mbedtls_mpi_exp_mod: remove spurious copy of the output variable

Clear some confusion between `X` as the output variable and "X" as a name
given to the accumulator. Previous iterations of the code used the variable
`X` as the accumulator, but now that the accumulator is `W[x_index]`, some
of the comments didn't make sense.

Remove the copy of the initial value of `X` into `W[x_index]`, which was
meaningless: the initial value of an output variable should not, and did
not, matter. `W[x_index]` is later overridden unconditionally to take the
value `RR`.

Signed-off-by: Gilles Peskine <[email protected]>

library/bignum.c

@@ -2121,8 +2121,9 @@ int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
      * and squarings. Firstly, when multiplying by an element of the window
      * W[i], we do a constant-trace table lookup to obfuscate i. This leaves
      * squarings as having a different memory access patterns from other
-     * multiplications. So secondly, we put the accumulator X in the table as
-     * well, and also do a constant-trace table lookup to multiply by X.
+     * multiplications. So secondly, we put the accumulator in the table as
+     * well, and also do a constant-trace table lookup to multiply by the
+     * accumulator which is W[x_index].
      *
      * This way, all multiplications take the form of a lookup-and-multiply.
      * The number of lookup-and-multiply operations inside each iteration of
@@ -2135,19 +2136,16 @@ int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
      * observe both memory accesses and branches. However, branch prediction
      * exploitation typically requires many traces of execution over the same
      * data, which is defeated by randomized blinding.
-     *
-     * To achieve this, we make a copy of X and we use the table entry in each
-     * calculation from this point on.
      */
     const size_t x_index = 0;
     mbedtls_mpi_init(&W[x_index]);
-    mbedtls_mpi_copy(&W[x_index], X);
 
     j = N->n + 1;
-    /* All W[i] and X must have at least N->n limbs for the mpi_montmul()
-     * and mpi_montred() calls later. Here we ensure that W[1] and X are
-     * large enough, and later we'll grow other W[i] to the same length.
-     * They must not be shrunk midway through this function!
+    /* All W[i] including the accumulator must have at least N->n limbs for
+     * the mpi_montmul() and mpi_montred() calls later. Here we ensure that
+     * W[1] and the accumulator W[x_index] are large enough. later we'll grow
+     * other W[i] to the same length. They must not be shrunk midway through
+     * this function!
      */
     MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[x_index], j));
     MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1],  j));