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"

/** Verifies mbedtls_mpi_core_add().
 *
 * \param[in] A       Little-endian presentation of the left operand.
 * \param[in] B       Little-endian presentation of the right operand.
 * \param limbs       Number of limbs in each MPI (\p A, \p B, \p S and \p X).
 * \param[in] S       Little-endian presentation of the expected sum.
 * \param carry       Expected carry from the addition.
 * \param[in,out] X   Temporary storage to be used for results.
 *
 * \return  1 if mbedtls_mpi_core_add() passes this test, otherwise 0.
 */
static int mpi_core_verify_add( mbedtls_mpi_uint *A,
                                mbedtls_mpi_uint *B,
                                size_t limbs,
                                mbedtls_mpi_uint *S,
                                int carry,
                                mbedtls_mpi_uint *X )
{
    int ret = 0;

    size_t bytes = limbs * sizeof( *A );

    /* 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 */

    /* A + B => correct result and carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, B, limbs ) );
    ASSERT_COMPARE( X, bytes, S, bytes );

    /* A + B; alias output and first operand => correct result and carry */
    memcpy( X, A, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, B, limbs ) );
    ASSERT_COMPARE( X, bytes, S, bytes );

    /* A + B; alias output and second operand => correct result and carry */
    memcpy( X, B, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, X, limbs ) );
    ASSERT_COMPARE( X, bytes, S, bytes );

    if ( memcmp( A, B, bytes ) == 0 )
    {
        /* A == B, so test where A and B are aliased */

        /* A + A => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, A, limbs ) );
        ASSERT_COMPARE( X, bytes, S, bytes );

        /* A + A, output aliased to both operands => correct result and carry */
        memcpy( X, A, bytes );
        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, X, limbs ) );
        ASSERT_COMPARE( X, bytes, S, bytes );
    }
    else
    {
        /* A != B, so test B + A */

        /* B + A => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, B, A, limbs ) );
        ASSERT_COMPARE( X, bytes, S, bytes );

        /* B + A; alias output and first operand => correct result and carry */
        memcpy( X, B, bytes );
        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, A, limbs ) );
        ASSERT_COMPARE( X, bytes, S, bytes );

        /* B + A; alias output and second operand => correct result and carry */
        memcpy( X, A, bytes );
        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, B, X, limbs ) );
        ASSERT_COMPARE( X, bytes, S, bytes );
    }

    ret = 1;

exit:
    return ret;
}

/** Verifies mbedtls_mpi_core_add_if().
 *
 * \param[in] A       Little-endian presentation of the left operand.
 * \param[in] B       Little-endian presentation of the right operand.
 * \param limbs       Number of limbs in each MPI (\p A, \p B, \p S and \p X).
 * \param[in] S       Little-endian presentation of the expected sum.
 * \param carry       Expected carry from the addition.
 * \param[in,out] X   Temporary storage to be used for results.
 *
 * \return  1 if mbedtls_mpi_core_add_if() passes this test, otherwise 0.
 */
static int mpi_core_verify_add_if( mbedtls_mpi_uint *A,
                                   mbedtls_mpi_uint *B,
                                   size_t limbs,
                                   mbedtls_mpi_uint *S,
                                   int carry,
                                   mbedtls_mpi_uint *X )
{
    int ret = 0;

    size_t bytes = limbs * sizeof( *A );

    /* 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 => X unchanged, no carry */
    memcpy( X, A, bytes );
    TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, B, limbs, 0 ) );
    ASSERT_COMPARE( X, bytes, A, bytes );

    /* cond = 1 => correct result and carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, B, limbs, 1 ) );
    ASSERT_COMPARE( X, bytes, S, bytes );

    if ( memcmp( A, B, bytes ) == 0 )
    {
        /* A == B, so test where A and B are aliased */

        /* cond = 0 => X unchanged, no carry */
        memcpy( X, B, bytes );
        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, X, limbs, 0 ) );
        ASSERT_COMPARE( X, bytes, B, bytes );

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, X, limbs, 1 ) );
        ASSERT_COMPARE( X, bytes, S, bytes );
    }
    else
    {
        /* A != B, so test B + A */

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

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, A, limbs, 1 ) );
        ASSERT_COMPARE( X, bytes, S, bytes );
    }

    ret = 1;

exit:
    return ret;
}

/* 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( char * input_X,
                           char * input_Y,
                           int input_bytes )
{
    mbedtls_mpi_uint *X = NULL;
    mbedtls_mpi_uint *Y = NULL;
    size_t limbs_X;
    size_t limbs_Y;

