mbedtls/tests/suites/test_suite_bignum_core.function

/* BEGIN_HEADER */
#include "mbedtls/bignum.h"
#include "mbedtls/entropy.h"
#include "bignum_core.h"
#include "constant_time_internal.h"
#include "test/constant_flow.h"

/* END_HEADER */

/* BEGIN_DEPENDENCIES
 * depends_on:MBEDTLS_BIGNUM_C
 * END_DEPENDENCIES
 */

/* BEGIN_CASE */
void mpi_core_io_null()
{
    mbedtls_mpi_uint X = 0;
    int ret;

    ret = mbedtls_mpi_core_read_be( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_be( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_be( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_be( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_le( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_le( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_le( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_le( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_io_be( data_t *input, int nb_int, int nx_32_int, int iret,
                     int oret )
{
    if( iret != 0 )
        TEST_ASSERT( oret == 0 );

    TEST_LE_S( 0, nb_int );
    size_t nb = nb_int;

    unsigned char buf[1024];
    TEST_LE_U( nb, sizeof( buf ) );

    /* nx_32_int is the number of 32 bit limbs, if we have 64 bit limbs we need
     * to halve the number of limbs to have the same size. */
    size_t nx;
    TEST_LE_S( 0, nx_32_int );
    if( sizeof( mbedtls_mpi_uint ) == 8 )
        nx = nx_32_int / 2 + nx_32_int % 2;
    else
        nx = nx_32_int;

    mbedtls_mpi_uint X[sizeof( buf ) / sizeof( mbedtls_mpi_uint )];
    TEST_LE_U( nx, sizeof( X ) / sizeof( X[0] ) );

    int ret = mbedtls_mpi_core_read_be( X, nx, input->x, input->len );
    TEST_EQUAL( ret, iret );

    if( iret == 0 )
    {
        ret =  mbedtls_mpi_core_write_be( X, nx, buf, nb );
        TEST_EQUAL( ret, oret );
    }

    if( ( iret == 0 ) && ( oret == 0 ) )
    {
        if( nb > input->len )
        {
            size_t leading_zeroes = nb - input->len;
            TEST_ASSERT( memcmp( buf + nb - input->len, input->x, input->len ) == 0 );
            for( size_t i = 0; i < leading_zeroes; i++ )
                TEST_EQUAL( buf[i], 0 );
        }
        else
        {
            size_t leading_zeroes = input->len - nb;
            TEST_ASSERT( memcmp( input->x + input->len - nb, buf, nb ) == 0 );
            for( size_t i = 0; i < leading_zeroes; i++ )
                TEST_EQUAL( input->x[i], 0 );
        }
    }

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_io_le( data_t *input, int nb_int, int nx_32_int, int iret,
                     int oret )
{
    if( iret != 0 )
        TEST_ASSERT( oret == 0 );

    TEST_LE_S( 0, nb_int );
    size_t nb = nb_int;

    unsigned char buf[1024];
    TEST_LE_U( nb, sizeof( buf ) );

    /* nx_32_int is the number of 32 bit limbs, if we have 64 bit limbs we need
     * to halve the number of limbs to have the same size. */
    size_t nx;
    TEST_LE_S( 0, nx_32_int );
    if( sizeof( mbedtls_mpi_uint ) == 8 )
        nx = nx_32_int / 2 + nx_32_int % 2;
    else
        nx = nx_32_int;

    mbedtls_mpi_uint X[sizeof( buf ) / sizeof( mbedtls_mpi_uint )];
    TEST_LE_U( nx, sizeof( X ) / sizeof( X[0] ) );

    int ret =  mbedtls_mpi_core_read_le( X, nx, input->x, input->len );
    TEST_EQUAL( ret, iret );

    if( iret == 0 )
    {
        ret =  mbedtls_mpi_core_write_le( X, nx, buf, nb );
        TEST_EQUAL( ret, oret );
    }

    if( ( iret == 0 ) && ( oret == 0 ) )
    {
        if( nb > input->len )
        {
            TEST_ASSERT( memcmp( buf, input->x, input->len ) == 0 );
            for( size_t i = input->len; i < nb; i++ )
                TEST_EQUAL( buf[i], 0 );
        }
        else
        {
            TEST_ASSERT( memcmp( input->x, buf, nb ) == 0 );
            for( size_t i = nb; i < input->len; i++ )
                TEST_EQUAL( input->x[i], 0 );
        }
    }

