The signature of mbedtls_mpi_cmp_mpi_ct() meant to support using it in
place of mbedtls_mpi_cmp_mpi(). This meant full comparison functionality
and a signed result.
To make the function more universal and friendly to constant time
coding, we change the result type to unsigned. Theoretically, we could
encode the comparison result in an unsigned value, but it would be less
intuitive.
Therefore we won't be able to represent the result as unsigned anymore
and the functionality will be constrained to checking if the first
operand is less than the second. This is sufficient to support the
current use case and to check any relationship between MPIs.
The only drawback is that we need to call the function twice when
checking for equality, but this can be optimised later if an when it is
needed.
Multiplication is known to have measurable timing variations based on
the operands. For example it typically is much faster if one of the
operands is zero. Remove them from constant time code.
In mbedtls_mpi_exp_mod(), the limit check on wsize is never true when
MBEDTLS_MPI_WINDOW_SIZE is at least 6. Wrap in a preprocessor guard
to remove the dead code and resolve a Coverity finding from the
DEADCODE checker.
Change-Id: Ice7739031a9e8249283a04de11150565b613ae89
Fixes memory leak in mpi_miller_rabin() that occurs when the function has
failed to obtain a usable random 'A' 30 turns in a row.
Signed-off-by: Jens Wiklander <jens.wiklander@linaro.org>
mbedtls_mpi_read_binary() calls memcpy() with the source pointer being
the source pointer passed to mbedtls_mpi_read_binary(), the latter may
be NULL if the buffer length is 0 (and this happens e.g. in the ECJPAKE
test suite). The behavior of memcpy(), in contrast, is undefined when
called with NULL source buffer, even if the length of the copy operation
is 0.
This commit fixes this by explicitly checking that the source pointer is
not NULL before calling memcpy(), and skipping the call otherwise.
Context: The function `mbedtls_mpi_fill_random()` uses a temporary stack
buffer to hold the random data before reading it into the target MPI.
Problem: This is inefficient both computationally and memory-wise.
Memory-wise, it may lead to a stack overflow on constrained devices with
limited stack.
Fix: This commit introduces the following changes to get rid of the
temporary stack buffer entirely:
1. It modifies the call to the PRNG to output the random data directly
into the target MPI's data buffer.
This alone, however, constitutes a change of observable behaviour:
The previous implementation guaranteed to interpret the bytes emitted by
the PRNG in a big-endian fashion, while rerouting the PRNG output into the
target MPI's limb array leads to an interpretation that depends on the
endianness of the host machine.
As a remedy, the following change is applied, too:
2. Reorder the bytes emitted from the PRNG within the target MPI's
data buffer to ensure big-endian semantics.
Luckily, the byte reordering was already implemented as part of
`mbedtls_mpi_read_binary()`, so:
3. Extract bigendian-to-host byte reordering from
`mbedtls_mpi_read_binary()` to a separate internal function
`mpi_bigendian_to_host()` to be used by `mbedtls_mpi_read_binary()`
and `mbedtls_mpi_fill_random()`.
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.
Refactor `mpi_write_hlp()` to not be recursive, to fix stack overflows.
Iterate over the `mbedtls_mpi` division of the radix requested,
until it is zero. Each iteration, put the residue in the next LSB
of the output buffer. Fixes#2190
In mbedtls_mpi_write_binary, avoid leaking the size of the number
through timing or branches, if possible. More precisely, if the number
fits in the output buffer based on its allocated size, the new code's
trace doesn't depend on the value of the number.
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.
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
Setting the dh_flag to 1 used to indicate that the caller requests safe
primes from mbedtls_mpi_gen_prime. We generalize the functionality to
make room for more flags in that parameter.
The specification requires that numbers are the raw entropy (except for odd/
even) and at least 2^(nbits-0.5). If not, new random bits need to be used for
the next number. Similarly, if the number is not prime new random bits need to
be used.
This commit modifies mpi_read_binary to always allocate the minimum number of
limbs required to hold the entire buffer provided to the function, regardless of
its content. Previously, leading zero bytes in the input data were detected and
used to reduce memory footprint and time, but this non-constant behavior turned
out to be non-tolerable for the cryptographic applications this function is used
for.
