Merge pull request #3412 from gilles-peskine-arm/montmul-cmp-branch-2.7
Backport 2.7: Remove a secret-dependent branch in Montgomery multiplication
diff --git a/ChangeLog.d/montmul-cmp-branch.txt b/ChangeLog.d/montmul-cmp-branch.txt
new file mode 100644
index 0000000..5994518
--- /dev/null
+++ b/ChangeLog.d/montmul-cmp-branch.txt
@@ -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.
diff --git a/library/bignum.c b/library/bignum.c
index 827a3cb..68460df 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -227,6 +227,22 @@
}
/*
+ * 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.
* (Leaking information about the respective sizes of X and Y is ok however.)
@@ -243,10 +259,9 @@
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:
@@ -1089,10 +1104,24 @@
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;
@@ -1103,24 +1132,18 @@
c = ( *d < *s ) + z; *d -= *s;
}
- while( c != 0 )
- {
- z = ( *d < c ); *d -= c;
- c = z; i++; 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;
size_t n;
-
- if( mbedtls_mpi_cmp_abs( A, B ) < 0 )
- return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
+ mbedtls_mpi_uint carry;
mbedtls_mpi_init( &TB );
@@ -1144,7 +1167,18 @@
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:
@@ -1696,18 +1730,34 @@
*mm = ~x + 1;
}
-/*
- * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
+/** 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 int mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
+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;
@@ -1728,21 +1778,33 @@
*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;
@@ -1750,7 +1812,7 @@
U.n = U.s = (int) z;
U.p = &z;
- return( mpi_montmul( A, &U, N, mm, T ) );
+ mpi_montmul( A, &U, N, mm, T );
}
/*
@@ -1829,13 +1891,13 @@
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 )
{
@@ -1848,7 +1910,7 @@
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]
@@ -1858,7 +1920,7 @@
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 );
}
}
@@ -1895,7 +1957,7 @@
/*
* out of window, square X
*/
- MBEDTLS_MPI_CHK( mpi_montmul( X, X, N, mm, &T ) );
+ mpi_montmul( X, X, N, mm, &T );
continue;
}
@@ -1913,12 +1975,12 @@
* 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;
@@ -1931,18 +1993,18 @@
*/
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 )
{