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_bitlen( char *input_X, int nr_bits )
{
    mbedtls_mpi_uint *X = NULL;
    size_t limbs;

    TEST_EQUAL( mbedtls_test_read_mpi_core( &X, &limbs, input_X ), 0 );
    TEST_EQUAL( mbedtls_mpi_core_bitlen( X, limbs ), nr_bits );

exit:
    mbedtls_free( X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_lt_ct( char *input_X, char *input_Y, int exp_ret )
{
    mbedtls_mpi_uint *X = NULL;
    size_t X_limbs;
    mbedtls_mpi_uint *Y = NULL;
    size_t Y_limbs;
    int ret;

    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &X, &X_limbs, input_X ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &Y, &Y_limbs, input_Y ) );

    /* We need two same-length limb arrays */
    TEST_EQUAL( X_limbs, Y_limbs );

    TEST_CF_SECRET( X, X_limbs * sizeof( mbedtls_mpi_uint ) );
    TEST_CF_SECRET( Y, X_limbs * sizeof( mbedtls_mpi_uint ) );

    ret = mbedtls_mpi_core_lt_ct( X, Y, X_limbs );
    TEST_EQUAL( ret, exp_ret );

exit:
    mbedtls_free( X );
    mbedtls_free( Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_cond_assign( data_t * input_X,
                           data_t * input_Y,
                           int input_bytes )
{
    mbedtls_mpi_uint *X = NULL;
    mbedtls_mpi_uint *Y = NULL;
    size_t limbs_X = CHARS_TO_LIMBS( input_X->len );
    size_t limbs_Y = CHARS_TO_LIMBS( input_Y->len );
    size_t limbs = limbs_X;
    size_t copy_limbs = CHARS_TO_LIMBS( input_bytes );
    size_t bytes = limbs * sizeof( mbedtls_mpi_uint );
    size_t copy_bytes = copy_limbs * sizeof( mbedtls_mpi_uint );

    TEST_EQUAL( limbs_X, limbs_Y );
    TEST_ASSERT( copy_limbs <= limbs );

    ASSERT_ALLOC( X, limbs );
    ASSERT_ALLOC( Y, limbs );

    TEST_ASSERT( mbedtls_mpi_core_read_be( X, limbs, input_X->x, input_X->len )
                 == 0 );

    TEST_ASSERT( mbedtls_mpi_core_read_be( Y, limbs, input_Y->x, input_Y->len )
                 == 0 );

    /* condition is false */
    TEST_CF_SECRET( X, bytes );
    TEST_CF_SECRET( Y, bytes );

    mbedtls_mpi_core_cond_assign( X, Y, copy_limbs, 0 );

    TEST_CF_PUBLIC( X, bytes );
    TEST_CF_PUBLIC( Y, bytes );

    TEST_ASSERT( memcmp( X, Y, bytes ) != 0 );

    /* condition is true */
    TEST_CF_SECRET( X, bytes );
    TEST_CF_SECRET( Y, bytes );

    mbedtls_mpi_core_cond_assign( X, Y, copy_limbs, 1 );

    TEST_CF_PUBLIC( X, bytes );
    TEST_CF_PUBLIC( Y, bytes );

