diff --git a/library/bignum.c b/library/bignum.c
index d3d72ab..3926da4 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -1683,13 +1683,7 @@
                         mbedtls_mpi *prec_RR)
 {
     int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t window_bitsize;
-    size_t i, j, nblimbs;
-    size_t bufsize, nbits;
-    size_t exponent_bits_in_window = 0;
-    mbedtls_mpi_uint ei, mm, state;
-    mbedtls_mpi RR, T, W[(size_t) 1 << MBEDTLS_MPI_WINDOW_SIZE], WW, Apos;
-    int neg;
+    mbedtls_mpi RR, T, E_core;
 
     if (mbedtls_mpi_cmp_int(N, 0) <= 0 || (N->p[0] & 1) == 0) {
         return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
@@ -1704,89 +1698,15 @@
         return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
     }
 
-    /*
-     * Init temps and window size
-     */
-    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);
-
-    window_bitsize = (i > 671) ? 6 : (i > 239) ? 5 :
-                     (i >  79) ? 4 : (i >  23) ? 3 : 1;
-
-#if (MBEDTLS_MPI_WINDOW_SIZE < 6)
-    if (window_bitsize > MBEDTLS_MPI_WINDOW_SIZE) {
-        window_bitsize = MBEDTLS_MPI_WINDOW_SIZE;
-    }
-#endif
-
-    const size_t w_table_used_size = (size_t) 1 << window_bitsize;
-
-    /*
-     * This function is not constant-trace: its memory accesses depend on the
-     * exponent value. To defend against timing attacks, callers (such as RSA
-     * and DHM) should use exponent blinding. However this is not enough if the
-     * adversary can find the exponent in a single trace, so this function
-     * takes extra precautions against adversaries who can observe memory
-     * access patterns.
-     *
-     * This function performs a series of multiplications by table elements and
-     * squarings, and we want the prevent the adversary from finding out which
-     * table element was used, and from distinguishing between multiplications
-     * 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 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
-     * the main loop still depends on the bits of the exponent, but since the
-     * other operations in the loop don't have an easily recognizable memory
-     * trace, an adversary is unlikely to be able to observe the exact
-     * patterns.
-     *
-     * An adversary may still be able to recover the exponent if they can
-     * 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.
-     */
-    const size_t x_index = 0;
-    mbedtls_mpi_init(&W[x_index]);
-
-    j = N->n + 1;
-    /* 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));
-    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T, j * 2));
-
-    /*
-     * Compensate for negative A (and correct at the end)
-     */
-    neg = (A->s == -1);
-    if (neg) {
-        MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Apos, A));
-        Apos.s = 1;
-        A = &Apos;
-    }
+    mbedtls_mpi_init(&RR);
+    mbedtls_mpi_init(&T);
+    mbedtls_mpi_init(&E_core);
 
     /*
      * If 1st call, pre-compute R^2 mod N
      */
     if (prec_RR == NULL || prec_RR->p == NULL) {
-        MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&RR, 1));
-        MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&RR, N->n * 2 * biL));
-        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&RR, &RR, N));
+        MBEDTLS_MPI_CHK(mbedtls_mpi_core_get_mont_r2_unsafe(&RR, N));
 
         if (prec_RR != NULL) {
             memcpy(prec_RR, &RR, sizeof(mbedtls_mpi));
@@ -1796,175 +1716,68 @@
     }
 
