* origin/pr/2497:
Re-generate library/certs.c from script
Add new line at the end of test-ca2.key.enc
Use strict syntax to annotate origin of test data in certs.c
Add run to all.sh exercising !MBEDTLS_PEM_PARSE_C + !MBEDTLS_FS_IO
Allow DHM self test to run without MBEDTLS_PEM_PARSE_C
ssl-opt.sh: Auto-skip tests that use files if MBEDTLS_FS_IO unset
Document origin of hardcoded certificates in library/certs.c
Adapt ChangeLog
Rename server1.der to server1.crt.der
Add DER encoded files to git tree
Add build instructions to generate DER versions of CRTs and keys
Document "none" value for ca_path/ca_file in ssl_client2/ssl_server2
ssl_server2: Skip CA setup if `ca_path` or `ca_file` argument "none"
ssl_client2: Skip CA setup if `ca_path` or `ca_file` argument "none"
Correct white spaces in ssl_server2 and ssl_client2
Adapt ssl_client2 to parse DER encoded test CRTs if PEM is disabled
Adapt ssl_server2 to parse DER encoded test CRTs if PEM is disabled
Remove the "Decrypt empty buffer" test, as ChaCha20 is a stream cipher
and 0 bytes encrypted is identical to a 0 length buffer. The "ChaCha20
Encrypt and decrypt 0 bytes" test will test decryption of a 0 length
buffer.
Previously, even in the Chacha20 and Chacha20-Poly1305 tests, we would
test that decryption of an empty buffer would work with
MBEDTLS_CIPHER_AES_128_CBC.
Make the cipher used with the dec_empty_buf() test configurable, so that
Chacha20 and Chacha20-Poly1305 empty buffer tests can use ciphers other
than AES CBC. Then, make the Chacha20 and Chacha20-Poly1305 empty buffer
tests use the MBEDTLS_CIPHER_CHACHA20 and
MBEDTLS_CIPHER_CHACHA20_POLY1305 cipher suites.
Some functions within the X.509 module return an ASN.1 low level
error code where instead this error code should be wrapped by a
high-level X.509 error code as in the bulk of the module.
Specifically, the following functions are affected:
- mbedtls_x509_get_ext()
- x509_get_version()
- x509_get_uid()
This commit modifies these functions to always return an
X.509 high level error code.
Care has to be taken when adapting `mbetls_x509_get_ext()`:
Currently, the callers `mbedtls_x509_crt_ext()` treat the
return code `MBEDTLS_ERR_ASN1_UNEXPECTED_TAG` specially to
gracefully detect and continue if the extension structure is not
present. Wrapping the ASN.1 error with
`MBEDTLS_ERR_X509_INVALID_EXTENSIONS` and adapting the check
accordingly would mean that an unexpected tag somewhere
down the extension parsing would be ignored by the caller.
The way out of this is the following: Luckily, the extension
structure is always the last field in the surrounding structure,
so if there is some data remaining, it must be an Extension
structure, so we don't need to deal with a tag mismatch gracefully
in the first place.
We may therefore wrap the return code from the initial call to
`mbedtls_asn1_get_tag()` in `mbedtls_x509_get_ext()` by
`MBEDTLS_ERR_X509_INVALID_EXTENSIONS` and simply remove
the special treatment of `MBEDTLS_ERR_ASN1_UNEXPECTED_TAG`
in the callers `x509_crl_get_ext()` and `x509_crt_get_ext()`.
This renders `mbedtls_x509_get_ext()` unsuitable if it ever
happened that an Extension structure is optional and does not
occur at the end of its surrounding structure, but for CRTs
and CRLs, it's fine.
The following tests need to be adapted:
- "TBSCertificate v3, issuerID wrong tag"
The issuerID is optional, so if we look for its presence
but find a different tag, we silently continue and try
parsing the subjectID, and then the extensions. The tag '00'
used in this test doesn't match either of these, and the
previous code would hence return LENGTH_MISMATCH after
unsucessfully trying issuerID, subjectID and Extensions.
With the new code, any data remaining after issuerID and
subjectID _must_ be Extension data, so we fail with
UNEXPECTED_TAG when trying to parse the Extension data.
