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mbedtls/library/rsa.c

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/*
* The RSA public-key cryptosystem
*
* Copyright (C) 2006-2007 Christophe Devine
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
/*
* RSA was designed by Ron Rivest, Adi Shamir and Len Adleman.
*
* http://theory.lcs.mit.edu/~rivest/rsapaper.pdf
* http://www.cacr.math.uwaterloo.ca/hac/about/chap8.pdf
*/
#include "polarssl/config.h"
#if defined(POLARSSL_RSA_C)
#include "polarssl/rsa.h"
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
/*
* Initialize an RSA context
*/
void rsa_init( rsa_context *ctx,
int padding,
int hash_id,
int (*f_rng)(void *),
void *p_rng )
{
memset( ctx, 0, sizeof( rsa_context ) );
ctx->padding = padding;
ctx->hash_id = hash_id;
ctx->f_rng = f_rng;
ctx->p_rng = p_rng;
}
#if defined(POLARSSL_GENPRIME)
/*
* Generate an RSA keypair
*/
int rsa_gen_key( rsa_context *ctx, int nbits, int exponent )
{
int ret;
mpi P1, Q1, H, G;
if( ctx->f_rng == NULL || nbits < 128 || exponent < 3 )
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
mpi_init( &P1, &Q1, &H, &G, NULL );
/*
* find primes P and Q with Q < P so that:
* GCD( E, (P-1)*(Q-1) ) == 1
*/
MPI_CHK( mpi_lset( &ctx->E, exponent ) );
do
{
MPI_CHK( mpi_gen_prime( &ctx->P, ( nbits + 1 ) >> 1, 0,
ctx->f_rng, ctx->p_rng ) );
MPI_CHK( mpi_gen_prime( &ctx->Q, ( nbits + 1 ) >> 1, 0,
ctx->f_rng, ctx->p_rng ) );
if( mpi_cmp_mpi( &ctx->P, &ctx->Q ) < 0 )
mpi_swap( &ctx->P, &ctx->Q );
if( mpi_cmp_mpi( &ctx->P, &ctx->Q ) == 0 )
continue;
MPI_CHK( mpi_mul_mpi( &ctx->N, &ctx->P, &ctx->Q ) );
if( mpi_msb( &ctx->N ) != nbits )
continue;
MPI_CHK( mpi_sub_int( &P1, &ctx->P, 1 ) );
MPI_CHK( mpi_sub_int( &Q1, &ctx->Q, 1 ) );
MPI_CHK( mpi_mul_mpi( &H, &P1, &Q1 ) );
MPI_CHK( mpi_gcd( &G, &ctx->E, &H ) );
}
while( mpi_cmp_int( &G, 1 ) != 0 );
/*
* D = E^-1 mod ((P-1)*(Q-1))
* DP = D mod (P - 1)
* DQ = D mod (Q - 1)
* QP = Q^-1 mod P
*/
MPI_CHK( mpi_inv_mod( &ctx->D , &ctx->E, &H ) );
MPI_CHK( mpi_mod_mpi( &ctx->DP, &ctx->D, &P1 ) );
MPI_CHK( mpi_mod_mpi( &ctx->DQ, &ctx->D, &Q1 ) );
MPI_CHK( mpi_inv_mod( &ctx->QP, &ctx->Q, &ctx->P ) );
ctx->len = ( mpi_msb( &ctx->N ) + 7 ) >> 3;
cleanup:
mpi_free( &G, &H, &Q1, &P1, NULL );
if( ret != 0 )
{
rsa_free( ctx );
return( POLARSSL_ERR_RSA_KEY_GEN_FAILED | ret );
}
return( 0 );
}
#endif
/*
* Check a public RSA key
*/
int rsa_check_pubkey( rsa_context *ctx )
{
if( ( ctx->N.p[0] & 1 ) == 0 ||
( ctx->E.p[0] & 1 ) == 0 )
return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
if( mpi_msb( &ctx->N ) < 128 ||
mpi_msb( &ctx->N ) > 4096 )
return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
if( mpi_msb( &ctx->E ) < 2 ||
