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Remove a secret-dependent branch in Montgomery multiplication #3398

Merged
merged 12 commits into from
Jun 9, 2020
Merged

Remove a secret-dependent branch in Montgomery multiplication #3398

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742f1a4
Add a const annotation to the non-changing argument of mpi_sub_mul
gilles-peskine-arm Jun 4, 2020
4e91d47
Revert "Shut up a clang-analyzer warning"
gilles-peskine-arm Jun 4, 2020
2a82f72
Document some internal bignum functions
gilles-peskine-arm Jun 4, 2020
f04d11e
Separate out low-level mpi_safe_cond_assign
gilles-peskine-arm Jun 4, 2020
132c097
Remove a secret-dependent branch in Montgomery multiplication
gilles-peskine-arm Jun 4, 2020
d55bfe9
Add changelog entry: fix #3394
gilles-peskine-arm Jun 4, 2020
026f555
Explicitly cast down from mbedtls_mpi_uint to unsigned char
gilles-peskine-arm Jun 5, 2020
37ecc61
More logical parameter order for mpi_sub_hlp
gilles-peskine-arm Jun 8, 2020
c097e9e
Move carry propagation out of mpi_sub_hlp
gilles-peskine-arm Jun 8, 2020
221626f
Simplify the final reduction in mpi_montmul
gilles-peskine-arm Jun 8, 2020
0e5faf6
mbedtls_mpi_sub_abs: check the range of the result when it happens
gilles-peskine-arm Jun 8, 2020
09ec10a
Clean up some comments
gilles-peskine-arm Jun 9, 2020
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69 changes: 45 additions & 24 deletions library/bignum.c
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Original file line number Diff line number Diff line change
Expand Up @@ -1328,9 +1328,12 @@ int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
}

/*
* Helper for mbedtls_mpi subtraction
* Helper for mbedtls_mpi subtraction:
* d -= s where d and s have the same size and d >= s.
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*/
static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
static void mpi_sub_hlp( size_t n,
const mbedtls_mpi_uint *s,
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mbedtls_mpi_uint *d )
{
size_t i;
mbedtls_mpi_uint c, z;
Expand Down Expand Up @@ -1975,18 +1978,34 @@ static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
*mm = ~x + 1;
}

/*
* Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
*/
static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
/** Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
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*
* \param[in,out] A One of the numbers to multiply.
* It must have at least one more limb than N
* (A->n >= N->n + 1).
* On successful completion, A contains the result of
* the multiplication A * B * R^-1 mod N where
* R = (2^ciL)^n.
* \param[in] B One of the numbers to multiply.
* It must be nonzero and must not have more limbs than N
* (B->n <= N->n).
* \param[in] N The modulo. N must be odd.
* \param mm The value calculated by `mpi_montg_init(&mm, N)`.
* This is -N^-1 mod 2^ciL.
* \param[in,out] T A bignum for temporary storage.
* It must be at least twice the limb size of N plus 2
* (T->n >= 2 * (N->n + 1)).
* Its initial content is unused and
* its final content is indeterminate.
* Note that unlike the usual convention in the library
* for `const mbedtls_mpi*`, the content of T can change.
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*/
static void mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
const mbedtls_mpi *T )
{
size_t i, n, m;
mbedtls_mpi_uint u0, u1, *d;

if( T->n < N->n + 1 || T->p == NULL )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );

memset( T->p, 0, T->n * ciL );

d = T->p;
Expand All @@ -2009,28 +2028,30 @@ static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi

memcpy( A->p, d, ( n + 1 ) * ciL );

/* If A >= N then A -= N. Do the subtraction unconditionally to prevent
* timing attacks. Modify T as a side effect. */
if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
mpi_sub_hlp( n, N->p, A->p );
else
/* prevent timing attacks */
mpi_sub_hlp( n, A->p, T->p );

return( 0 );
}

/*
* Montgomery reduction: A = A * R^-1 mod N
*
* See mpi_montmul() regarding constraints and guarantees on the parameters.
*/
static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T )
static void mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T )
{
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;

U.n = U.s = (int) z;
U.p = &z;

return( mpi_montmul( A, &U, N, mm, T ) );
mpi_montmul( A, &U, N, mm, T );
}

/*
Expand Down Expand Up @@ -2116,13 +2137,13 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
else
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );

MBEDTLS_MPI_CHK( mpi_montmul( &W[1], &RR, N, mm, &T ) );
mpi_montmul( &W[1], &RR, N, mm, &T );

/*
* X = R^2 * R^-1 mod N = R mod N
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
mpi_montred( X, N, mm, &T );

if( wsize > 1 )
{
Expand All @@ -2135,7 +2156,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[j], &W[1] ) );

for( i = 0; i < wsize - 1; i++ )
MBEDTLS_MPI_CHK( mpi_montmul( &W[j], &W[j], N, mm, &T ) );
mpi_montmul( &W[j], &W[j], N, mm, &T );

/*
* W[i] = W[i - 1] * W[1]
Expand All @@ -2145,7 +2166,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &W[i], N->n + 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[i], &W[i - 1] ) );

MBEDTLS_MPI_CHK( mpi_montmul( &W[i], &W[1], N, mm, &T ) );
mpi_montmul( &W[i], &W[1], N, mm, &T );
}
}

Expand Down Expand Up @@ -2182,7 +2203,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
/*
* out of window, square X
*/
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
mpi_montmul( X, X, N, mm, &T );
continue;
}

Expand All @@ -2200,12 +2221,12 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
* X = X^wsize R^-1 mod N
*/
for( i = 0; i < wsize; i++ )
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
mpi_montmul( X, X, N, mm, &T );

/*
* X = X * W[wbits] R^-1 mod N
*/
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[wbits], N, mm, &T ) );
mpi_montmul( X, &W[wbits], N, mm, &T );

state--;
nbits = 0;
Expand All @@ -2218,18 +2239,18 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
*/
for( i = 0; i < nbits; i++ )
{
MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
mpi_montmul( X, X, N, mm, &T );

wbits <<= 1;

if( ( wbits & ( one << wsize ) ) != 0 )
MBEDTLS_MPI_CHK( mpi_montmul( X, &W[1], N, mm, &T ) );
mpi_montmul( X, &W[1], N, mm, &T );
}

/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
MBEDTLS_MPI_CHK( mpi_montred( X, N, mm, &T ) );
mpi_montred( X, N, mm, &T );

if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
{
Expand Down