    /* Check if the given length is copied even it is smaller
       than the length of the given MPIs. */
    if( copy_limbs < limbs )
    {
        ASSERT_COMPARE( X, copy_bytes, Y, copy_bytes );
        TEST_ASSERT( memcmp( X, Y, bytes ) != 0 );
    }
    else
        ASSERT_COMPARE( X, bytes, Y, bytes );

exit:
    mbedtls_free( X );
    mbedtls_free( Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_cond_swap( data_t * input_X,
                         data_t * input_Y,
                         int input_bytes )
{
    mbedtls_mpi_uint *tmp_X = NULL;
    mbedtls_mpi_uint *tmp_Y = NULL;
    mbedtls_mpi_uint *X = NULL;
    mbedtls_mpi_uint *Y = NULL;
    size_t limbs_X = CHARS_TO_LIMBS( input_X->len );
    size_t limbs_Y = CHARS_TO_LIMBS( input_Y->len );
    size_t limbs = limbs_X;
    size_t copy_limbs = CHARS_TO_LIMBS( input_bytes );
    size_t bytes = limbs * sizeof( mbedtls_mpi_uint );
    size_t copy_bytes = copy_limbs * sizeof( mbedtls_mpi_uint );

    TEST_EQUAL( limbs_X, limbs_Y );
    TEST_ASSERT( copy_limbs <= limbs );

    ASSERT_ALLOC( tmp_X, limbs );
    ASSERT_ALLOC( tmp_Y, limbs );

    TEST_ASSERT( mbedtls_mpi_core_read_be( tmp_X, limbs,
                                           input_X->x, input_X->len )
                 == 0 );
    ASSERT_ALLOC( X, limbs );
    memcpy( X, tmp_X, bytes );

    TEST_ASSERT( mbedtls_mpi_core_read_be( tmp_Y, limbs,
                                           input_Y->x, input_Y->len )
                 == 0 );
    ASSERT_ALLOC( Y, limbs );
    memcpy( Y, tmp_Y, bytes );

    /* condition is false */
    TEST_CF_SECRET( X, bytes );
    TEST_CF_SECRET( Y, bytes );

    mbedtls_mpi_core_cond_swap( X, Y, copy_limbs, 0 );

    TEST_CF_PUBLIC( X, bytes );
    TEST_CF_PUBLIC( Y, bytes );

    ASSERT_COMPARE( X, bytes, tmp_X, bytes );
    ASSERT_COMPARE( Y, bytes, tmp_Y, bytes );

    /* condition is true */
    TEST_CF_SECRET( X, bytes );
    TEST_CF_SECRET( Y, bytes );

    mbedtls_mpi_core_cond_swap( X, Y, copy_limbs, 1 );

    TEST_CF_PUBLIC( X, bytes );
    TEST_CF_PUBLIC( Y, bytes );

    /* Check if the given length is copied even it is smaller
       than the length of the given MPIs. */
    if( copy_limbs < limbs )
    {
        ASSERT_COMPARE( X, copy_bytes, tmp_Y, copy_bytes );
        ASSERT_COMPARE( Y, copy_bytes, tmp_X, copy_bytes );
        TEST_ASSERT( memcmp( X, tmp_X, bytes ) != 0 );
        TEST_ASSERT( memcmp( X, tmp_Y, bytes ) != 0 );
        TEST_ASSERT( memcmp( Y, tmp_X, bytes ) != 0 );
        TEST_ASSERT( memcmp( Y, tmp_Y, bytes ) != 0 );
    }
    else
    {
        ASSERT_COMPARE( X, bytes, tmp_Y, bytes );
        ASSERT_COMPARE( Y, bytes, tmp_X, bytes );
    }

exit:
    mbedtls_free( tmp_X );
    mbedtls_free( tmp_Y );
    mbedtls_free( X );
    mbedtls_free( Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_add_if( char * input_A, char * input_B,
                      char * input_S4, int carry4,
                      char * input_S8, int carry8 )
{
    mbedtls_mpi S4, S8, A, B;
    mbedtls_mpi_uint *a = NULL; /* first value to add */
    mbedtls_mpi_uint *b = NULL; /* second value to add */
    mbedtls_mpi_uint *sum = NULL;
    mbedtls_mpi_uint *d = NULL; /* destination - the in/out first operand */

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &S4 );
    mbedtls_mpi_init( &S8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S4, input_S4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S8, input_S8 ) );

