Add tests for rsa_export

This commit adds tests for the new library function mbedtls_rsa_export. Each
test case performs the following steps:

- Parse and convert a set of hex-string decoded core RSA parameters into MPI's.
- Use these to initialize an RSA context
- Export core RSA parameters as MPI's again afterwards
- Compare initial MPI's to exported ones.

In the private key case, all core parameters are exported and sanity-checked,
regardless of whether they were also used during setup.

Each test split is performed twice, once with successive and once with
simultaneous exporting.
This commit is contained in:
Hanno Becker 2017-08-23 11:44:51 +01:00
parent c77ab892e5
commit 417f2d6107
2 changed files with 146 additions and 0 deletions

View file

@ -451,6 +451,27 @@ mbedtls_rsa_import_raw:"b38ac65c8141f7f5c96e14470e851936a67bf94cc6821a39ac12c05f
RSA Import Raw (N,-,-,-,E), successive RSA Import Raw (N,-,-,-,E), successive
mbedtls_rsa_import_raw:"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":"":"":"":"03":1:0 mbedtls_rsa_import_raw:"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":"":"":"":"03":1:0
RSA Export (N,P,Q,D,E)
mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
RSA Export (N,P,Q,D,E), successive
mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
RSA Export (N,-,-,D,E)
mbedtls_rsa_export:16:"b38ac65c8141f7f5c96e14470e851936a67bf94cc6821a39ac12c05f7c0b06d9e6ddba2224703b02e25f31452f9c4a8417b62675fdc6df46b94813bc7b9769a892c482b830bfe0ad42e46668ace68903617faf6681f4babf1cc8e4b0420d3c7f61dc45434c6b54e2c3ee0fc07908509d79c9826e673bf8363255adb0add2401039a7bcd1b4ecf0fbe6ec8369d2da486eec59559dd1d54c9b24190965eafbdab203b35255765261cd0909acf93c3b8b8428cbb448de4715d1b813d0c94829c229543d391ce0adab5351f97a3810c1f73d7b1458b97daed4209c50e16d064d2d5bfda8c23893d755222793146d0a78c3d64f35549141486c3b0961a7b4c1a2034f":16:"":16:"":16:"77B1D99300D6A54E864962DA09AE10CF19A7FB888456BC2672B72AEA52B204914493D16C184AD201EC3F762E1FBD8702BA796EF953D9EA2F26300D285264F11B0C8301D0207FEB1E2C984445C899B0ACEBAA74EF014DD1D4BDDB43202C08D2FF9692D8D788478DEC829EB52AFB5AE068FBDBAC499A27FACECC391E75C936D55F07BB45EE184DAB45808E15722502F279F89B38C1CB292557E5063597F52C75D61001EDC33F4739353E33E56AD273B067C1A2760208529EA421774A5FFFCB3423B1E0051E7702A55D80CBF2141569F18F87BFF538A1DA8EDBB2693A539F68E0D62D77743F89EACF3B1723BDB25CE2F333FA63CACF0E67DF1A431893BB9B352FCB":16:"3":0
RSA Export (N,-,-,D,E), succesive
mbedtls_rsa_export:16:"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
RSA Export (N,P,Q,-,E)
mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":0
RSA Export (N,P,Q,-,E), successive
mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1
RSA Export (N,-,-,-,E)
mbedtls_rsa_export:16:"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":16:"":16:"":16:"":16:"3":0
RSA PKCS1 Encrypt Bad RNG RSA PKCS1 Encrypt Bad RNG
depends_on:MBEDTLS_PKCS1_V15 depends_on:MBEDTLS_PKCS1_V15
rsa_pkcs1_encrypt_bad_rng:"4E636AF98E40F3ADCFCCB698F4E80B9F":MBEDTLS_RSA_PKCS_V15:2048:16:"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":16:"3":"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":MBEDTLS_ERR_RSA_RNG_FAILED rsa_pkcs1_encrypt_bad_rng:"4E636AF98E40F3ADCFCCB698F4E80B9F":MBEDTLS_RSA_PKCS_V15:2048:16:"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":16:"3":"a42eda41e56235e666e7faaa77100197f657288a1bf183e4820f0c37ce2c456b960278d6003e0bbcd4be4a969f8e8fd9231e1f492414f00ed09844994c86ec32db7cde3bec7f0c3dbf6ae55baeb2712fa609f5fc3207a824eb3dace31849cd6a6084318523912bccb84cf42e3c6d6d1685131d69bb545acec827d2b0dfdd5568b7dcc4f5a11d6916583fefa689d367f8c9e1d95dcd2240895a9470b0c1730f97cd6e8546860bd254801769f54be96e16362ddcbf34d56035028890199e0f48db38642cb66a4181e028a6443a404fea284ce02b4614b683367d40874e505611d23142d49f06feea831d52d347b13610b413c4efc43a6de9f0b08d2a951dc503b6":MBEDTLS_ERR_RSA_RNG_FAILED

