diff --git a/ChangeLog.d/fix-rsa-leak.txt b/ChangeLog.d/fix-rsa-leak.txt
new file mode 100644
index 0000000000..b7d3e3e758
--- /dev/null
+++ b/ChangeLog.d/fix-rsa-leak.txt
@@ -0,0 +1,6 @@
+Security
+   * An adversary with access to precise enough information about memory
+     accesses (typically, an untrusted operating system attacking a secure
+     enclave) could recover an RSA private key after observing the victim
+     performing a single private-key operation. Found and reported by
+     Zili KOU, Wenjian HE, Sharad Sinha, and Wei ZHANG.
diff --git a/library/bignum.c b/library/bignum.c
index b09e8e8302..967d2a7bc2 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -258,6 +258,36 @@ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
     memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
 }
 
+/**
+ * Select between two sign values in constant-time.
+ *
+ * This is functionally equivalent to second ? a : b but uses only bit
+ * operations in order to avoid branches.
+ *
+ * \param[in] a         The first sign; must be either +1 or -1.
+ * \param[in] b         The second sign; must be either +1 or -1.
+ * \param[in] second    Must be either 1 (return b) or 0 (return a).
+ *
+ * \return The selected sign value.
+ */
+static int mpi_safe_cond_select_sign( int a, int b, unsigned char second )
+{
+    /* In order to avoid questions about what we can reasonnably assume about
+     * the representations of signed integers, move everything to unsigned
+     * by taking advantage of the fact that a and b are either +1 or -1. */
+    unsigned ua = a + 1;
+    unsigned ub = b + 1;
+
+    /* second was 0 or 1, mask is 0 or 2 as are ua and ub */
+    const unsigned mask = second << 1;
+
+    /* select ua or ub */
+    unsigned ur = ( ua & ~mask ) | ( ub & mask );
+
+    /* ur is now 0 or 2, convert back to -1 or +1 */
+    return( (int) ur - 1 );
+}
+
 /*
  * Conditionally assign dest = src, without leaking information
  * about whether the assignment was made or not.
@@ -270,8 +300,23 @@ static void mpi_safe_cond_assign( size_t n,
                                   unsigned char assign )
 {
     size_t i;
+
+    /* MSVC has a warning about unary minus on unsigned integer types,
+     * but this is well-defined and precisely what we want to do here. */
+#if defined(_MSC_VER)
+#pragma warning( push )
+#pragma warning( disable : 4146 )
+#endif
+
+    /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */
+    const mbedtls_mpi_uint mask = -assign;
+
+#if defined(_MSC_VER)
+#pragma warning( pop )
+#endif
+
     for( i = 0; i < n; i++ )
-        dest[i] = dest[i] * ( 1 - assign ) + src[i] * assign;
+        dest[i] = ( src[i] & mask ) | ( dest[i] & ~mask );
 }
 
 /*
@@ -283,20 +328,34 @@ int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned
 {
     int ret = 0;
     size_t i;
+    mbedtls_mpi_uint limb_mask;
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( Y != NULL );
 
+    /* MSVC has a warning about unary minus on unsigned integer types,
+     * but this is well-defined and precisely what we want to do here. */
+#if defined(_MSC_VER)
+#pragma warning( push )
+#pragma warning( disable : 4146 )
+#endif
+
     /* make sure assign is 0 or 1 in a time-constant manner */
-    assign = (assign | (unsigned char)-assign) >> 7;
+    assign = (assign | (unsigned char)-assign) >> (sizeof( assign ) * 8 - 1);
+    /* all-bits 1 if assign is 1, all-bits 0 if assign is 0 */
+    limb_mask = -assign;
+
+#if defined(_MSC_VER)
+#pragma warning( pop )
+#endif
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
 
-    X->s = X->s * ( 1 - assign ) + Y->s * assign;
+    X->s = mpi_safe_cond_select_sign( X->s, Y->s, assign );
 
     mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );
 
     for( i = Y->n; i < X->n; i++ )
-        X->p[i] *= ( 1 - assign );
+        X->p[i] &= ~limb_mask;
 
 cleanup:
     return( ret );
@@ -312,6 +371,7 @@ int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char sw
 {
     int ret, s;
     size_t i;
+    mbedtls_mpi_uint limb_mask;
     mbedtls_mpi_uint tmp;
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( Y != NULL );
@@ -319,22 +379,35 @@ int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char sw
     if( X == Y )
         return( 0 );
 
