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Merge pull request #3398 from gilles-peskine-arm/montmul-cmp-branch-d…
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…evelopment

Remove a secret-dependent branch in Montgomery multiplication
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@yanesca
yanesca authored Jun 9, 2020
2 parents 21b3d12 + 09ec10a commit 3c4a46c
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Showing 2 changed files with 112 additions and 44 deletions.
6 changes: 6 additions & 0 deletions ChangeLog.d/montmul-cmp-branch.txt
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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
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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 )
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)
*
* \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.
*/
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

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