- "TBSCertificate v3, UIDs, invalid length"
The test hardcodes the expectation of
MBEDTLS_ERR_ASN1_INVALID_LENGTH, which needs to be
wrapped in MBEDTLS_ERR_X509_INVALID_FORMAT now.
Fixes#2431.
When parsing a substructure of an ASN.1 structure, no field within
the substructure must exceed the bounds of the substructure.
Concretely, the `end` pointer passed to the ASN.1 parsing routines
must be updated to point to the end of the substructure while parsing
the latter.
This was previously not the case for the routines
- x509_get_attr_type_and_value(),
- mbedtls_x509_get_crt_ext(),
- mbedtls_x509_get_crl_ext().
These functions kept using the end of the parent structure as the
`end` pointer and would hence allow substructure fields to cross
the substructure boundary. This could lead to successful parsing
of ill-formed X.509 CRTs.
This commit fixes this.
Care has to be taken when adapting `mbedtls_x509_get_crt_ext()`
and `mbedtls_x509_get_crl_ext()`, as the underlying function
`mbedtls_x509_get_ext()` returns `0` if no extensions are present
but doesn't set the variable which holds the bounds of the Extensions
structure in case the latter is present. This commit addresses
this by returning early from `mbedtls_x509_get_crt_ext()` and
`mbedtls_x509_get_crl_ext()` if parsing has reached the end of
the input buffer.
The following X.509 parsing tests need to be adapted:
- "TBSCertificate, issuer two inner set datas"
This test exercises the X.509 CRT parser with a Subject name
which has two empty `AttributeTypeAndValue` structures.
This is supposed to fail with `MBEDTLS_ERR_ASN1_OUT_OF_DATA`
because the parser should attempt to parse the first structure
and fail because of a lack of data. Previously, it failed to
obey the (0-length) bounds of the first AttributeTypeAndValue
structure and would try to interpret the beginning of the second
AttributeTypeAndValue structure as the first field of the first
AttributeTypeAndValue structure, returning an UNEXPECTED_TAG error.
- "TBSCertificate, issuer, no full following string"
This test exercises the parser's behaviour on an AttributeTypeAndValue
structure which contains more data than expected; it should therefore
fail with MBEDTLS_ERR_ASN1_LENGTH_MISMATCH. Because of the missing bounds
check, it previously failed with UNEXPECTED_TAG because it interpreted
the remaining byte in the first AttributeTypeAndValue structure as the
first byte in the second AttributeTypeAndValue structure.
- "SubjectAltName repeated"
This test should exercise two SubjectAltNames extensions in succession,
but a wrong length values makes the second SubjectAltNames extension appear
outside of the Extensions structure. With the new bounds in place, this
therefore fails with a LENGTH_MISMATCH error. This commit adapts the test
data to put the 2nd SubjectAltNames extension inside the Extensions
structure, too.
The X.509 parsing test suite test_suite_x509parse contains a test
exercising X.509 verification for a valid MD4/MD5 certificate in a
profile which doesn't allow MD4/MD5. This commit adds an analogous
test for MD2.
- Replace 'RSA with MD2' OID '2a864886f70d010102' by
'RSA with SHA-256' OID '2a864886f70d01010b':
Only the last byte determines the hash, and
`MBEDTLS_OID_PKCS1_MD2 == MBEDTLS_OID_PKCS1 "\x02"`
`MBEDTLS_OID_PKCS1_SHA256 == MBEDTLS_OID_PKCS1 "\x0b"`
See oid.h.
- Replace MD2 dependency by SHA256 dependency.
- Adapt expected CRT info output.
* origin/pr/2364:
Increase okm_hex buffer to contain null character
Minor modifications to hkdf test
Add explanation for okm_string size
Update ChangeLog
Reduce buffer size of okm
Reduce Stack usage of hkdf test function
* restricted/pr/553:
Fix mbedtls_ecdh_get_params with new ECDH context
Add changelog entry for mbedtls_ecdh_get_params robustness
Fix ecdh_get_params with mismatching group
Add test case for ecdh_get_params with mismatching group
Add test case for ecdh_calc_secret
Fix typo in documentation
It was failing to set the key in the ENCRYPT direction before encrypting.
This just happened to work for GCM and CCM.