+    /* MSVC has a warning about unary minus on unsigned integer types,
+     * but this is well-defined and precisely what we want to do here. */
+#if defined(_MSC_VER)
+#pragma warning( push )
+#pragma warning( disable : 4146 )
+#endif
+
     /* make sure swap is 0 or 1 in a time-constant manner */
-    swap = (swap | (unsigned char)-swap) >> 7;
+    swap = (swap | (unsigned char)-swap) >> (sizeof( swap ) * 8 - 1);
+    /* all-bits 1 if swap is 1, all-bits 0 if swap is 0 */
+    limb_mask = -swap;
+
+#if defined(_MSC_VER)
+#pragma warning( pop )
+#endif
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
 
     s = X->s;
-    X->s = X->s * ( 1 - swap ) + Y->s * swap;
-    Y->s = Y->s * ( 1 - swap ) +    s * swap;
+    X->s = mpi_safe_cond_select_sign( X->s, Y->s, swap );
+    Y->s = mpi_safe_cond_select_sign( Y->s, s, swap );
 
 
     for( i = 0; i < X->n; i++ )
     {
         tmp = X->p[i];
-        X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
-        Y->p[i] = Y->p[i] * ( 1 - swap ) +     tmp * swap;
+        X->p[i] = ( X->p[i] & ~limb_mask ) | ( Y->p[i] & limb_mask );
+        Y->p[i] = ( Y->p[i] & ~limb_mask ) | (     tmp & limb_mask );
     }
 
 cleanup:
@@ -2126,6 +2199,71 @@ static void mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
     mpi_montmul( A, &U, N, mm, T );
 }
 
+/*
+ * Constant-flow boolean "equal" comparison:
+ * return x == y
+ *
+ * This function can be used to write constant-time code by replacing branches
+ * with bit operations - it can be used in conjunction with
+ * mbedtls_ssl_cf_mask_from_bit().
+ *
+ * This function is implemented without using comparison operators, as those
+ * might be translated to branches by some compilers on some platforms.
+ */
+static size_t mbedtls_mpi_cf_bool_eq( size_t x, size_t y )
+{
+    /* diff = 0 if x == y, non-zero otherwise */
+    const size_t diff = x ^ y;
+
+    /* MSVC has a warning about unary minus on unsigned integer types,
+     * but this is well-defined and precisely what we want to do here. */
+#if defined(_MSC_VER)
+#pragma warning( push )
+#pragma warning( disable : 4146 )
+#endif
+
+    /* diff_msb's most significant bit is equal to x != y */
+    const size_t diff_msb = ( diff | (size_t) -diff );
+
+#if defined(_MSC_VER)
+#pragma warning( pop )
+#endif
+
+    /* diff1 = (x != y) ? 1 : 0 */
+    const size_t diff1 = diff_msb >> ( sizeof( diff_msb ) * 8 - 1 );
+
+    return( 1 ^ diff1 );
+}
+
+/**
+ * Select an MPI from a table without leaking the index.
+ *
+ * This is functionally equivalent to mbedtls_mpi_copy(R, T[idx]) except it
+ * reads the entire table in order to avoid leaking the value of idx to an
+ * attacker able to observe memory access patterns.
+ *
+ * \param[out] R        Where to write the selected MPI.
+ * \param[in] T         The table to read from.
+ * \param[in] T_size    The number of elements in the table.
+ * \param[in] idx       The index of the element to select;
+ *                      this must satisfy 0 <= idx < T_size.
+ *
+ * \return \c 0 on success, or a negative error code.
+ */
+static int mpi_select( mbedtls_mpi *R, const mbedtls_mpi *T, size_t T_size, size_t idx )
+{
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+
+    for( size_t i = 0; i < T_size; i++ )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( R, &T[i],
+                        (unsigned char) mbedtls_mpi_cf_bool_eq( i, idx ) ) );
+    }
+
+cleanup:
+    return( ret );
+}
+
 /*
  * Sliding-window exponentiation: X = A^E mod N  (HAC 14.85)
  */
@@ -2138,7 +2276,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
     size_t i, j, nblimbs;
     size_t bufsize, nbits;
     mbedtls_mpi_uint ei, mm, state;
-    mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
+    mbedtls_mpi RR, T, W[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], WW, Apos;
     int neg;
 
     MPI_VALIDATE_RET( X != NULL );
@@ -2162,6 +2300,7 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
     mpi_montg_init( &mm, N );
     mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &T );
     mbedtls_mpi_init( &Apos );
+    mbedtls_mpi_init( &WW );
     memset( W, 0, sizeof( W ) );
 
     i = mbedtls_mpi_bitlen( E );
@@ -2302,7 +2441,8 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
             /*
              * X = X * W[wbits] R^-1 mod N
              */
-            mpi_montmul( X, &W[wbits], N, mm, &T );
+            MBEDTLS_MPI_CHK( mpi_select( &WW, W, (size_t) 1 << wsize, wbits ) );
+            mpi_montmul( X, &WW, N, mm, &T );
 
             state--;
             nbits = 0;
@@ -2340,6 +2480,7 @@ cleanup:
         mbedtls_mpi_free( &W[i] );
 
     mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
+    mbedtls_mpi_free( &WW );
 
     if( _RR == NULL || _RR->p == NULL )
         mbedtls_mpi_free( &RR );