    /* We only need to work with one of (S4, carry4) or (S8, carry8) depending
     * on sizeof(mbedtls_mpi_uint)
     */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &S4 : &S8;
    mbedtls_mpi_uint carry = ( sizeof(mbedtls_mpi_uint) == 4 ) ? carry4 : carry8;

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, X->s );

    /* Test cases are such that A <= B, so #limbs should be <= */
    TEST_LE_U( A.n, B.n );
    TEST_LE_U( X->n, B.n );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* mbedtls_mpi_core_add_if() uses input arrays of mbedtls_mpi_uints which
     * must be the same size. The MPIs we've read in will only have arrays
     * large enough for the number they represent. Therefore we create new
     * raw arrays of mbedtls_mpi_uints and populate them from the MPIs we've
     * just read in.
     *
     * We generated test data such that B was always >= A, so that's how many
     * limbs each of these need.
     */
    size_t limbs = B.n;
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( b, bytes );
    ASSERT_ALLOC( sum, bytes );
    ASSERT_ALLOC( d, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_add_if()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC())
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( b, B.p, B.n * sizeof(mbedtls_mpi_uint) );
    memcpy( sum, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* The test cases have a <= b to avoid repetition, so we test a + b then,
     * if a != b, b + a. If a == b, we can test when a and b are aliased */

    /* a + b */

    /* cond = 0 => d unchanged, no carry */
    memcpy( d, a, bytes );
    TEST_EQUAL( 0, mbedtls_mpi_core_add_if( d, b, limbs, 0 ) );
    ASSERT_COMPARE( d, bytes, a, bytes );

    /* cond = 1 => correct result and carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_add_if( d, b, limbs, 1 ) );
    ASSERT_COMPARE( d, bytes, sum, bytes );

    if ( A.n == B.n && memcmp( A.p, B.p, bytes ) == 0 )
    {
        /* a == b, so test where a and b are aliased */

        /* cond = 0 => d unchanged, no carry */
        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( b, b, limbs, 0 ) );
        ASSERT_COMPARE( b, bytes, B.p, bytes );

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( b, b, limbs, 1 ) );
        ASSERT_COMPARE( b, bytes, sum, bytes );
    }
    else
    {
        /* a != b, so test b + a */

        /* cond = 0 => d unchanged, no carry */
        memcpy( d, b, bytes );
        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( d, a, limbs, 0 ) );
        ASSERT_COMPARE( d, bytes, b, bytes );

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( d, a, limbs, 1 ) );
        ASSERT_COMPARE( d, bytes, sum, bytes );
    }

exit:
    mbedtls_free( a );
    mbedtls_free( b );
    mbedtls_free( sum );
    mbedtls_free( d );

    mbedtls_mpi_free( &S4 );
    mbedtls_mpi_free( &S8 );
    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_sub( char * input_A, char * input_B,
                   char * input_X4, char * input_X8,
                   int carry )
{
    mbedtls_mpi A, B, X4, X8;
    mbedtls_mpi_uint *a = NULL;
    mbedtls_mpi_uint *b = NULL;
    mbedtls_mpi_uint *x = NULL; /* expected */
    mbedtls_mpi_uint *r = NULL; /* result */

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &X4 );
    mbedtls_mpi_init( &X8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, X4.s );
    TEST_EQUAL( 1, X8.s );

    /* Get the number of limbs we will need */
    size_t limbs = MAX( A.n, B.n );
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* We only need to work with X4 or X8, depending on sizeof(mbedtls_mpi_uint) */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;

    /* The result shouldn't have more limbs than the longest input */
    TEST_LE_U( X->n, limbs );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( b, bytes );
    ASSERT_ALLOC( x, bytes );
    ASSERT_ALLOC( r, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_sub()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC())
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( b, B.p, B.n * sizeof(mbedtls_mpi_uint) );
    memcpy( x, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* 1a) r = a - b => we should get the correct carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, a, b, limbs ) );