After re-encrypting, compare the length to the expected ciphertext
length not the plaintext length. Again this just happens to work for
GCM and CCM since they do not perform any kind of padding.
* public/pr/2429:
Add ChangeLog entry for unused bits in bitstrings
Improve docs for ASN.1 bitstrings and their usage
Add tests for (named) bitstring to suite_asn1write
Fix ASN1 bitstring writing
Add a test case for doing an ECDH calculation by calling
mbedtls_ecdh_get_params on both keys, with keys belonging to
different groups. This should fail, but currently passes.
`test_hkdf` in the hkdf test suites consumed stack of ~6KB with
6 buffers of ~1KB each. This causes stack overflow on some platforms
with smaller stack. The buffer sizes were reduced. By testing, the sizes
can be reduced even further, as the largest seen size is 82 bytes(for okm).
The test suites `test_suite_gcm.aes{128,192,256}_en.data` contains
numerous NIST test vectors for AES-*-GCM against which the GCM
API mbedtls_gcm_xxx() is tested.
However, one level higher at the cipher API, no tests exist which
exercise mbedtls_cipher_auth_{encrypt/decrypt}() for GCM ciphers,
although test_suite_cipher.function contains the test auth_crypt_tv
which does precisely that and is already used e.g. in
test_suite_cipher.ccm.
This commit replicates the test vectors from
test_suite_gcm.aes{128,192,256}_en.data in test_suite_cipher.gcm.data
and adds a run of auth_crypt_tv for each of them.
The conversion was mainly done through the sed command line
```
s/gcm_decrypt_and_verify:\([^:]*\):\([^:]*\):\([^:]*\):\([^:]*\):
\([^:]*\):\([^:]*\):\([^:]*\):\([^:]*\):\([^:]*\):\([^:]*\)/auth_crypt_tv:
\1:\2:\4:\5:\3:\7:\8:\9/
```
Dependent on configured options, not all of the helper functions were being
used, which was leading to warning of unused functions with Clang.
To avoid any complex compile time options, or adding more logic to
generate_test_code.py to screen out unused functions, those functions which were
provoking the warning were changed to remove static, remove them from file
scope, and expose them to the linker.
Document when a context must be initialized or not, when it must be
set up or not, and whether it needs a private key or a public key will
do.
The implementation is sometimes more liberal than the documentation,
accepting a non-set-up context as a context that can't perform the
requested information. This preserves backward compatibility.
The MPI_VALIDATE_RET() macro cannot be used for parameter
validation of mbedtls_mpi_lsb() because this function returns
a size_t.
Use the underlying MBEDTLS_INTERNAL_VALIDATE_RET() insteaed,
returning 0 on failure.
Also, add a test for this behaviour.
For mbedtls_pk_parse_key and mbedtls_pk_parse_keyfile, the password is
optional. Clarify what this means: NULL is ok and means no password.
Validate parameters and test accordingly.
The test that mbedtls_aria_free() accepts NULL parameters
can be performed even if MBEDTLS_CHECK_PARAMS is unset, but
was previously included in the test case aria_invalid_params()
which is only executed if MBEDTLS_CHECK_PARAMS is set.
Parameter validation was previously performed and tested unconditionally
for the ChaCha/Poly modules. This commit therefore only needs go guard the
existing tests accordingly and use the appropriate test macros for parameter
validation.
Previously, one could change the definition of AES_VALIDATE_RET() to return
some other code than MBEDTLS_ERR_AES_BAD_INPUT_DATA, and the test suite
wouldn't notice. Now this modification would make the suite fail as expected.
The test framework for validation of parameters depends on the macro
MBEDTLS_PARAM_FAILED() being set to its default value when building the
library. So far the test framework attempted to define this macro but this was
the wrong place - this definition wouldn't be picked by the library.
Instead, a different approach is taken: skip those tests when the macro is
defined in config.h, as in that case we have no way to know if it will indeed
end up calling mbedtls_param_failed() as we need it to.