mpi_msb( &ctx->E ) > 64 )
return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED );
return( 0 );
}
/*
* Check a private RSA key
*/
int rsa_check_privkey( rsa_context *ctx )
{
int ret;
mpi PQ, DE, P1, Q1, H, I, G;
if( ( ret = rsa_check_pubkey( ctx ) ) != 0 )
return( ret );
mpi_init( &PQ, &DE, &P1, &Q1, &H, &I, &G, NULL );
MPI_CHK( mpi_mul_mpi( &PQ, &ctx->P, &ctx->Q ) );
MPI_CHK( mpi_mul_mpi( &DE, &ctx->D, &ctx->E ) );
MPI_CHK( mpi_sub_int( &P1, &ctx->P, 1 ) );
MPI_CHK( mpi_sub_int( &Q1, &ctx->Q, 1 ) );
MPI_CHK( mpi_mul_mpi( &H, &P1, &Q1 ) );
MPI_CHK( mpi_mod_mpi( &I, &DE, &H ) );
MPI_CHK( mpi_gcd( &G, &ctx->E, &H ) );
if( mpi_cmp_mpi( &PQ, &ctx->N ) == 0 &&
mpi_cmp_int( &I, 1 ) == 0 &&
mpi_cmp_int( &G, 1 ) == 0 )
{
mpi_free( &G, &I, &H, &Q1, &P1, &DE, &PQ, NULL );
return( 0 );
}
cleanup:
mpi_free( &G, &I, &H, &Q1, &P1, &DE, &PQ, NULL );
return( POLARSSL_ERR_RSA_KEY_CHECK_FAILED | ret );
}
/*
* Do an RSA public key operation
*/
int rsa_public( rsa_context *ctx,
unsigned char *input,
unsigned char *output )
{
int ret, olen;
mpi T;
mpi_init( &T, NULL );
MPI_CHK( mpi_read_binary( &T, input, ctx->len ) );
if( mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
{
mpi_free( &T, NULL );
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
}
olen = ctx->len;
MPI_CHK( mpi_exp_mod( &T, &T, &ctx->E, &ctx->N, &ctx->RN ) );
MPI_CHK( mpi_write_binary( &T, output, olen ) );
cleanup:
mpi_free( &T, NULL );
if( ret != 0 )
return( POLARSSL_ERR_RSA_PUBLIC_FAILED | ret );
return( 0 );
}
/*
* Do an RSA private key operation
*/
int rsa_private( rsa_context *ctx,
unsigned char *input,
unsigned char *output )
{
int ret, olen;
mpi T, T1, T2;
mpi_init( &T, &T1, &T2, NULL );
MPI_CHK( mpi_read_binary( &T, input, ctx->len ) );
if( mpi_cmp_mpi( &T, &ctx->N ) >= 0 )
{
mpi_free( &T, NULL );
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
}
#if 0
MPI_CHK( mpi_exp_mod( &T, &T, &ctx->D, &ctx->N, &ctx->RN ) );
#else
/*
* faster decryption using the CRT
*
* T1 = input ^ dP mod P
* T2 = input ^ dQ mod Q
*/
MPI_CHK( mpi_exp_mod( &T1, &T, &ctx->DP, &ctx->P, &ctx->RP ) );
MPI_CHK( mpi_exp_mod( &T2, &T, &ctx->DQ, &ctx->Q, &ctx->RQ ) );
/*
* T = (T1 - T2) * (Q^-1 mod P) mod P
*/
MPI_CHK( mpi_sub_mpi( &T, &T1, &T2 ) );
MPI_CHK( mpi_mul_mpi( &T1, &T, &ctx->QP ) );
MPI_CHK( mpi_mod_mpi( &T, &T1, &ctx->P ) );
/*
* output = T2 + T * Q
*/
MPI_CHK( mpi_mul_mpi( &T1, &T, &ctx->Q ) );
MPI_CHK( mpi_add_mpi( &T, &T2, &T1 ) );
#endif
olen = ctx->len;
MPI_CHK( mpi_write_binary( &T, output, olen ) );
cleanup:
mpi_free( &T, &T1, &T2, NULL );
if( ret != 0 )
return( POLARSSL_ERR_RSA_PRIVATE_FAILED | ret );
return( 0 );
}
/*
* Add the message padding, then do an RSA operation
*/
int rsa_pkcs1_encrypt( rsa_context *ctx,