     /*
-     * W[1] = A * R^2 * R^-1 mod N = A * R mod N
+     * Ensure that the exponent that we are passing to the core is not NULL.
      */
-    if (mbedtls_mpi_cmp_mpi(A, N) >= 0) {
-        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&W[1], A, N));
-        /* This should be a no-op because W[1] is already that large before
-         * mbedtls_mpi_mod_mpi(), but it's necessary to avoid an overflow
-         * in mpi_montmul() below, so let's make sure. */
-        MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1], N->n + 1));
+    if (E->n == 0) {
+        mbedtls_mpi_lset(&E_core, 0);
     } else {
-        MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[1], A));
-    }
-
-    /* Note that this is safe because W[1] always has at least N->n limbs
-     * (it grew above and was preserved by mbedtls_mpi_copy()). */
-    mpi_montmul(&W[1], &RR, N, mm, &T);
-
-    /*
-     * W[x_index] = R^2 * R^-1 mod N = R mod N
-     */
-    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[x_index], &RR));
-    mpi_montred(&W[x_index], N, mm, &T);
-
-
-    if (window_bitsize > 1) {
-        /*
-         * W[i] = W[1] ^ i
-         *
-         * The first bit of the sliding window is always 1 and therefore we
-         * only need to store the second half of the table.
-         *
-         * (There are two special elements in the table: W[0] for the
-         * accumulator/result and W[1] for A in Montgomery form. Both of these
-         * are already set at this point.)
-         */
-        j = w_table_used_size / 2;
-
-        MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[j], N->n + 1));
-        MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[j], &W[1]));
-
-        for (i = 0; i < window_bitsize - 1; i++) {
-            mpi_montmul(&W[j], &W[j], N, mm, &T);
-        }
-
-        /*
-         * W[i] = W[i - 1] * W[1]
-         */
-        for (i = j + 1; i < w_table_used_size; i++) {
-            MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[i], N->n + 1));
-            MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[i], &W[i - 1]));
-
-            mpi_montmul(&W[i], &W[1], N, mm, &T);
-        }
-    }
-
-    nblimbs = E->n;
-    bufsize = 0;
-    nbits   = 0;
-    state   = 0;
-
-    while (1) {
-        if (bufsize == 0) {
-            if (nblimbs == 0) {
-                break;
-            }
-
-            nblimbs--;
-
-            bufsize = sizeof(mbedtls_mpi_uint) << 3;
-        }
-
-        bufsize--;
-
-        ei = (E->p[nblimbs] >> bufsize) & 1;
-
-        /*
-         * skip leading 0s
-         */
-        if (ei == 0 && state == 0) {
-            continue;
-        }
-
-        if (ei == 0 && state == 1) {
-            /*
-             * out of window, square W[x_index]
-             */
-            MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, x_index));
-            mpi_montmul(&W[x_index], &WW, N, mm, &T);
-            continue;
-        }
-
-        /*
-         * add ei to current window
-         */
-        state = 2;
-
-        nbits++;
-        exponent_bits_in_window |= (ei << (window_bitsize - nbits));
-
-        if (nbits == window_bitsize) {
-            /*
-             * W[x_index] = W[x_index]^window_bitsize R^-1 mod N
-             */
-            for (i = 0; i < window_bitsize; i++) {
-                MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size,
-                                           x_index));
-                mpi_montmul(&W[x_index], &WW, N, mm, &T);
-            }
-
-            /*
-             * W[x_index] = W[x_index] * W[exponent_bits_in_window] R^-1 mod N
-             */
-            MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size,
-                                       exponent_bits_in_window));
-            mpi_montmul(&W[x_index], &WW, N, mm, &T);
-
-            state--;
-            nbits = 0;
-            exponent_bits_in_window = 0;
-        }
+        memcpy(&E_core, E, sizeof(mbedtls_mpi));
     }
 
     /*
-     * process the remaining bits
+     * To preserve constness we need to make a copy of A. Using X for this to
+     * save memory.
      */
-    for (i = 0; i < nbits; i++) {
-        MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, x_index));
-        mpi_montmul(&W[x_index], &WW, N, mm, &T);
-
-        exponent_bits_in_window <<= 1;
-
-        if ((exponent_bits_in_window & ((size_t) 1 << window_bitsize)) != 0) {
-            MBEDTLS_MPI_CHK(mpi_select(&WW, W, w_table_used_size, 1));
-            mpi_montmul(&W[x_index], &WW, N, mm, &T);
-        }
-    }
+    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
 
     /*
-     * W[x_index] = A^E * R * R^-1 mod N = A^E mod N
+     * Compensate for negative A (and correct at the end).
      */
-    mpi_montred(&W[x_index], N, mm, &T);
-
-    if (neg && E->n != 0 && (E->p[0] & 1) != 0) {
-        W[x_index].s = -1;
-        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&W[x_index], N, &W[x_index]));
-    }
+    X->s = 1;
 
     /*
-     * Load the result in the output variable.
+     * Make sure that A has exactly as many limbs as N.
      */
-    MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &W[x_index]));
+    if (mbedtls_mpi_cmp_mpi(X, N) >= 0) {
+        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(X, X, N));
+    }
+    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, N->n));
+
+    /*
+     * Allocate working memory for mbedtls_mpi_core_exp_mod()
+     */
+    MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T,
+                                     mbedtls_mpi_core_exp_mod_working_limbs(N->n, E_core.n)));
+
+    /*
+     * Convert to and from Montgomery around mbedtls_mpi_core_exp_mod().
+     */
+    mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init(N->p);
+    mbedtls_mpi_core_to_mont_rep(X->p, X->p, N->p, N->n, mm, RR.p, T.p);
+    mbedtls_mpi_core_exp_mod(X->p, X->p, N->p, N->n, E_core.p, E_core.n, RR.p,
+                             T.p);
+    mbedtls_mpi_core_from_mont_rep(X->p, X->p, N->p, N->n, mm, T.p);
+
+    /*
+     * Correct for negative A.
+     */
+    if (A->s == -1 && (E_core.p[0] & 1) != 0) {
+        X->s = -1;
+        MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, N, X));
+    }
 
 cleanup:
 
-    /* The first bit of the sliding window is always 1 and therefore the first
-     * half of the table was unused. */
-    for (i = w_table_used_size/2; i < w_table_used_size; i++) {
-        mbedtls_mpi_free(&W[i]);
-    }
-
-    mbedtls_mpi_free(&W[x_index]);
-    mbedtls_mpi_free(&W[1]);
     mbedtls_mpi_free(&T);
-    mbedtls_mpi_free(&Apos);
-    mbedtls_mpi_free(&WW);
 
     if (prec_RR == NULL || prec_RR->p == NULL) {
         mbedtls_mpi_free(&RR);
     }
 
+    if (E->n == 0) {
+        mbedtls_mpi_free(&E_core);
+    }
+
     return ret;
 }