This commit was tested by manually ensuring that aes_invalid_params:
- passes (and is not skipped) in the default configuration
- is skipped when MBEDTLS_PARAM_FAILED() is defined in config.h
The previous prototype gave warnings are the strings produced by #cond and
__FILE__ are const, so we shouldn't implicitly cast them to non-const.
While at it modifying most example programs:
- include the header that has the function declaration, so that the definition
can be checked to match by the compiler
- fix whitespace
- make it work even if PLATFORM_C is not defined:
- CHECK_PARAMS is not documented as depending on PLATFORM_C and there is
no reason why it should
- so, remove the corresponding #if defined in each program...
- and add missing #defines for mbedtls_exit when needed
The result has been tested (make all test with -Werror) with the following
configurations:
- full with CHECK_PARAMS with PLATFORM_C
- full with CHECK_PARAMS without PLATFORM_C
- full without CHECK_PARAMS without PLATFORM_C
- full without CHECK_PARAMS with PLATFORM_C
Additionally, it has been manually tested that adding
mbedtls_aes_init( NULL );
near the normal call to mbedtls_aes_init() in programs/aes/aescrypt2.c has the
expected effect when running the program.
It was inconsistent between files: sometimes 3 arguments, sometimes one.
Align to 1 argument for the macro and 3 for the function, because:
- we don't need 3 arguments for the macro, it can add __FILE__ and __LINE__
in its expansion, while the function needs them as parameters to be correct;
- people who re-defined the macro should have flexibility, and 3 arguments
can give the impression they they don't have as much as they actually do;
- the design document has the macro with 1 argument, so let's stick to that.
Change the use of setjmp and longjmp in signalling parameter validation failures
when using the MBEDTLS_CHECK_PARAMS config.h option. This change allows
all calls which might result in a call to the parameter validation failure
handler to always be caught, even without use of the new macros, by placing a
setjmp() in the outer function which calls the test function, which the handler
can jump to.
This has several benefits:
* it allows us to remove the clang compiler warning (-Wclobbered) caused
by local auto variables being in the same function as the call to setjmp.
* removes the need to wrap all function calls in the test functions with the
TEST_ASSERT() macro. Now all parameter validation function calls should be
caught.
The tests for the ECDH key exchange that use the context accessed it
directly. This can't work with the new context, where we can't make any
assumptions about the implementation of the context. This commit works
around this problem and comes with the cost of allocating an extra
structures on the stack when executing the test.
One of the tests is testing an older interface for the sake of backward
compatibility. The new ECDH context is not backward compatible and this
test doesn't make any sense for it, therefore we skip this test in
non-legacy mode.
The recently added `mbedtls_ecdh_setup()` function is not used in the
tests yet. This commit adapts the tests to the new workflow.
Having done that, the old lifecycle is not tested anymore, so we add a
new test to ensure backward compatibility.
Since the AD too long is a limitation on Mbed TLS,
HW accelerators may support this. Run the test for AD too long,
only if `MBEDTLS_CCM_ALT` is not defined.
Addresses comment in #1996.
This commit introduces variants test-ca_utf8.crt,
test-ca_printablestring.crt and test-ca_uppercase.crt
of tests/data_files/test-ca.crt which differ from
test-ca.crt in their choice of string encoding and
upper and lower case letters in the DN field. These
changes should be immaterial to the recovation check,
and three tests are added that crl.pem, which applies
to test-ca.crt, is also considered as applying to
test-ca_*.crt.
The test files were generated using PR #1641 which
- adds a build instruction for test-ca.crt to
tests/data_files/Makefile which allows easy
change of the subject DN.
- changes the default string format from `PrintableString`
to `UTF8String`.
Specifically:
- `test-ca_utf8.crt` was generated by running
`rm test-ca.crt && make test-ca.crt`
on PR #1641.
- `test-ca_uppercase.crt`, too, was generated by running
`rm test-ca.crt && make test-ca.crt`
on PR #1641, after modifying the subject DN line in the build
instruction for `test-ca.crt` in `tests/data_files/Makefile`.
- `test-ca_printable.crt` is a copy of `test-ca.crt`
because at the time of this commit, `PrintableString` is
still the default string format.
This commit introduces variants test-ca_utf8.crt,
test-ca_printablestring.crt and test-ca_uppercase.crt
of tests/data_files/test-ca.crt which differ from
test-ca.crt in their choice of string encoding and
upper and lower case letters in the DN field. These
changes should be immaterial to the recovation check,
and three tests are added that crl.pem, which applies
to test-ca.crt, is also considered as applying to
test-ca_*.crt.