    /* 1b) r = a - b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

    /* 2 and 3 test "r may be aliased to a or b" */
    /* 2a) r = a; r -= b => we should get the correct carry (use r to avoid clobbering a) */
    memcpy( r, a, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, r, b, limbs ) );

    /* 2b) r -= b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

    /* 3a) r = b; r = a - r => we should get the correct carry (use r to avoid clobbering b) */
    memcpy( r, b, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, a, r, limbs ) );

    /* 3b) r = a - b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

    /* 4 tests "r may be aliased to [...] both" */
    if ( A.n == B.n && memcmp( A.p, B.p, bytes ) == 0 )
    {
        memcpy( r, b, bytes );
        TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, r, r, limbs ) );
        ASSERT_COMPARE( r, bytes, x, bytes );
    }

exit:
    mbedtls_free( a );
    mbedtls_free( b );
    mbedtls_free( x );
    mbedtls_free( r );

    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_mla( char * input_A, char * input_B, char * input_S,
                   char * input_X4, char * input_cy4,
                   char * input_X8, char * input_cy8 )
{
    /* We are testing A += B * s; A, B are MPIs, s is a scalar.
     *
     * However, we encode s as an MPI in the .data file as the test framework
     * currently only supports `int`-typed scalars, and that doesn't cover the
     * full range of `mbedtls_mpi_uint`.
     *
     * We also have the different results for sizeof(mbedtls_mpi_uint) == 4 or 8.
     */
    mbedtls_mpi A, B, S, X4, X8, cy4, cy8;
    mbedtls_mpi_uint *a = NULL;
    mbedtls_mpi_uint *x = NULL;

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &S );
    mbedtls_mpi_init( &X4 );
    mbedtls_mpi_init( &X8 );
    mbedtls_mpi_init( &cy4 );
    mbedtls_mpi_init( &cy8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S, input_S ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &cy4, input_cy4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &cy8, input_cy8 ) );

    /* The MPI encoding of scalar s must be only 1 limb */
    TEST_EQUAL( 1, S.n );

    /* We only need to work with X4 or X8, and cy4 or cy8, depending on sizeof(mbedtls_mpi_uint) */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;
    mbedtls_mpi *cy = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &cy4 : &cy8;

    /* The carry should only have one limb */
    TEST_EQUAL( 1, cy->n );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, S.s );
    TEST_EQUAL( 1, X->s );
    TEST_EQUAL( 1, cy->s );

    /* Get the (max) number of limbs we will need */
    size_t limbs = MAX( A.n, B.n );
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* The result shouldn't have more limbs than the longest input */
    TEST_LE_U( X->n, limbs );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( x, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_mla()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC()).
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( x, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* 1a) A += B * s => we should get the correct carry */
    TEST_EQUAL( mbedtls_mpi_core_mla( a, limbs, B.p, B.n, *S.p ), *cy->p );

    /* 1b) A += B * s => we should get the correct result */
    ASSERT_COMPARE( a, bytes, x, bytes );

    if ( A.n == B.n && memcmp( A.p, B.p, bytes ) == 0 )
    {
        /* Check when A and B are aliased */
        memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
        TEST_EQUAL( mbedtls_mpi_core_mla( a, limbs, a, limbs, *S.p ), *cy->p );
        ASSERT_COMPARE( a, bytes, x, bytes );
    }

exit:
    mbedtls_free( a );
    mbedtls_free( x );

    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &S );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
    mbedtls_mpi_free( &cy4 );
    mbedtls_mpi_free( &cy8 );
}
/* END_CASE */


/* BEGIN_CASE */
void mpi_montg_init( char * input_N, char * input_mm )
{
    mbedtls_mpi N, mm;

    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &mm );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &mm, input_mm ) );

    /* The MPI encoding of mm should be 1 limb (sizeof(mbedtls_mpi_uint) == 8) or
     * 2 limbs (sizeof(mbedtls_mpi_uint) == 4).
     *
     * The data file contains the expected result for sizeof(mbedtls_mpi_uint) == 8;
     * for sizeof(mbedtls_mpi_uint) == 4 it's just the LSW of this.
     */
    TEST_ASSERT( mm.n == 1  || mm.n == 2 );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, N.s );
    TEST_EQUAL( 1, mm.s );