View file

@ -905,6 +905,131 @@ exit:
} }
/* END_CASE */ /* END_CASE */
/* BEGIN_CASE */
void mbedtls_rsa_export( int radix_N, char *input_N,
int radix_P, char *input_P,
int radix_Q, char *input_Q,
int radix_D, char *input_D,
int radix_E, char *input_E,
int successive )
{
/* Original MPI's with which we set up the RSA context */
mbedtls_mpi N, P, Q, D, E;
/* Exported MPI's */
mbedtls_mpi Ne, Pe, Qe, De, Ee;
const int have_N = ( strlen( input_N ) > 0 );
const int have_P = ( strlen( input_P ) > 0 );
const int have_Q = ( strlen( input_Q ) > 0 );
const int have_D = ( strlen( input_D ) > 0 );
const int have_E = ( strlen( input_E ) > 0 );
const int is_priv = have_P || have_Q || have_D;
mbedtls_rsa_context ctx;
mbedtls_rsa_init( &ctx, 0, 0 );
mbedtls_mpi_init( &N );
mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E );
mbedtls_mpi_init( &Ne );
mbedtls_mpi_init( &Pe ); mbedtls_mpi_init( &Qe );
mbedtls_mpi_init( &De ); mbedtls_mpi_init( &Ee );
/* Setup RSA context */
if( have_N )
TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
if( have_P )
TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
if( have_Q )
TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
if( have_D )
TEST_ASSERT( mbedtls_mpi_read_string( &D, radix_D, input_D ) == 0 );
if( have_E )
TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
TEST_ASSERT( mbedtls_rsa_import( &ctx,
strlen( input_N ) ? &N : NULL,
strlen( input_P ) ? &P : NULL,
strlen( input_Q ) ? &Q : NULL,
strlen( input_D ) ? &D : NULL,
strlen( input_E ) ? &E : NULL ) == 0 );
TEST_ASSERT( mbedtls_rsa_complete( &ctx, NULL, NULL ) == 0 );
/*
* Export parameters and compare to original ones.
*/
/* N and E must always be present. */
if( !successive )
{
TEST_ASSERT( mbedtls_rsa_export( &ctx, &Ne, NULL, NULL, NULL, &Ee ) == 0 );
}
else
{
TEST_ASSERT( mbedtls_rsa_export( &ctx, &Ne, NULL, NULL, NULL, NULL ) == 0 );
TEST_ASSERT( mbedtls_rsa_export( &ctx, NULL, NULL, NULL, NULL, &Ee ) == 0 );
}
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &N, &Ne ) == 0 );
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &E, &Ee ) == 0 );
/* If we were providing enough information to setup a complete private context,
* we expect to be able to export all core parameters. */
if( is_priv )
{
if( !successive )
{
TEST_ASSERT( mbedtls_rsa_export( &ctx, NULL, &Pe, &Qe,
&De, NULL ) == 0 );
}
else
{
TEST_ASSERT( mbedtls_rsa_export( &ctx, NULL, &Pe, NULL,
NULL, NULL ) == 0 );
TEST_ASSERT( mbedtls_rsa_export( &ctx, NULL, NULL, &Qe,
NULL, NULL ) == 0 );
TEST_ASSERT( mbedtls_rsa_export( &ctx, NULL, NULL, NULL,
&De, NULL ) == 0 );
}
if( have_P )
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P, &Pe ) == 0 );
if( have_Q )
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Q, &Qe ) == 0 );
if( have_D )
TEST_ASSERT( mbedtls_mpi_cmp_mpi( &D, &De ) == 0 );
/* While at it, perform a sanity check */
TEST_ASSERT( mbedtls_rsa_check_params( &Ne, &Pe, &Qe, &De, &Ee,
NULL, NULL ) == 0 );
}
exit:
mbedtls_rsa_free( &ctx );
mbedtls_mpi_free( &N );
mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E );
mbedtls_mpi_free( &Ne );
mbedtls_mpi_free( &Pe ); mbedtls_mpi_free( &Qe );
mbedtls_mpi_free( &De ); mbedtls_mpi_free( &Ee );
}
/* END_CASE */
/* BEGIN_CASE depends_on:MBEDTLS_CTR_DRBG_C:MBEDTLS_ENTROPY_C */ /* BEGIN_CASE depends_on:MBEDTLS_CTR_DRBG_C:MBEDTLS_ENTROPY_C */
void mbedtls_rsa_import_raw( char *input_N, void mbedtls_rsa_import_raw( char *input_N,
char *input_P, char *input_Q, char *input_P, char *input_Q,