int mode, int ilen,
unsigned char *input,
unsigned char *output )
{
int nb_pad, olen;
unsigned char *p = output;
olen = ctx->len;
switch( ctx->padding )
{
case RSA_PKCS_V15:
if( ilen < 0 || olen < ilen + 11 )
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
nb_pad = olen - 3 - ilen;
*p++ = 0;
*p++ = RSA_CRYPT;
while( nb_pad-- > 0 )
{
do {
*p = (unsigned char) rand();
} while( *p == 0 );
p++;
}
*p++ = 0;
memcpy( p, input, ilen );
break;
default:
return( POLARSSL_ERR_RSA_INVALID_PADDING );
}
return( ( mode == RSA_PUBLIC )
? rsa_public( ctx, output, output )
: rsa_private( ctx, output, output ) );
}
/*
* Do an RSA operation, then remove the message padding
*/
int rsa_pkcs1_decrypt( rsa_context *ctx,
int mode, int *olen,
unsigned char *input,
unsigned char *output )
{
int ret, ilen;
unsigned char *p;
unsigned char buf[512];
ilen = ctx->len;
if( ilen < 16 || ilen > (int) sizeof( buf ) )
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
ret = ( mode == RSA_PUBLIC )
? rsa_public( ctx, input, buf )
: rsa_private( ctx, input, buf );
if( ret != 0 )
return( ret );
p = buf;
switch( ctx->padding )
{
case RSA_PKCS_V15:
if( *p++ != 0 || *p++ != RSA_CRYPT )
return( POLARSSL_ERR_RSA_INVALID_PADDING );
while( *p != 0 )
{
if( p >= buf + ilen - 1 )
return( POLARSSL_ERR_RSA_INVALID_PADDING );
p++;
}
p++;
break;
default:
return( POLARSSL_ERR_RSA_INVALID_PADDING );
}
*olen = ilen - (int)(p - buf);
memcpy( output, p, *olen );
return( 0 );
}
/*
* Do an RSA operation to sign the message digest
*/
int rsa_pkcs1_sign( rsa_context *ctx,
int mode,
int hash_id,
int hashlen,
unsigned char *hash,
unsigned char *sig )
{
int nb_pad, olen;
unsigned char *p = sig;
olen = ctx->len;
switch( ctx->padding )
{
case RSA_PKCS_V15:
switch( hash_id )
{
case RSA_RAW:
nb_pad = olen - 3 - hashlen;
break;
case RSA_MD2:
case RSA_MD4:
case RSA_MD5:
nb_pad = olen - 3 - 34;
break;
case RSA_SHA1:
nb_pad = olen - 3 - 35;
break;
default:
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
}
if( nb_pad < 8 )
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
*p++ = 0;
*p++ = RSA_SIGN;
memset( p, 0xFF, nb_pad );
p += nb_pad;
*p++ = 0;
break;
default:
return( POLARSSL_ERR_RSA_INVALID_PADDING );
}
switch( hash_id )
{
case RSA_RAW:
memcpy( p, hash, hashlen );
break;
case RSA_MD2:
memcpy( p, ASN1_HASH_MDX, 18 );
memcpy( p + 18, hash, 16 );
p[13] = 2; break;
case RSA_MD4:
memcpy( p, ASN1_HASH_MDX, 18 );
memcpy( p + 18, hash, 16 );
p[13] = 4; break;
case RSA_MD5:
memcpy( p, ASN1_HASH_MDX, 18 );
memcpy( p + 18, hash, 16 );
p[13] = 5; break;
case RSA_SHA1:
memcpy( p, ASN1_HASH_SHA1, 15 );
memcpy( p + 15, hash, 20 );
break;
default:
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
}
