pl);
int RSA_padding_add_SSLv23(unsigned char *to,int tlen,
unsigned char *f,int fl);
int RSA_padding_check_SSLv23(unsigned char *to,int tlen,
@@ -284,6 +289,8 @@
int RSA_padding_check_PKCS1_type_1();
int RSA_padding_add_PKCS1_type_2();
int RSA_padding_check_PKCS1_type_2();
+int RSA_padding_add_PKCS1_OAEP();
+int RSA_padding_check_PKCS1_OAEP();
int RSA_padding_add_SSLv23();
int RSA_padding_check_SSLv23();
int RSA_padding_add_none();
@@ -309,17 +316,19 @@
#define RSA_F_RSA_PADDING_ADD_NONE 107
#define RSA_F_RSA_PADDING_ADD_PKCS1_TYPE_1 108
#define RSA_F_RSA_PADDING_ADD_PKCS1_TYPE_2 109
-#define RSA_F_RSA_PADDING_ADD_SSLV23 110
-#define RSA_F_RSA_PADDING_CHECK_NONE 111
-#define RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_1 112
-#define RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_2 113
-#define RSA_F_RSA_PADDING_CHECK_SSLV23 114
-#define RSA_F_RSA_PRINT 115
-#define RSA_F_RSA_PRINT_FP 116
-#define RSA_F_RSA_SIGN 117
-#define RSA_F_RSA_SIGN_ASN1_OCTET_STRING 118
-#define RSA_F_RSA_VERIFY 119
-#define RSA_F_RSA_VERIFY_ASN1_OCTET_STRING 120
+#define RSA_F_RSA_PADDING_ADD_PKCS1_OAEP 110
+#define RSA_F_RSA_PADDING_ADD_SSLV23 111
+#define RSA_F_RSA_PADDING_CHECK_NONE 112
+#define RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_1 113
+#define RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_2 114
+#define RSA_F_RSA_PADDING_CHECK_PKCS1_OAEP 115
+#define RSA_F_RSA_PADDING_CHECK_SSLV23 116
+#define RSA_F_RSA_PRINT 117
+#define RSA_F_RSA_PRINT_FP 118
+#define RSA_F_RSA_SIGN 119
+#define RSA_F_RSA_SIGN_ASN1_OCTET_STRING 120
+#define RSA_F_RSA_VERIFY 121
+#define RSA_F_RSA_VERIFY_ASN1_OCTET_STRING 122
/* Reason codes. */
#define RSA_R_ALGORITHM_MISMATCH 100
@@ -342,6 +351,8 @@
#define RSA_R_UNKNOWN_ALGORITHM_TYPE 117
#define RSA_R_UNKNOWN_PADDING_TYPE 118
#define RSA_R_WRONG_SIGNATURE_LENGTH 119
+#define RSA_R_KEY_SIZE_TOO_SMALL 120
+#define RSA_R_OAEP_DECODING_ERROR 121
#ifdef __cplusplus
}
diff -u orig/rsa_eay.c ./rsa_eay.c
--- orig/rsa_eay.c Fri Feb 5 22:08:26 1999
+++ ./rsa_eay.c Sat Feb 6 15:06:39 1999
@@ -130,6 +130,9 @@
case RSA_PKCS1_PADDING:
i=RSA_padding_add_PKCS1_type_2(buf,num,from,flen);
break;
+ case RSA_PKCS1_OAEP_PADDING:
+ i=RSA_padding_add_PKCS1_OAEP(buf,num,from,flen,NULL,0);
+ break;
case RSA_SSLV23_PADDING:
i=RSA_padding_add_SSLv23(buf,num,from,flen);
break;
@@ -318,6 +321,9 @@
{
case RSA_PKCS1_PADDING:
r=RSA_padding_check_PKCS1_type_2(to,num,buf,j,num);