Extend the mbedtls_mpi_is_prime_det test to check that it reports
the number as prime when testing rounds-1 rounds, then reports the
number as composite when testing the full number of rounds.
When using a primality testing function the tolerable error rate depends
on the scheme in question, the required security strength and wether it
is used for key generation or parameter validation. To support all use
cases we need more flexibility than what the old API provides.
Primality tests have to deal with different distribution when generating
primes and when validating primes.
These new tests are testing if mbedtls_mpi_is_prime() is working
properly in the latter setting.
The new tests involve pseudoprimes with maximum number of
non-witnesses. The non-witnesses were generated by printing them
from mpi_miller_rabin(). The pseudoprimes were generated by the
following function:
void gen_monier( mbedtls_mpi* res, int nbits )
{
mbedtls_mpi p_2x_plus_1, p_4x_plus_1, x, tmp;
mbedtls_mpi_init( &p_2x_plus_1 );
mbedtls_mpi_init( &p_4x_plus_1 );
mbedtls_mpi_init( &x ); mbedtls_mpi_init( &tmp );
do
{
mbedtls_mpi_gen_prime( &p_2x_plus_1, nbits >> 1, 0,
rnd_std_rand, NULL );
mbedtls_mpi_sub_int( &x, &p_2x_plus_1, 1 );
mbedtls_mpi_div_int( &x, &tmp, &x, 2 );
if( mbedtls_mpi_get_bit( &x, 0 ) == 0 )
continue;
mbedtls_mpi_mul_int( &p_4x_plus_1, &x, 4 );
mbedtls_mpi_add_int( &p_4x_plus_1, &p_4x_plus_1, 1 );
if( mbedtls_mpi_is_prime( &p_4x_plus_1, rnd_std_rand,
NULL ) == 0 )
break;
} while( 1 );
mbedtls_mpi_mul_mpi( res, &p_2x_plus_1, &p_4x_plus_1 );
}
Functional tests for various payload sizes and output buffer sizes.
When the padding is bad or the plaintext is too large for the output
buffer, verify that function writes some outputs. This doesn't
validate that the implementation is time-constant, but it at least
validates that it doesn't just return early without outputting anything.
Add signing tests with 528-bit and 520-bit RSA keys with SHA-512. These
selections of key and hash size should lead to an error returned, as
there is not enough room for our chosen minimum salt size of two bytes
less than the hash size. These test the boundary around an available
salt length of 0 or -1 bytes.
The RSA keys were generated with OpenSSL 1.1.1-pre8.
$ openssl genrsa 520
Generating RSA private key, 520 bit long modulus (2 primes)
.............++++++++++++
.................++++++++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----
MIIBPwIBAAJCANWgb4bludh0KFQBZcqWb6iJOmLipZ0L/XYXeAuwOfkWWjc6jhGd
B2b43lVnEPM/ZwGRU7rYIjd155fUUdSCBvO/AgMBAAECQgDOMq+zy6XZEjWi8D5q
j05zpRGgRRiKP/qEtB6BWbZ7gUV9DDgZhD4FFsqfanwjWNG52LkM9D1OQmUOtGGq
a9COwQIhD+6l9iIPrCkblQjsK6jtKB6zmu5NXcaTJUEGgW68cA7PAiENaJGHhcOq
/jHqqi2NgVbc5kWUD/dzSkVzN6Ub0AvIiBECIQIeL2Gw1XSFYm1Fal/DbQNQUX/e
/dnhc94X7s118wbScQIhAMPVgbDc//VurZ+155vYc9PjZlYe3QIAwlkLX3HYKkGx
AiEND8ndKyhkc8jLGlh8aRP8r03zpDIiZNKqCKiijMWVRYQ=
-----END RSA PRIVATE KEY-----
$ openssl genrsa 528
Generating RSA private key, 528 bit long modulus (2 primes)
.........++++++++++++
....++++++++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----
MIIBQgIBAAJDAKJVTrpxW/ZuXs3z1tcY4+XZB+hmbnv1p2tBUQbgTrgn7EyyGZz/
ZkkdRUGQggWapbVLDPXu9EQ0AvMEfAsObwJQgQIDAQABAkJhHVXvFjglElxnK7Rg
lERq0k73yqfYQts4wCegTHrrkv3HzqWQVVi29mGLSXTqoQ45gzWZ5Ru5NKjkTjko
YtWWIVECIgDScqoo7SCFrG3zwFxnGe7V3rYYr6LkykpvczC0MK1IZy0CIgDFeINr