return( ( mode == RSA_PUBLIC )
? rsa_public( ctx, sig, sig )
: rsa_private( ctx, sig, sig ) );
}
/*
* Do an RSA operation and check the message digest
*/
int rsa_pkcs1_verify( rsa_context *ctx,
int mode,
int hash_id,
int hashlen,
unsigned char *hash,
unsigned char *sig )
{
int ret, len, siglen;
unsigned char *p, c;
unsigned char buf[512];
siglen = ctx->len;
if( siglen < 16 || siglen > (int) sizeof( buf ) )
return( POLARSSL_ERR_RSA_BAD_INPUT_DATA );
ret = ( mode == RSA_PUBLIC )
? rsa_public( ctx, sig, buf )
: rsa_private( ctx, sig, buf );
if( ret != 0 )
return( ret );
p = buf;
switch( ctx->padding )
{
case RSA_PKCS_V15:
if( *p++ != 0 || *p++ != RSA_SIGN )
return( POLARSSL_ERR_RSA_INVALID_PADDING );
while( *p != 0 )
{
if( p >= buf + siglen - 1 || *p != 0xFF )
return( POLARSSL_ERR_RSA_INVALID_PADDING );
p++;
}
p++;
break;
default:
return( POLARSSL_ERR_RSA_INVALID_PADDING );
}
len = siglen - (int)( p - buf );
if( len == 34 )
{
c = p[13];
p[13] = 0;
if( memcmp( p, ASN1_HASH_MDX, 18 ) != 0 )
return( POLARSSL_ERR_RSA_VERIFY_FAILED );
if( ( c == 2 && hash_id == RSA_MD2 ) ||
( c == 4 && hash_id == RSA_MD4 ) ||
( c == 5 && hash_id == RSA_MD5 ) )
{
if( memcmp( p + 18, hash, 16 ) == 0 )
return( 0 );
else
return( POLARSSL_ERR_RSA_VERIFY_FAILED );
}
}
if( len == 35 && hash_id == RSA_SHA1 )
{
if( memcmp( p, ASN1_HASH_SHA1, 15 ) == 0 &&
memcmp( p + 15, hash, 20 ) == 0 )
return( 0 );
else
return( POLARSSL_ERR_RSA_VERIFY_FAILED );
}
if( len == hashlen && hash_id == RSA_RAW )
{
if( memcmp( p, hash, hashlen ) == 0 )
return( 0 );
else
return( POLARSSL_ERR_RSA_VERIFY_FAILED );
}
return( POLARSSL_ERR_RSA_INVALID_PADDING );
}
/*
* Free the components of an RSA key
*/
void rsa_free( rsa_context *ctx )
{
mpi_free( &ctx->RQ, &ctx->RP, &ctx->RN,
&ctx->QP, &ctx->DQ, &ctx->DP,
&ctx->Q, &ctx->P, &ctx->D,
&ctx->E, &ctx->N, NULL );
}
#if defined(POLARSSL_SELF_TEST)
#include "polarssl/sha1.h"
/*
* Example RSA-1024 keypair, for test purposes
*/
#define KEY_LEN 128
#define RSA_N "9292758453063D803DD603D5E777D788" \
"8ED1D5BF35786190FA2F23EBC0848AEA" \
"DDA92CA6C3D80B32C4D109BE0F36D6AE" \
"7130B9CED7ACDF54CFC7555AC14EEBAB" \
"93A89813FBF3C4F8066D2D800F7C38A8" \
"1AE31942917403FF4946B0A83D3D3E05" \
"EE57C6F5F5606FB5D4BC6CD34EE0801A" \
"5E94BB77B07507233A0BC7BAC8F90F79"
#define RSA_E "10001"
#define RSA_D "24BF6185468786FDD303083D25E64EFC" \
"66CA472BC44D253102F8B4A9D3BFA750" \
"91386C0077937FE33FA3252D28855837" \
"AE1B484A8A9A45F7EE8C0C634F99E8CD" \
"DF79C5CE07EE72C7F123142198164234" \
"CABB724CF78B8173B9F880FC86322407" \
"AF1FEDFDDE2BEB674CA15F3E81A1521E" \
"071513A1E85B5DFA031F21ECAE91A34D"
#define RSA_P "C36D0EB7FCD285223CFB5AABA5BDA3D8" \
"2C01CAD19EA484A87EA4377637E75500" \
