/* * The RSA public-key cryptosystem * * Based on XySSL: Copyright (C) 2006-2008 Christophe Devine * * Copyright (C) 2009 Paul Bakker <polarssl_maintainer at polarssl dot org> * * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * Neither the names of PolarSSL or XySSL nor the names of its contributors * may be used to endorse or promote products derived from this software * without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED * TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* * 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 output_max_len) { 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 ); } if (ilen - (int)(p - buf) > output_max_len) return( POLARSSL_ERR_RSA_OUTPUT_TO_LARGE ); *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, sizeof(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