Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

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

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
12 commits
Select commit Hold shift + click to select a range
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
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 6 additions & 0 deletions ChangeLog.d/montmul-cmp-branch.txt
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,6 @@
Security
* Fix a side channel vulnerability in modular exponentiation that could
reveal an RSA private key used in a secure enclave. Noticed by Sangho Lee,
Ming-Wei Shih, Prasun Gera, Taesoo Kim and Hyesoon Kim (Georgia Institute
of Technology); and Marcus Peinado (Microsoft Research). Reported by Raoul
Strackx (Fortanix) in #3394.
150 changes: 106 additions & 44 deletions library/bignum.c
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -243,6 +243,22 @@ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
memcpy( Y, &T, sizeof( mbedtls_mpi ) );
}

/*
* Conditionally assign dest = src, without leaking information
* about whether the assignment was made or not.
* dest and src must be arrays of limbs of size n.
* assign must be 0 or 1.
*/
static void mpi_safe_cond_assign( size_t n,
mbedtls_mpi_uint *dest,
const mbedtls_mpi_uint *src,
unsigned char assign )
{
size_t i;
for( i = 0; i < n; i++ )
dest[i] = dest[i] * ( 1 - assign ) + src[i] * assign;
}

/*
* Conditionally assign X = Y, without leaking information
* about whether the assignment was made or not.
Expand All @@ -262,10 +278,9 @@ int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned

X->s = X->s * ( 1 - assign ) + Y->s * assign;

for( i = 0; i < Y->n; i++ )
X->p[i] = X->p[i] * ( 1 - assign ) + Y->p[i] * assign;
mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );

for( ; i < X->n; i++ )
for( i = Y->n; i < X->n; i++ )
X->p[i] *= ( 1 - assign );

cleanup:
Expand Down Expand Up @@ -1327,10 +1342,24 @@ int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
return( ret );
}

/*
* Helper for mbedtls_mpi subtraction
/**
* Helper for mbedtls_mpi subtraction.
*
* Calculate d - s where d and s have the same size.
* This function operates modulo (2^ciL)^n and returns the carry
* (1 if there was a wraparound, i.e. if `d < s`, and 0 otherwise).
*
* \param n Number of limbs of \p d and \p s.
* \param[in,out] d On input, the left operand.
* On output, the result of the subtraction:
* \param[in] s The right operand.
*
* \return 1 if `d < s`.
* 0 if `d >= s`.
*/
static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
static mbedtls_mpi_uint mpi_sub_hlp( size_t n,
mbedtls_mpi_uint *d,
const mbedtls_mpi_uint *s )
{
size_t i;
mbedtls_mpi_uint c, z;
Expand All @@ -1341,28 +1370,22 @@ static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
c = ( *d < *s ) + z; *d -= *s;
}

while( c != 0 )
{
z = ( *d < c ); *d -= c;
c = z; d++;
}
return( c );
}

/*
* Unsigned subtraction: X = |A| - |B| (HAC 14.9)
* Unsigned subtraction: X = |A| - |B| (HAC 14.9, 14.10)
*/
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
mbedtls_mpi TB;
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t n;
mbedtls_mpi_uint carry;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );

if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
Copy link
Contributor Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

The initial check that A >= B is no longer needed, since the function now checks that the carry propagation terminates, which is equivalent.

Oops. The carry propagation check is equivalent, but that's assuming it is reached. If B->n > A->n, or more precisely if B without leading null limbs is larger than A (with its leading null limbs), then mpi_sub_hlp overflows X->p.

return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );

mbedtls_mpi_init( &TB );

if( X == B )
Expand All @@ -1385,7 +1408,18 @@ int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
if( B->p[n - 1] != 0 )
break;

mpi_sub_hlp( n, B->p, X->p );
carry = mpi_sub_hlp( n, X->p, B->p );
if( carry != 0 )
{
/* Propagate the carry to the first nonzero limb of X. */
for( ; n < X->n && X->p[n] == 0; n++ )
--X->p[n];
/* If we ran out of space for the carry, it means that the result
* is negative. */
if( n == X->n )
return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
--X->p[n];
}

cleanup:

Expand Down Expand Up @@ -1975,18 +2009,34 @@ 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)
yanesca marked this conversation as resolved.
Show resolved Hide resolved
*
* \param[in,out] A One of the numbers to multiply.
* It must have at least as many limbs as N
* (A->n >= N->n), and any limbs beyond n are ignored.
* 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.
yanesca marked this conversation as resolved.
Show resolved Hide resolved
*/
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 @@ -2007,30 +2057,42 @@ static int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi
*d++ = u0; d[n + 1] = 0;
}

memcpy( A->p, d, ( n + 1 ) * ciL );
/* At this point, d is either the desired result or the desired result
* plus N. We now potentially subtract N, avoiding leaking whether the
* subtraction is performed through side channels. */

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 );
/* Copy the n least significant limbs of d to A, so that
* A = d if d < N (recall that N has n limbs). */
memcpy( A->p, d, n * ciL );
/* If d >= N then we want to set A to d - N. To prevent timing attacks,
* do the calculation without using conditional tests. */
/* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */
d[n] += 1;
d[n] -= mpi_sub_hlp( n, d, N->p );
/* If d0 < N then d < (2^biL)^n
* so d[n] == 0 and we want to keep A as it is.
* If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n
* so d[n] == 1 and we want to set A to the result of the subtraction
* which is d - (2^biL)^n, i.e. the n least significant limbs of d.
* This exactly corresponds to a conditional assignment. */
mpi_safe_cond_assign( n, A->p, d, (unsigned char) d[n] );
}

/*
* 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 +2178,13 @@ 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 +2197,7 @@ 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 +2207,7 @@ 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 +2244,7 @@ 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 +2262,12 @@ 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 +2280,18 @@ 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