"FCB2005C5C7DD6EC4AC023CDA285D796" \
"C3D9E75E1EFC42488BB4F1D13AC30A57"
#define RSA_Q "C000DF51A7C77AE8D7C7370C1FF55B69" \
"E211C2B9E5DB1ED0BF61D0D9899620F4" \
"910E4168387E3C30AA1E00C339A79508" \
"8452DD96A9A5EA5D9DCA68DA636032AF"
#define RSA_DP "C1ACF567564274FB07A0BBAD5D26E298" \
"3C94D22288ACD763FD8E5600ED4A702D" \
"F84198A5F06C2E72236AE490C93F07F8" \
"3CC559CD27BC2D1CA488811730BB5725"
#define RSA_DQ "4959CBF6F8FEF750AEE6977C155579C7" \
"D8AAEA56749EA28623272E4F7D0592AF" \
"7C1F1313CAC9471B5C523BFE592F517B" \
"407A1BD76C164B93DA2D32A383E58357"
#define RSA_QP "9AE7FBC99546432DF71896FC239EADAE" \
"F38D18D2B2F0E2DD275AA977E2BF4411" \
"F5A3B2A5D33605AEBBCCBA7FEB9F2D2F" \
"A74206CEC169D74BF5A8C50D6F48EA08"
#define PT_LEN 24
#define RSA_PT "\xAA\xBB\xCC\x03\x02\x01\x00\xFF\xFF\xFF\xFF\xFF" \
"\x11\x22\x33\x0A\x0B\x0C\xCC\xDD\xDD\xDD\xDD\xDD"
/*
* Checkup routine
*/
int rsa_self_test( int verbose )
{
int len;
rsa_context rsa;
unsigned char sha1sum[20];
unsigned char rsa_plaintext[PT_LEN];
unsigned char rsa_decrypted[PT_LEN];
unsigned char rsa_ciphertext[KEY_LEN];
memset( &rsa, 0, sizeof( rsa_context ) );
rsa.len = KEY_LEN;
mpi_read_string( &rsa.N , 16, RSA_N );
mpi_read_string( &rsa.E , 16, RSA_E );
mpi_read_string( &rsa.D , 16, RSA_D );
mpi_read_string( &rsa.P , 16, RSA_P );
mpi_read_string( &rsa.Q , 16, RSA_Q );
mpi_read_string( &rsa.DP, 16, RSA_DP );
mpi_read_string( &rsa.DQ, 16, RSA_DQ );
mpi_read_string( &rsa.QP, 16, RSA_QP );
if( verbose != 0 )
printf( " RSA key validation: " );
if( rsa_check_pubkey( &rsa ) != 0 ||
rsa_check_privkey( &rsa ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( verbose != 0 )
printf( "passed\n PKCS#1 encryption : " );
memcpy( rsa_plaintext, RSA_PT, PT_LEN );
if( rsa_pkcs1_encrypt( &rsa, RSA_PUBLIC, PT_LEN,
rsa_plaintext, rsa_ciphertext ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( verbose != 0 )
printf( "passed\n PKCS#1 decryption : " );
if( rsa_pkcs1_decrypt( &rsa, RSA_PRIVATE, &len,
rsa_ciphertext, rsa_decrypted ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( memcmp( rsa_decrypted, rsa_plaintext, len ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( verbose != 0 )
printf( "passed\n PKCS#1 data sign : " );
sha1( rsa_plaintext, PT_LEN, sha1sum );
if( rsa_pkcs1_sign( &rsa, RSA_PRIVATE, RSA_SHA1, 20,
sha1sum, rsa_ciphertext ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( verbose != 0 )
printf( "passed\n PKCS#1 sig. verify: " );
if( rsa_pkcs1_verify( &rsa, RSA_PUBLIC, RSA_SHA1, 20,
sha1sum, rsa_ciphertext ) != 0 )
{
if( verbose != 0 )
printf( "failed\n" );
return( 1 );
}
if( verbose != 0 )
printf( "passed\n\n" );
rsa_free( &rsa );
return( 0 );
}
#endif
#endif
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