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.
Previous commits attempted to use `gmtime_s()` for IAR systems; however,
this attempt depends on the use of C11 extensions which lead to incompatibility
with other pieces of the library, such as the use of `memset()` which is
being deprecated in favor of `memset_s()` in C11.