    /* mbedtls_mpi_core_montmul_init() only returns a result, no error possible */
    mbedtls_mpi_uint result = mbedtls_mpi_core_montmul_init( N.p );

    /* Check we got the correct result */
    TEST_EQUAL( result, mm.p[0] );

exit:
    mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &mm );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_montmul( int limbs_AN4, int limbs_B4,
                       int limbs_AN8, int limbs_B8,
                       char * input_A,
                       char * input_B,
                       char * input_N,
                       char * input_X4,
                       char * input_X8 )
{
    mbedtls_mpi A, B, N, X4, X8, T, R;

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &X4 );    /* expected result, sizeof(mbedtls_mpi_uint) == 4 */
    mbedtls_mpi_init( &X8 );    /* expected result, sizeof(mbedtls_mpi_uint) == 8 */
    mbedtls_mpi_init( &T );
    mbedtls_mpi_init( &R );     /* for the result */

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );

    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;

    int limbs_AN = ( sizeof(mbedtls_mpi_uint) == 4 ) ? limbs_AN4 : limbs_AN8;
    int limbs_B = ( sizeof(mbedtls_mpi_uint) == 4 ) ? limbs_B4 : limbs_B8;

    TEST_LE_U( A.n, (size_t)limbs_AN );
    TEST_LE_U( X->n, (size_t)limbs_AN );
    TEST_LE_U( B.n, (size_t)limbs_B );
    TEST_LE_U( limbs_B, limbs_AN );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, N.s );
    TEST_EQUAL( 1, X->s );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &A, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( &N, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( X, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( &B, limbs_B ) );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &T, limbs_AN * 2 + 1 ) );

    /* Calculate the Montgomery constant (this is unit tested separately) */
    mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init( N.p );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &R, limbs_AN ) ); /* ensure it's got the right number of limbs */

    mbedtls_mpi_core_montmul( R.p, A.p, B.p, B.n, N.p, N.n, mm, T.p );
    size_t bytes = N.n * sizeof(mbedtls_mpi_uint);
    ASSERT_COMPARE( R.p, bytes, X->p, bytes );

    /* The output (R, above) may be aliased to A - use R to save the value of A */

    memcpy( R.p, A.p, bytes );

    mbedtls_mpi_core_montmul( A.p, A.p, B.p, B.n, N.p, N.n, mm, T.p );
    ASSERT_COMPARE( A.p, bytes, X->p, bytes );

    memcpy( A.p, R.p, bytes );  /* restore A */

    /* The output may be aliased to N - use R to save the value of N */

    memcpy( R.p, N.p, bytes );

    mbedtls_mpi_core_montmul( N.p, A.p, B.p, B.n, N.p, N.n, mm, T.p );
    ASSERT_COMPARE( N.p, bytes, X->p, bytes );

    memcpy( N.p, R.p, bytes );

    if (limbs_AN == limbs_B)
    {
        /* Test when A aliased to B (requires A == B on input values) */
        if ( memcmp( A.p, B.p, bytes ) == 0 )
        {
            /* Test with A aliased to B and output, since this is permitted -
             * don't bother with yet another test with only A and B aliased */

            mbedtls_mpi_core_montmul( B.p, B.p, B.p, B.n, N.p, N.n, mm, T.p );
            ASSERT_COMPARE( B.p, bytes, X->p, bytes );

            memcpy( B.p, A.p, bytes );  /* restore B from equal value A */
        }

        /* The output may be aliased to B - last test, so we don't save B */

        mbedtls_mpi_core_montmul( B.p, A.p, B.p, B.n, N.p, N.n, mm, T.p );
        ASSERT_COMPARE( B.p, bytes, X->p, bytes );
    }

exit:
    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
    mbedtls_mpi_free( &T );
    mbedtls_mpi_free( &R );
}
/* END_CASE */