+ break;
+ case RSA_PKCS1_OAEP_PADDING:
+ r=RSA_padding_check_PKCS1_OAEP(to,num,buf,j,num,NULL,0);
break;
case RSA_SSLV23_PADDING:
r=RSA_padding_check_SSLv23(to,num,buf,j,num);
diff -u orig/rsa_enc.c ./rsa_enc.c
--- orig/rsa_enc.c Fri Feb 5 22:08:26 1999
+++ ./rsa_enc.c Fri Feb 5 22:14:20 1999
@@ -111,6 +111,7 @@
BN_CTX *ctx=NULL;
if ( (padding != RSA_PKCS1_PADDING) &&
+ (padding != RSA_PKCS1_OAEP_PADDING) &&
(padding != RSA_SSLV23_PADDING))
{
RSAerr(RSA_F_RSA_EAY_PUBLIC_ENCRYPT,RSA_R_UNKNOWN_PADDING_TYPE);
@@ -279,7 +280,9 @@
unsigned char *buf=NULL;
BN_CTX *ctx=NULL;
- if ((padding != RSA_PKCS1_PADDING) && (padding != RSA_SSLV23_PADDING))
+ if ((padding != RSA_PKCS1_PADDING) &&
+ (padding != RSA_SSLV23_PADDING) &&
+ (padding != RSA_SSLV23_PADDING))
{
RSAerr(RSA_F_RSA_EAY_PRIVATE_DECRYPT,RSA_R_UNKNOWN_PADDING_TYPE);
goto err;
diff -u orig/rsa_err.c ./rsa_err.c
--- orig/rsa_err.c Fri Feb 5 22:08:27 1999
+++ ./rsa_err.c Sat Feb 6 02:12:58 1999
@@ -73,10 +73,12 @@
{ERR_PACK(0,RSA_F_RSA_PADDING_ADD_NONE,0), "RSA_padding_add_none"},
{ERR_PACK(0,RSA_F_RSA_PADDING_ADD_PKCS1_TYPE_1,0),
"RSA_padding_add_PKCS1_type_1"},
{ERR_PACK(0,RSA_F_RSA_PADDING_ADD_PKCS1_TYPE_2,0),
"RSA_padding_add_PKCS1_type_2"},
+{ERR_PACK(0,RSA_F_RSA_PADDING_ADD_PKCS1_OAEP,0),"RSA_padding_add_PKCS1_OAEP"},
{ERR_PACK(0,RSA_F_RSA_PADDING_ADD_SSLV23,0), "RSA_padding_add_SSLv23"},
{ERR_PACK(0,RSA_F_RSA_PADDING_CHECK_NONE,0), "RSA_padding_check_none"},
{ERR_PACK(0,RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_1,0),
"RSA_padding_check_PKCS1_type_1"},
{ERR_PACK(0,RSA_F_RSA_PADDING_CHECK_PKCS1_TYPE_2,0),
"RSA_padding_check_PKCS1_type_2"},
+{ERR_PACK(0,RSA_F_RSA_PADDING_CHECK_PKCS1_OAEP,0),"RSA_padding_check_PKCS1_OAEP"},
{ERR_PACK(0,RSA_F_RSA_PADDING_CHECK_SSLV23,0), "RSA_padding_check_SSLv23"},
{ERR_PACK(0,RSA_F_RSA_PRINT,0), "RSA_print"},
{ERR_PACK(0,RSA_F_RSA_PRINT_FP,0), "RSA_print_fp"},
@@ -97,10 +99,12 @@
{RSA_R_BAD_ZERO_BYTE ,"bad zero byte"},
{RSA_R_BLOCK_TYPE_IS_NOT_01 ,"block type is not 01"},
{RSA_R_BLOCK_TYPE_IS_NOT_02 ,"block type is not 02"},
+{RSA_R_OAEP_DECODING_ERROR ,"oaep decoding error"},
{RSA_R_DATA_GREATER_THAN_MOD_LEN ,"data greater than mod len"},
{RSA_R_DATA_TOO_LARGE ,"data too large"},
{RSA_R_DATA_TOO_LARGE_FOR_KEY_SIZE ,"data too large for key size"},
{RSA_R_DATA_TOO_SMALL ,"data too small"},
+{RSA_R_KEY_SIZE_TOO_SMALL ,"key size too small"},
{RSA_R_DIGEST_TOO_BIG_FOR_RSA_KEY ,"digest too big for rsa key"},
