Context: This commit makes a change to mbedtls_pk_parse_key() which
is responsible for parsing of private keys. The function doesn't know
the key format in advance (PEM vs. DER, encrypted vs. unencrypted) and
tries them one by one, resetting the PK context in between.
Issue: The previous code resets the PK context through a call to
mbedtls_pk_free() along, lacking the accompanying mbedtls_pk_init()
call. Practically, this is not an issue because functionally
mbedtls_pk_free() + mbedtls_pk_init() is equivalent to mbedtls_pk_free()
with the current implementation of these functions, but strictly
speaking it's nonetheless a violation of the API semantics according
to which xxx_free() functions leave a context in uninitialized state.
(yet not entirely random, because xxx_free() functions must be idempotent,
so they cannot just fill the context they operate on with garbage).
Change: The commit adds calls to mbedtls_pk_init() after those calls
to mbedtls_pk_free() within mbedtls_pk_parse_key() after which the
PK context might still be used.
This commit removes the definition of the API function
`mbedtls_platform_set_calloc_free()`
from `library/platform.c` in case the macros
`MBEDTLS_PLATFORM_CALLOC_MACRO`
`MBEDTLS_PLATFORM_FREE_MACRO`
for compile time configuration of calloc/free are set.
This is in line with the corresponding header `mbedtls/platform.h`
which declares `mbedtls_platform_set_calloc_free()` only if
`MBEDTLS_PLATFORM_{CALLOC/FREE}_MACRO` are not defined.
Fixes#1642.
This commit adds a test to tests/scripts/all.sh exercising an
ASan build of the default configuration with
MBEDTLS_PLATFORM_MEMORY enabled,
MBEDTLS_PLATFORM_CALLOC_MACRO set to std calloc
MBEDTLS_PLATFORM_FREE_MACRO set to std free
(This should functionally be indistinguishable from a default build)
The previous code triggered a compiler warning because of a comparison
of a signed and an unsigned integer.
The conversion is safe because `len` is representable by 16-bits,
hence smaller than the maximum integer.
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 a random number is generated for the Miller-Rabin primality test,
if the bit length of the random number is larger than the number being
tested, the random number is shifted right to have the same bit length.
This introduces bias, as the random number is now guaranteed to be
larger than 2^(bit length-1).
Changing this to instead zero all bits higher than the tested numbers
bit length will remove this bias and keep the random number being
uniformly generated.
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.
The input distribution to primality testing functions is completely
different when used for generating primes and when for validating
primes. The constants used in the library are geared towards the prime
generation use case and are weak when used for validation. (Maliciously
constructed composite numbers can pass the test with high probability)
The mbedtls_mpi_is_prime() function is in the public API and although it
is not documented, it is reasonable to assume that the primary use case
is validating primes. The RSA module too uses it for validating key
material.
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 );
}
The FIPS 186-4 RSA key generation prescribes lower failure probability
in primality testing and this makes key generation slower. We enable the
caller to decide between compliance/security and performance.
This python script calculates the base two logarithm of the formulas in
HAC Fact 4.48 and was used to determine the breakpoints and number of
rounds:
def mrpkt_log_2(k, t):
if t <= k/9.0:
return 3*math.log(k,2)/2+t-math.log(t,2)/2+4-2*math.sqrt(t*k)
elif t <= k/4.0:
c1 = math.log(7.0*k/20,2)-5*t
c2 = math.log(1/7.0,2)+15*math.log(k,2)/4.0-k/2.0-2*t
c3 = math.log(12*k,2)-k/4.0-3*t
return max(c1, c2, c3)
else:
return math.log(1/7.0)+15*math.log(k,2)/4.0-k/2.0-2*t
If `MBEDTLS_MEMORY_BUFFER_ALLOC_C` is configured and Mbed TLS'
custom buffer allocator is used for calloc() and free(), the
read buffer used by the server example application is allocated
from the buffer allocator, but freed after the buffer allocator
has been destroyed. If memory backtracing is enabled, this leaves
a memory leak in the backtracing structure allocated for the buffer,
as found by valgrind.
Fixes#2069.
In the previous bounds check `(*p) > end - len`, the computation
of `end - len` might underflow if `end` is within the first 64KB
of the address space (note that the length `len` is controlled by
the peer). In this case, the bounds check will be bypassed, leading
to `*p` exceed the message bounds by up to 64KB when leaving
`ssl_parse_server_psk_hint()`. In a pure PSK-based handshake,
this doesn't seem to have any consequences, as `*p*` is not accessed
afterwards. In a PSK-(EC)DHE handshake, however, `*p` is read from
in `ssl_parse_server_ecdh_params()` and `ssl_parse_server_dh_params()`
which might lead to an application crash of information leakage.
* The variables `csr` and `issuer_crt` are initialized but not freed.
* The variable `entropy` is unconditionally freed in the cleanup section
but there's a conditional jump to that section before its initialization.
This cmmot Moves it to the other initializations happening before the
first conditional jump to the cleanup section.
Fixes#1422.
The Cortex M4, M7 MCUs and the Cortex A CPUs support the ARM DSP
instructions, and especially the umaal instruction which greatly
speed up MULADDC code. In addition the patch switched the ASM
constraints to registers instead of memory, giving the opportunity
for the compiler to load them the best way.