    TEST_EQUAL( mbedtls_test_read_mpi_core( &X, &limbs_X, input_X ), 0 );
    TEST_EQUAL( mbedtls_test_read_mpi_core( &Y, &limbs_Y, input_Y ), 0 );

    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 );

    /* 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 )
    {
        TEST_CF_PUBLIC( X, bytes );
        TEST_CF_PUBLIC( Y, bytes );

        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( char * input_X,
                         char * 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;
    size_t limbs_Y;

    TEST_EQUAL( mbedtls_test_read_mpi_core( &tmp_X, &limbs_X, input_X ), 0 );
    TEST_EQUAL( mbedtls_test_read_mpi_core( &tmp_Y, &limbs_Y, input_Y ), 0 );

    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 );
    memcpy( X, tmp_X, bytes );

    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_shift_r( char *input, int count, char *result )
{
    mbedtls_mpi_uint *X = NULL;
    mbedtls_mpi_uint *Y = NULL;
    size_t limbs, n;

    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &X, &limbs, input ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &Y, &n, result ) );
    TEST_EQUAL( limbs, n );

    mbedtls_mpi_core_shift_r( X, limbs, count );
    ASSERT_COMPARE( X, limbs * ciL, Y, limbs * ciL );

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

/* BEGIN_CASE */
void mpi_core_add_and_add_if( char * input_A, char * input_B,
                              char * input_S, int carry )
{
    mbedtls_mpi_uint *A = NULL; /* first value to add */
    mbedtls_mpi_uint *B = NULL; /* second value to add */
    mbedtls_mpi_uint *S = NULL; /* expected result */
    mbedtls_mpi_uint *X = NULL; /* destination - the in/out first operand */
    size_t A_limbs, B_limbs, S_limbs;

    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &A, &A_limbs, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &B, &B_limbs, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &S, &S_limbs, input_S ) );

    /* add and add_if expect all operands to be the same length */
    TEST_EQUAL( A_limbs, B_limbs );
    TEST_EQUAL( A_limbs, S_limbs );

    size_t limbs = A_limbs;
    ASSERT_ALLOC( X, limbs );

    TEST_ASSERT( mpi_core_verify_add( A, B, limbs, S, carry, X ) );
    TEST_ASSERT( mpi_core_verify_add_if( A, B, limbs, S, carry, X ) );

exit:
    mbedtls_free( A );
    mbedtls_free( B );
    mbedtls_free( S );
    mbedtls_free( X );
}
/* 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 */

/* BEGIN_CASE */
void mpi_core_get_mont_r2_unsafe_neg(  )
{
    mbedtls_mpi N, RR;
    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &RR );
    const char * n = "7ffffffffffffff1";

    /* Test for zero divisor */
    TEST_EQUAL( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO,
               mbedtls_mpi_core_get_mont_r2_unsafe( &RR, &N ) );

    /* Test for negative input */
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, n ) );
    N.s = -1;
    TEST_EQUAL( MBEDTLS_ERR_MPI_NEGATIVE_VALUE,
               mbedtls_mpi_core_get_mont_r2_unsafe( &RR, &N ) );
    N.s = 1;

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

/* BEGIN_CASE */
void mpi_core_get_mont_r2_unsafe( char * input_N,
                                  char * input_RR_X4,
                                  char * input_RR_X8 )
{
    mbedtls_mpi N, RR, RR_REF;

    /* Select the appropriate output */
    char * input_rr = ( sizeof(mbedtls_mpi_uint) == 4 ) ? input_RR_X4: input_RR_X8;

    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &RR );
    mbedtls_mpi_init( &RR_REF );

    /* Read inputs */
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &RR_REF, input_rr ) );

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

    /* Test valid input */
    TEST_EQUAL( 0, mbedtls_mpi_core_get_mont_r2_unsafe( &RR, &N ) );

    /* Test that the moduli is odd */
    TEST_EQUAL( N.p[0] ^ 1, N.p[0] - 1 );

   /* Output is +ve (or zero) */
    TEST_EQUAL( 1, RR_REF.s );

    /* rr is updated to a valid pointer */
    TEST_ASSERT( RR.p != NULL );

    /* Calculated rr matches expected value */
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &RR, &RR_REF ) == 0 );

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

/* BEGIN_CASE depends_on:MBEDTLS_TEST_HOOKS */
void mpi_core_ct_uint_table_lookup( int bitlen, int window_size )
{
    size_t limbs = BITS_TO_LIMBS( bitlen );
    size_t count = ( (size_t) 1 ) << window_size;

    mbedtls_mpi_uint *table = NULL;
    mbedtls_mpi_uint *dest = NULL;