{RSA_R_NULL_BEFORE_BLOCK_MISSING ,"null before block missing"},
{RSA_R_PADDING_CHECK_FAILED ,"padding check failed"},
------------------------------------------------------------------------------
/* crypto/rsa/rsa_oaep.c */
/* Written by Ulf Moeller. This software is distributed on an "AS IS"
basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. */
/* EME_OAEP as defined in RFC 2437 (PKCS #1 v2.0) */
#include <stdio.h>
#include "cryptlib.h"
#include "bn.h"
#include "rsa.h"
#include "sha.h"
#include "rand.h"
int MGF1(unsigned char *mask, long len, unsigned char *seed, long seedlen);
int RSA_padding_add_PKCS1_OAEP(to, tlen, from, flen, param, plen)
unsigned char *to;
int tlen;
unsigned char *from;
int flen;
unsigned char *param;
int plen;
{
int i, emlen = tlen - 1;
unsigned char *db, *seed;
unsigned char *dbmask, seedmask[SHA_DIGEST_LENGTH];
if (flen > emlen - 2 * SHA_DIGEST_LENGTH - 1) {
RSAerr(RSA_F_RSA_PADDING_ADD_PKCS1_OAEP, RSA_R_DATA_TOO_LARGE_FOR_KEY_SIZE);
return (0);
}
if (emlen < 2 * SHA_DIGEST_LENGTH + 1) {
RSAerr(RSA_F_RSA_PADDING_ADD_PKCS1_OAEP, RSA_R_KEY_SIZE_TOO_SMALL);
return (0);
}
dbmask = Malloc(emlen - SHA_DIGEST_LENGTH);
if (dbmask == NULL) {
RSAerr(RSA_F_RSA_PADDING_ADD_PKCS1_OAEP, ERR_R_MALLOC_FAILURE);
return (0);
}
to[0] = 0;
seed = to + 1;
db = to + SHA_DIGEST_LENGTH + 1;
SHA1(param, plen, db);
memset(db + SHA_DIGEST_LENGTH, 0, emlen - flen - 2 * SHA_DIGEST_LENGTH - 1);
db[emlen - flen - SHA_DIGEST_LENGTH - 1] = 0x01;
memcpy(db + emlen - flen - SHA_DIGEST_LENGTH, from, (unsigned int) flen);
RAND_bytes(seed, SHA_DIGEST_LENGTH);
#ifdef PKCS_TESTVECT
memcpy(seed,
"\xaa\xfd\x12\xf6\x59\xca\xe6\x34\x89\xb4\x79\xe5\x07\x6d\xde\xc2\xf0\x6c\xb5\x8f",
20);
#endif
MGF1(dbmask, emlen - SHA_DIGEST_LENGTH, seed, SHA_DIGEST_LENGTH);
for (i = 0; i < emlen - SHA_DIGEST_LENGTH; i++)
db[i] ^= dbmask[i];
MGF1(seedmask, SHA_DIGEST_LENGTH, db, emlen - SHA_DIGEST_LENGTH);
for (i = 0; i < SHA_DIGEST_LENGTH; i++)
seed[i] ^= seedmask[i];
Free(dbmask);
return (1);
}
int RSA_padding_check_PKCS1_OAEP(to, tlen, from, flen, num, param, plen)
unsigned char *to;
int tlen;
unsigned char *from;
int flen;
int num;
unsigned char *param;
int plen;
{
int i, dblen, mlen = -1;
unsigned char *maskeddb;
unsigned char *db, seed[SHA_DIGEST_LENGTH], phash[SHA_DIGEST_LENGTH];
if (flen < 2 * SHA_DIGEST_LENGTH + 1) {
RSAerr(RSA_F_RSA_PADDING_CHECK_PKCS1_OAEP, RSA_R_OAEP_DECODING_ERROR);
return (-1);
}