qycUXbndZvF0cLYtSmEA+MoN7fRX7jY5w7lZYyUCIUxyiOurEDhe5eY5B5gQbJlW
ePHIw7S244lO3+9lC12U1QIhWgzQ8YKFObZcEejl5xGXIiQvBEBv89Y1fPu2YrUs
iuS5AiFE64NJs8iI+zZxp72esKHPXq/chJ1BvhHsXI0y1OBK8m8=
-----END RSA PRIVATE KEY-----
Since we wish to generate RSASSA-PSS signatures even when hashes are
relatively large for the chosen RSA key size, we need some tests. Our
main focus will be on 1024-bit keys and the couple key sizes larger than
it. For example, we test for a signature generated using a salt length
of 63 when a 1032-bit key is used. Other tests check the boundary
conditions around other key sizes. We want to make sure we don't use a
salt length larger than the hash length (because FIPS 186-4 requires
this). We also want to make sure we don't use a salt that is too small
(no smaller than 2 bytes away from the hash length).
Test RSASSA-PSS signatures with:
- 1024-bit key and SHA-512 (slen 62)
- 1032-bit key and SHA-512 (slen 63)
- 1040-bit key and SHA-512 (slen 64)
- 1048-bit key and SHA-512 (slen 64)
The tests also verify that we can properly verify the RSASSA-PSS
signatures we've generated.
We've manually verified that OpenSSL 1.1.1-pre8 can verify the
RSASSA-PSS signatures we've generated.
$ openssl rsa -in rsa1024.pem -pubout -out pub1024.pem
writing RSA key
$ openssl rsa -in rsa1032.pem -pubout -out pub1032.pem
writing RSA key
$ openssl rsa -in rsa1040.pem -pubout -out pub1040.pem
writing RSA key
$ openssl rsa -in rsa1048.pem -pubout -out pub1048.pem
writing RSA key
$ cat message.bin | openssl dgst -sha512 -sigopt rsa_padding_mode:pss -sigopt rsa_pss_saltlen:62 -verify pub1024.pem -signature valid1024.bin
Verified OK
$ cat message.bin | openssl dgst -sha512 -sigopt rsa_padding_mode:pss -sigopt rsa_pss_saltlen:63 -verify pub1032.pem -signature valid1032.bin
Verified OK
$ cat message.bin | openssl dgst -sha512 -sigopt rsa_padding_mode:pss -sigopt rsa_pss_saltlen:64 -verify pub1040.pem -signature valid1040.bin
Verified OK
$ cat message.bin | openssl dgst -sha512 -sigopt rsa_padding_mode:pss -sigopt rsa_pss_saltlen:64 -verify pub1048.pem -signature valid1048.bin
Verified OK
We've also added a new test that ensures we can properly validate a
RSASSA-PSS 1032-bit signature with SHA-512 generated by OpenSSL. This
has been added as the "RSASSA-PSS Verify OpenSSL-generated Signature
1032-bit w/SHA-512" test. The signature to verify was generated with the
following command line.
$ cat message.bin | openssl dgst -sha512 -sigopt rsa_padding_mode:pss -sigopt rsa_pss_saltlen:63 -sign rsa1032.pem > valid.bin
The RSA private keys used by these tests were generated with OpenSSL
1.1.1-pre8.
$ openssl genrsa 1024
Generating RSA private key, 1024 bit long modulus (2 primes)
........................................++++++
......++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
$ openssl genrsa 1032
Generating RSA private key, 1032 bit long modulus (2 primes)
....................++++++
.................................++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
$ openssl genkey 1040
Generating RSA private key, 1040 bit long modulus
........++++++
........++++++
e is 65537 (0x10001)
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
$ openssl genrsa 1048
Generating RSA private key, 1048 bit long modulus (2 primes)
...............................++++++
.++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