    ASSERT_ALLOC( table, limbs * count );
    ASSERT_ALLOC( dest, limbs );

    /*
     * Fill the table with a unique counter so that differences are easily
     * detected. (And have their relationship to the index relatively non-trivial just
     * to be sure.)
     */
    for( size_t i = 0; i < count * limbs; i++ )
    {
        table[i] = ~i - 1;
    }

    for( size_t i = 0; i < count; i++ )
    {
        mbedtls_mpi_uint *current = table + i * limbs;
        memset( dest, 0x00, limbs * sizeof( *dest ) );

        /*
         * We shouldn't leak anything through timing.
         * We need to set these in every loop as we need to make the loop
         * variable public for the loop head and the buffers for comparison.
         */
        TEST_CF_SECRET( &i, sizeof( i ) );
        TEST_CF_SECRET( dest, limbs * sizeof( *dest ) );
        TEST_CF_SECRET( table, count * limbs * sizeof( *table ) );

        mbedtls_mpi_core_ct_uint_table_lookup( dest, table, limbs, count, i );

        TEST_CF_PUBLIC( dest, limbs * sizeof( *dest ) );
        TEST_CF_PUBLIC( table, count * limbs * sizeof( *table ) );
        ASSERT_COMPARE( dest, limbs * sizeof( *dest ),
                        current, limbs * sizeof( *current ) );
        TEST_CF_PUBLIC( &i, sizeof( i ) );
    }

exit:
    mbedtls_free(table);
    mbedtls_free(dest);
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_fill_random( int wanted_bytes_arg, int extra_rng_bytes,
                           int extra_limbs, int before, int expected_ret )
{
    size_t wanted_bytes = wanted_bytes_arg;
    mbedtls_mpi_uint *X = NULL;
    size_t X_limbs = CHARS_TO_LIMBS( wanted_bytes ) + extra_limbs;
    size_t rng_bytes = wanted_bytes + extra_rng_bytes;
    unsigned char *rnd_data = NULL;
    mbedtls_test_rnd_buf_info rnd_info = {NULL, rng_bytes, NULL, NULL};
    int ret;

    /* Prepare an RNG with known output, limited to rng_bytes. */
    ASSERT_ALLOC( rnd_data, rng_bytes );
    TEST_EQUAL( 0, mbedtls_test_rnd_std_rand( NULL, rnd_data, rng_bytes ) );
    rnd_info.buf = rnd_data;

    /* Allocate an MPI with room for wanted_bytes plus extra_limbs.
     * extra_limbs may be negative but the total limb count must be positive.
     * Fill the MPI with the byte value in before. */
    TEST_LE_U( 1, X_limbs );
    ASSERT_ALLOC( X, X_limbs );
    memset( X, before, X_limbs * sizeof( *X ) );

    ret = mbedtls_mpi_core_fill_random( X, X_limbs, wanted_bytes,
                                        mbedtls_test_rnd_buffer_rand,
                                        &rnd_info );
    TEST_EQUAL( expected_ret, ret );

    if( expected_ret == 0 )
    {
        /* mbedtls_mpi_core_fill_random is documented to use bytes from the
         * RNG as a big-endian representation of the number. We used an RNG
         * with known output, so check that the output contains the
         * expected value. Bytes above wanted_bytes must be zero. */
        for( size_t i = 0; i < wanted_bytes; i++ )
        {
            mbedtls_test_set_step( i );
            TEST_EQUAL( GET_BYTE( X, i ), rnd_data[wanted_bytes - 1 - i] );
        }
        for( size_t i = wanted_bytes; i < X_limbs * ciL; i++ )
        {
            mbedtls_test_set_step( i );
            TEST_EQUAL( GET_BYTE( X, i ), 0 );
        }
    }

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

/* BEGIN MERGE SLOT 1 */

/* BEGIN_CASE */
void mpi_core_exp_mod( char * input_N, char * input_A,
                       char * input_E, char * input_X )
{
    mbedtls_mpi_uint *A = NULL;
    size_t A_limbs;
    mbedtls_mpi_uint *E = NULL;
    size_t E_limbs;
    mbedtls_mpi_uint *N = NULL;
    size_t N_limbs;
    mbedtls_mpi_uint *X = NULL;
    size_t X_limbs;
    const mbedtls_mpi_uint *R2 = NULL;
    mbedtls_mpi_uint *Y = NULL;
    /* Legacy MPIs for computing R2 */
    mbedtls_mpi N_mpi;
    mbedtls_mpi_init( &N_mpi );
    mbedtls_mpi R2_mpi;
    mbedtls_mpi_init( &R2_mpi );