dblen = flen - SHA_DIGEST_LENGTH;
db = Malloc(dblen);
if (db == NULL) {
RSAerr(RSA_F_RSA_PADDING_ADD_PKCS1_OAEP, ERR_R_MALLOC_FAILURE);
return (-1);
}
maskeddb = from + SHA_DIGEST_LENGTH;
MGF1(seed, SHA_DIGEST_LENGTH, maskeddb, dblen);
for (i = 0; i < SHA_DIGEST_LENGTH; i++)
seed[i] ^= from[i];
MGF1(db, dblen, seed, SHA_DIGEST_LENGTH);
for (i = 0; i < dblen; i++)
db[i] ^= maskeddb[i];
SHA1(param, plen, phash);
if (memcmp(db, phash, SHA_DIGEST_LENGTH) != 0)
RSAerr(RSA_F_RSA_PADDING_CHECK_PKCS1_OAEP, RSA_R_OAEP_DECODING_ERROR);
else {
for (i = SHA_DIGEST_LENGTH; i < dblen; i++)
if (db[i] != 0x00)
break;
if (db[i] != 0x01 || i++ >= dblen)
RSAerr(RSA_F_RSA_PADDING_CHECK_PKCS1_OAEP, RSA_R_OAEP_DECODING_ERROR);
else {
mlen = dblen - i;
if (tlen < mlen) {
RSAerr(RSA_F_RSA_PADDING_ADD_PKCS1_OAEP, RSA_R_DATA_TOO_LARGE);
mlen = -1;
}
else
memcpy(to, db + i, mlen);
}
}
Free(db);
return (mlen);
}
int MGF1(unsigned char *mask, long len, unsigned char *seed, long seedlen)
{
long i, outlen = 0;
unsigned char cnt[4];
SHA_CTX c;
unsigned char md[SHA_DIGEST_LENGTH];
for (i = 0; outlen < len; i++) {
cnt[0] = (i >> 24) & 255, cnt[1] = (i >> 16) & 255,
cnt[2] = (i >> 8) & 255, cnt[3] = i & 255;
SHA1_Init(&c);
SHA1_Update(&c, seed, seedlen);
SHA1_Update(&c, cnt, 4);
if (outlen + SHA_DIGEST_LENGTH <= len) {
SHA1_Final(mask + outlen, &c);
outlen += SHA_DIGEST_LENGTH;
} else {
SHA1_Final(md, &c);
memcpy(mask + outlen, md, len - outlen);
outlen = len;
}
}
return (0);
}
------------------------------------------------------------------------------
/* test vectors from p1ovect1.txt */
#include <stdio.h>
#include <rsa.h>
main()
{
int v;
RSA *key;
unsigned char ptext[256];
unsigned char ctext[256];
unsigned char ptext_ex[] = "\x54\x85\x9b\x34\x2c\x49\xea\x2a";
unsigned char ctext_ex[256];
int plen;
int clen;
int num;
plen = sizeof(ptext_ex) - 1;
for (v = 0; v < 3; v++) {
key = RSA_new();
switch (v) {
case 0:
clen = key1(key, ctext_ex);
break;
case 1:
clen = key2(key, ctext_ex);
break;
case 2:
clen = key3(key, ctext_ex);
break;
}
num = RSA_public_encrypt(plen, ptext_ex, ctext, key,
RSA_PKCS1_OAEP_PADDING);
if (num != clen) {
printf("Encryption failed!\n");
goto next;
}
num = RSA_private_decrypt(num, ctext, ptext, key, RSA_PKCS1_OAEP_PADDING);
if (num != plen || memcmp(ptext, ptext_ex, num) != 0) {
printf("Decryption failed!\n");
goto next;
}
if (memcmp(ctext, ctext_ex, num) == 0) {
printf("Vector %d passed!\n", v);
goto next;
}