The speed improvement is variable depending on the crypto operation
and the CPU. Here are the results on a Cortex M4, a Cortex M7 and a
Cortex A8. All tests have been done with GCC 6.3 using -O2. RSA uses a
RSA-4096 key. ECDSA uses a secp256r1 curve EC key pair.
+--------+--------+--------+
| M4 | M7 | A8 |
+----------------+--------+--------+--------+
| ECDSA signing | +6.3% | +7.9% | +4.1% |
+----------------+--------+--------+--------+
| RSA signing | +43.7% | +68.3% | +26.3% |
+----------------+--------+--------+--------+
| RSA encryption | +3.4% | +9.7% | +3.6% |
+----------------+--------+--------+--------+
| RSA decryption | +43.0% | +67.8% | +22.8% |
+----------------+--------+--------+--------+
I ran the whole testsuite on the Cortex A8 Linux environment, and it
all passes.
stdio.h was being included both conditionally if MBEDTLS_FS_IO was
defined, and also unconditionally, which made at least one of them
redundant.
This change removes the unconditional inclusion of stdio.h and makes it
conditional on MBEDTLS_PLATFORM_C.
Exclude ".git" directories anywhere. This avoids spurious errors in git
checkouts that contain branch names that look like a file
check-files.py would check. Fix#1713
Exclude "mbed-os" anywhere and "examples" from the root. Switch to the
new mechanism to exclude "yotta/module". These are directories where
we store third-party files that do not need to match our preferences.
Exclude "cov-int" from the root. Fix#1691
Changes run-test-suites.pl to filter out directories, and select only files
as on OSX, test coverage tests create .dSYM directories which were being
accidentally selected to execute.
We don't need to disable ASLR, so don't try. If gdb tries but fails,
the test runs normally, but all.sh then trips up because it sees
`warning: Error disabling address space randomization: Operation not permitted`
and interprets it as an error that indicates a test failure.
Generate the documentation from include and doxygen/input only. Don't
get snared by files containing Doxygen comments that lie in other
directories such as tests, yotta, crypto/include, ...
The only difference this makes in a fresh checkout is that the
documentation no longer lists target_config.h. This file is from
yotta, does not contain any Doxygen comment, and its inclusion in the
rendered documentation was clearly an oversight.
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-----
MIICaQIBAAKBhADHXQ+foX0dJLk5U3pDQBfzkMZgRETDWhM2DWsfyYa69AFZuEJ1
03uIMnjfUGTdnrDymw0yWsx5DEtZZyc32786y4j14vLVTJGcr9ByJyxJRZHVLhWJ
kzFeceLKYLHHT+/489d4QrQV1OcXNKSYIGpc2TFch7I+WD4l60ypcFa0XJaFbQID
AQABAoGDSqKtUa6sXze7XBnDYN/i151wluOX9qaHIKo/W4Qfu2fUBZm0z9Wfnqp+
k+PODyX0yq5/b0WM3RhcMRksFn5fBgzYHEmAj8IHhDsjavNtiv8nIl6EF2PfuT1p
6iEpo8IS15dp6j5AKH4Zmnq6TRYiqdaz/ry/kpQrmeJym83KksujZWUCQg85t5gJ
UWvswuNIG2tHWEqiKZvSAnq4owO53lsK3LSl04447bjB+sPqHb1+HVC4QyPjYs/0
3z9aUYLa+pu5IXpz1wJCDRgWT4vQ1Y0BmZjIyxfEwDVOYripRirMowgWiU+YLCrh
FOc5k+MGmJMEN7TuxErewk0yzLy658xMn4kRseshAGhbAkIBClKPIuPbWfwfB4hI
FkHkJ5xsNzdQJ1mMIaEd22olNcd0ylMD8s0tocuSbRGXuF9uDlVsHDE85PD43fmN
tmKhOVUCQgG6H5c2VcEU7BUaNcGzzNudLE2RFaKPmpYWRwKtYODSdwWOyeVbmE8f
dPrz/lodlewCyqR+cBiKtcCFD7Rr0tp+6QJCALZlz954leZ6UKkdeOiTb+fVFpsq
DNNALCL4VJ7XcJJMpjgSKYv9sr1C43nifr1M4YDH+B3NFRF+FWdVodaseOKF
-----END RSA PRIVATE KEY-----
It should be valid to RSASSA-PSS sign a SHA-512 hash with a 1024-bit or
1032-bit RSA key, but with the salt size being always equal to the hash
size, this isn't possible: the key is too small.
To enable use of hashes that are relatively large compared to the key
size, allow reducing the salt size to no less than the hash size minus 2
bytes. We don't allow salt sizes smaller than the hash size minus 2
bytes because that too significantly changes the security guarantees the
library provides compared to the previous implementation which always
used a salt size equal to the hash size. The new calculated salt size
remains compliant with FIPS 186-4.
We also need to update the "hash too large" test, since we now reduce
the salt size when certain key sizes are used. We used to not support
1024-bit keys with SHA-512, but now we support this by reducing the salt
size to 62. Update the "hash too large" test to use a 1016-bit RSA key
with SHA-512, which still has too large of a hash because we will not
reduce the salt size further than 2 bytes shorter than the hash size.
The RSA private key used for the test was generated using "openssl
genrsa 1016" using OpenSSL 1.1.1-pre8.
$ openssl genrsa 1016
Generating RSA private key, 1016 bit long modulus (2 primes)
..............++++++
....++++++
e is 65537 (0x010001)
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