    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &A, &A_limbs, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &E, &E_limbs, input_E ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &N, &N_limbs, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &X, &X_limbs, input_X ) );
    ASSERT_ALLOC( Y, N_limbs );

    TEST_EQUAL( A_limbs, N_limbs );
    TEST_EQUAL( X_limbs, N_limbs );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &N_mpi, N_limbs ) );
    memcpy( N_mpi.p, N, N_limbs * sizeof( *N ) );
    N_mpi.n = N_limbs;
    TEST_EQUAL( 0,
                mbedtls_mpi_core_get_mont_r2_unsafe( &R2_mpi, &N_mpi ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( &R2_mpi, N_limbs ) );
    R2 = R2_mpi.p;

    TEST_EQUAL( 0,
                mbedtls_mpi_core_exp_mod( Y, A, N, N_limbs, E, E_limbs, R2 ) );
    TEST_EQUAL( 0, memcmp( X, Y, N_limbs * sizeof( mbedtls_mpi_uint ) ) );

exit:
    mbedtls_free( A );
    mbedtls_free( E );
    mbedtls_free( N );
    mbedtls_free( X );
    mbedtls_free( Y );
    mbedtls_mpi_free( &N_mpi );
    mbedtls_mpi_free( &R2_mpi );
    // R2 doesn't need to be freed as it is only aliasing R2_mpi
}
/* END_CASE */

/* END MERGE SLOT 1 */

/* BEGIN MERGE SLOT 2 */

/* END MERGE SLOT 2 */

/* BEGIN MERGE SLOT 3 */

/* BEGIN_CASE */
void mpi_core_sub_int( char * input_A, char * input_B,
                       char * input_X, int borrow )
{
    /* We are testing A - b, where A is an MPI and b is a scalar, expecting
     * result X with borrow borrow.  However, for ease of handling we encode b
     * as a 1-limb MPI (B) in the .data file. */

    mbedtls_mpi_uint *A = NULL;
    mbedtls_mpi_uint *B = NULL;
    mbedtls_mpi_uint *X = NULL;
    mbedtls_mpi_uint *R = NULL;
    size_t A_limbs, B_limbs, X_limbs;

    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &A, &A_limbs, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &B, &B_limbs, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &X, &X_limbs, input_X ) );

    /* The MPI encoding of scalar b must be only 1 limb */
    TEST_EQUAL( B_limbs, 1 );

    /* The subtraction is fixed-width, so A and X must have the same number of limbs */
    TEST_EQUAL( A_limbs, X_limbs );
    size_t limbs = A_limbs;

    ASSERT_ALLOC( R, limbs );

#define TEST_COMPARE_CORE_MPIS( A, B, limbs ) \
                ASSERT_COMPARE( A, (limbs) * sizeof(mbedtls_mpi_uint), B, (limbs) * sizeof(mbedtls_mpi_uint) )

    /* 1. R = A - b. Result and borrow should be correct */
    TEST_EQUAL( mbedtls_mpi_core_sub_int( R, A, B[0], limbs ), borrow );
    TEST_COMPARE_CORE_MPIS( R, X, limbs );

    /* 2. A = A - b. Result and borrow should be correct */
    TEST_EQUAL( mbedtls_mpi_core_sub_int( A, A, B[0], limbs ), borrow );
    TEST_COMPARE_CORE_MPIS( A, X, limbs );

exit:
    mbedtls_free( A );
    mbedtls_free( B );
    mbedtls_free( X );
    mbedtls_free( R );
}
/* END_CASE */

/* END MERGE SLOT 3 */

/* BEGIN MERGE SLOT 4 */

/* END MERGE SLOT 4 */

/* BEGIN MERGE SLOT 5 */

/* END MERGE SLOT 5 */

/* BEGIN MERGE SLOT 6 */

/* END MERGE SLOT 6 */

/* BEGIN MERGE SLOT 7 */

/* END MERGE SLOT 7 */

/* BEGIN MERGE SLOT 8 */

/* END MERGE SLOT 8 */

/* BEGIN MERGE SLOT 9 */

/* END MERGE SLOT 9 */

/* BEGIN MERGE SLOT 10 */

/* END MERGE SLOT 10 */