/* Different ciphertexts (rsa_oaep.c without -DPKCS_TESTVECT).
Try decrypting ctext_ex */
num = RSA_private_decrypt(clen, ctext_ex, ptext, key,
RSA_PKCS1_OAEP_PADDING);
if (num != plen || memcmp(ptext, ptext_ex, num) != 0)
printf("Decryption failed!\n");
else
printf("Encyption/decryption successful!\n");
next:
RSA_free(key);
}
return (0);
}
#define SetKey \
key->n = BN_bin2bn(n, sizeof(n)-1, key->n); \
key->e = BN_bin2bn(e, sizeof(e)-1, key->e); \
key->d = BN_bin2bn(d, sizeof(d)-1, key->d); \
key->p = BN_bin2bn(p, sizeof(p)-1, key->p); \
key->q = BN_bin2bn(q, sizeof(q)-1, key->q); \
key->dmp1 = BN_bin2bn(dmp1, sizeof(dmp1)-1, key->dmp1); \
key->dmq1 = BN_bin2bn(dmq1, sizeof(dmq1)-1, key->dmq1); \
key->iqmp = BN_bin2bn(iqmp, sizeof(iqmp)-1, key->iqmp); \
memcpy(c, ctext_ex, sizeof(ctext_ex) - 1); \
return (sizeof(ctext_ex) - 1);
int key1(RSA *key, unsigned char *c)
{
unsigned char n[] = "\
\x00\xAA\x36\xAB\xCE\x88\xAC\xFD\xFF\x55\x52\x3C\x7F\xC4\x52\x3F\
\x90\xEF\xA0\x0D\xF3\x77\x4A\x25\x9F\x2E\x62\xB4\xC5\xD9\x9C\xB5\
\xAD\xB3\x00\xA0\x28\x5E\x53\x01\x93\x0E\x0C\x70\xFB\x68\x76\x93\
\x9C\xE6\x16\xCE\x62\x4A\x11\xE0\x08\x6D\x34\x1E\xBC\xAC\xA0\xA1\
\xF5";
unsigned char e[] = "\x11";
unsigned char d[] = "\
\x0A\x03\x37\x48\x62\x64\x87\x69\x5F\x5F\x30\xBC\x38\xB9\x8B\x44\
\xC2\xCD\x2D\xFF\x43\x40\x98\xCD\x20\xD8\xA1\x38\xD0\x90\xBF\x64\
\x79\x7C\x3F\xA7\xA2\xCD\xCB\x3C\xD1\xE0\xBD\xBA\x26\x54\xB4\xF9\
\xDF\x8E\x8A\xE5\x9D\x73\x3D\x9F\x33\xB3\x01\x62\x4A\xFD\x1D\x51";
unsigned char p[] = "\
\x00\xD8\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5\
\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x12\
\x0D";
unsigned char q[] = "\
\x00\xC9\x7F\xB1\xF0\x27\xF4\x53\xF6\x34\x12\x33\xEA\xAA\xD1\xD9\
\x35\x3F\x6C\x42\xD0\x88\x66\xB1\xD0\x5A\x0F\x20\x35\x02\x8B\x9D\
\x89";
unsigned char dmp1[] = "\
\x59\x0B\x95\x72\xA2\xC2\xA9\xC4\x06\x05\x9D\xC2\xAB\x2F\x1D\xAF\
\xEB\x7E\x8B\x4F\x10\xA7\x54\x9E\x8E\xED\xF5\xB4\xFC\xE0\x9E\x05";
unsigned char dmq1[] = "\
\x00\x8E\x3C\x05\x21\xFE\x15\xE0\xEA\x06\xA3\x6F\xF0\xF1\x0C\x99\
\x52\xC3\x5B\x7A\x75\x14\xFD\x32\x38\xB8\x0A\xAD\x52\x98\x62\x8D\
\x51";
unsigned char iqmp[] = "\
\x36\x3F\xF7\x18\x9D\xA8\xE9\x0B\x1D\x34\x1F\x71\xD0\x9B\x76\xA8\
\xA9\x43\xE1\x1D\x10\xB2\x4D\x24\x9F\x2D\xEA\xFE\xF8\x0C\x18\x26";
unsigned char ctext_ex[] ="\
\x1b\x8f\x05\xf9\xca\x1a\x79\x52\x6e\x53\xf3\xcc\x51\x4f\xdb\x89\
\x2b\xfb\x91\x93\x23\x1e\x78\xb9\x92\xe6\x8d\x50\xa4\x80\xcb\x52\
