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Bignum: Improve primality test for FIPS primes

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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
This commit is contained in:
Janos Follath
2018-08-14 13:34:01 +01:00
committed by Darryl Green
parent 7c025a9f50
commit f301d23ceb
2 changed files with 46 additions and 17 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
include/mbedtls/bignum.h
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@ -726,7 +726,8 @@ int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B
int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N );
/**
* \brief Miller-Rabin primality test
* \brief Miller-Rabin primality test with error probability of
* 2<sup>-80</sup>
*
* \param X MPI to check
* \param f_rng RNG function
@ -747,7 +748,8 @@ int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
* mbedtls_mpi_gen_prime().
*/
typedef enum {
MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
MBEDTLS_MPI_GEN_PRIME_FLAG_DH = 0x0001, /**< (X-1)/2 is prime too */
MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR = 0x0002, /**< lower error rate from 2<sup>-80</sup> to 2<sup>-128</sup> */
} mbedtls_mpi_gen_prime_flag_t;
/**