\x33\x89\x5c\x74\x95\x8d\x5d\x02\xab\x8c\x0f\xd0\x40\xeb\x58\x44\
\xb0\x05\xc3\x9e\xd8\x27\x4a\x9d\xbf\xa8\x06\x71\x40\x94\x39\xd2";
SetKey;
}
int key2(RSA *key, unsigned char *c)
{
unsigned char n[] = "\
\x00\xA3\x07\x9A\x90\xDF\x0D\xFD\x72\xAC\x09\x0C\xCC\x2A\x78\xB8\
\x74\x13\x13\x3E\x40\x75\x9C\x98\xFA\xF8\x20\x4F\x35\x8A\x0B\x26\
\x3C\x67\x70\xE7\x83\xA9\x3B\x69\x71\xB7\x37\x79\xD2\x71\x7B\xE8\
\x34\x77\xCF";
unsigned char e[] = "\x3";
unsigned char d[] = "\
\x6C\xAF\xBC\x60\x94\xB3\xFE\x4C\x72\xB0\xB3\x32\xC6\xFB\x25\xA2\
\xB7\x62\x29\x80\x4E\x68\x65\xFC\xA4\x5A\x74\xDF\x0F\x8F\xB8\x41\
\x3B\x52\xC0\xD0\xE5\x3D\x9B\x59\x0F\xF1\x9B\xE7\x9F\x49\xDD\x21\
\xE5\xEB";
unsigned char p[] = "\
\x00\xCF\x20\x35\x02\x8B\x9D\x86\x98\x40\xB4\x16\x66\xB4\x2E\x92\
\xEA\x0D\xA3\xB4\x32\x04\xB5\xCF\xCE\x91";
unsigned char q[] = "\
\x00\xC9\x7F\xB1\xF0\x27\xF4\x53\xF6\x34\x12\x33\xEA\xAA\xD1\xD9\
\x35\x3F\x6C\x42\xD0\x88\x66\xB1\xD0\x5F";
unsigned char dmp1[] = "\
\x00\x8A\x15\x78\xAC\x5D\x13\xAF\x10\x2B\x22\xB9\x99\xCD\x74\x61\
\xF1\x5E\x6D\x22\xCC\x03\x23\xDF\xDF\x0B";
unsigned char dmq1[] = "\
\x00\x86\x55\x21\x4A\xC5\x4D\x8D\x4E\xCD\x61\x77\xF1\xC7\x36\x90\
\xCE\x2A\x48\x2C\x8B\x05\x99\xCB\xE0\x3F";
unsigned char iqmp[] = "\
\x00\x83\xEF\xEF\xB8\xA9\xA4\x0D\x1D\xB6\xED\x98\xAD\x84\xED\x13\
\x35\xDC\xC1\x08\xF3\x22\xD0\x57\xCF\x8D";
unsigned char ctext_ex[] = "\
\x14\xbd\xdd\x28\xc9\x83\x35\x19\x23\x80\xe8\xe5\x49\xb1\x58\x2a\
\x8b\x40\xb4\x48\x6d\x03\xa6\xa5\x31\x1f\x1f\xd5\xf0\xa1\x80\xe4\
\x17\x53\x03\x29\xa9\x34\x90\x74\xb1\x52\x13\x54\x29\x08\x24\x52\
\x62\x51";
SetKey;
}
int key3(RSA *key, unsigned char *c)
{
unsigned char n[] = "\
\x00\xBB\xF8\x2F\x09\x06\x82\xCE\x9C\x23\x38\xAC\x2B\x9D\xA8\x71\
\xF7\x36\x8D\x07\xEE\xD4\x10\x43\xA4\x40\xD6\xB6\xF0\x74\x54\xF5\
\x1F\xB8\xDF\xBA\xAF\x03\x5C\x02\xAB\x61\xEA\x48\xCE\xEB\x6F\xCD\
\x48\x76\xED\x52\x0D\x60\xE1\xEC\x46\x19\x71\x9D\x8A\x5B\x8B\x80\
\x7F\xAF\xB8\xE0\xA3\xDF\xC7\x37\x72\x3E\xE6\xB4\xB7\xD9\x3A\x25\
\x84\xEE\x6A\x64\x9D\x06\x09\x53\x74\x88\x34\xB2\x45\x45\x98\x39\
\x4E\xE0\xAA\xB1\x2D\x7B\x61\xA5\x1F\x52\x7A\x9A\x41\xF6\xC1\x68\
\x7F\xE2\x53\x72\x98\xCA\x2A\x8F\x59\x46\xF8\xE5\xFD\x09\x1D\xBD\
\xCB";
unsigned char e[] = "\x11";
unsigned char d[] = "\
\x00\xA5\xDA\xFC\x53\x41\xFA\xF2\x89\xC4\xB9\x88\xDB\x30\xC1\xCD\
\xF8\x3F\x31\x25\x1E\x06\x68\xB4\x27\x84\x81\x38\x01\x57\x96\x41\
\xB2\x94\x10\xB3\xC7\x99\x8D\x6B\xC4\x65\x74\x5E\x5C\x39\x26\x69\
\xD6\x87\x0D\xA2\xC0\x82\xA9\x39\xE3\x7F\xDC\xB8\x2E\xC9\x3E\xDA\
\xC9\x7F\xF3\xAD\x59\x50\xAC\xCF\xBC\x11\x1C\x76\xF1\xA9\x52\x94\
\x44\xE5\x6A\xAF\x68\xC5\x6C\x09\x2C\xD3\x8D\xC3\xBE\xF5\xD2\x0A\
\x93\x99\x26\xED\x4F\x74\xA1\x3E\xDD\xFB\xE1\xA1\xCE\xCC\x48\x94\
\xAF\x94\x28\xC2\xB7\xB8\x88\x3F\xE4\x46\x3A\x4B\xC8\x5B\x1C\xB3\
\xC1";
unsigned char p[] = "\
\x00\xEE\xCF\xAE\x81\xB1\xB9\xB3\xC9\x08\x81\x0B\x10\xA1\xB5\x60\
\x01\x99\xEB\x9F\x44\xAE\xF4\xFD\xA4\x93\xB8\x1A\x9E\x3D\x84\xF6\
\x32\x12\x4E\xF0\x23\x6E\x5D\x1E\x3B\x7E\x28\xFA\xE7\xAA\x04\x0A\
\x2D\x5B\x25\x21\x76\x45\x9D\x1F\x39\x75\x41\xBA\x2A\x58\xFB\x65\
\x99";
unsigned char q[] = "\
\x00\xC9\x7F\xB1\xF0\x27\xF4\x53\xF6\x34\x12\x33\xEA\xAA\xD1\xD9\
\x35\x3F\x6C\x42\xD0\x88\x66\xB1\xD0\x5A\x0F\x20\x35\x02\x8B\x9D\
\x86\x98\x40\xB4\x16\x66\xB4\x2E\x92\xEA\x0D\xA3\xB4\x32\x04\xB5\
\xCF\xCE\x33\x52\x52\x4D\x04\x16\xA5\xA4\x41\xE7\x00\xAF\x46\x15\
\x03";
unsigned char dmp1[] = "\
\x54\x49\x4C\xA6\x3E\xBA\x03\x37\xE4\xE2\x40\x23\xFC\xD6\x9A\x5A\
\xEB\x07\xDD\xDC\x01\x83\xA4\xD0\xAC\x9B\x54\xB0\x51\xF2\xB1\x3E\
\xD9\x49\x09\x75\xEA\xB7\x74\x14\xFF\x59\xC1\xF7\x69\x2E\x9A\x2E\
\x20\x2B\x38\xFC\x91\x0A\x47\x41\x74\xAD\xC9\x3C\x1F\x67\xC9\x81";
unsigned char dmq1[] = "\
\x47\x1E\x02\x90\xFF\x0A\xF0\x75\x03\x51\xB7\xF8\x78\x86\x4C\xA9\
\x61\xAD\xBD\x3A\x8A\x7E\x99\x1C\x5C\x05\x56\xA9\x4C\x31\x46\xA7\
\xF9\x80\x3F\x8F\x6F\x8A\xE3\x42\xE9\x31\xFD\x8A\xE4\x7A\x22\x0D\
\x1B\x99\xA4\x95\x84\x98\x07\xFE\x39\xF9\x24\x5A\x98\x36\xDA\x3D";
unsigned char iqmp[] = "\
\x00\xB0\x6C\x4F\xDA\xBB\x63\x01\x19\x8D\x26\x5B\xDB\xAE\x94\x23\
\xB3\x80\xF2\x71\xF7\x34\x53\x88\x50\x93\x07\x7F\xCD\x39\xE2\x11\
\x9F\xC9\x86\x32\x15\x4F\x58\x83\xB1\x67\xA9\x67\xBF\x40\x2B\x4E\
\x9E\x2E\x0F\x96\x56\xE6\x98\xEA\x36\x66\xED\xFB\x25\x79\x80\x39\
\xF7";
unsigned char ctext_ex[] = "\
\xb8\x24\x6b\x56\xa6\xed\x58\x81\xae\xb5\x85\xd9\xa2\x5b\x2a\xd7\
\x90\xc4\x17\xe0\x80\x68\x1b\xf1\xac\x2b\xc3\xde\xb6\x9d\x8b\xce\
\xf0\xc4\x36\x6f\xec\x40\x0a\xf0\x52\xa7\x2e\x9b\x0e\xff\xb5\xb3\
\xf2\xf1\x92\xdb\xea\xca\x03\xc1\x27\x40\x05\x71\x13\xbf\x1f\x06\
\x69\xac\x22\xe9\xf3\xa7\x85\x2e\x3c\x15\xd9\x13\xca\xb0\xb8\x86\
\x3a\x95\xc9\x92\x94\xce\x86\x74\x21\x49\x54\x61\x03\x46\xf4\xd4\
\x74\xb2\x6f\x7c\x48\xb4\x2e\xe6\x8e\x1f\x57\x2a\x1f\xc4\x02\x6a\
\xc4\x56\xb4\xf5\x9f\x7b\x62\x1e\xa1\xb9\xd8\x8f\x64\x20\x2f\xb1";
SetKey;
}
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