Merge pull request #8831 from yanesca/switch_to_new_exp
Use mpi_core_exp_mod in bignum
diff --git a/ChangeLog.d/use_exp_mod_core.txt b/ChangeLog.d/use_exp_mod_core.txt
new file mode 100644
index 0000000..8f7193a
--- /dev/null
+++ b/ChangeLog.d/use_exp_mod_core.txt
@@ -0,0 +1,6 @@
+Changes
+ * mbedtls_mpi_exp_mod and code that uses it, notably RSA and DHM operations,
+ have changed their speed/memory compromise as part of a proactive security
+ improvement. The new default value of MBEDTLS_MPI_WINDOW_SIZE roughly
+ preserves the current speed, at the expense of increasing memory
+ consumption.
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 931e06d..71d7b97 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -51,15 +51,15 @@
#if !defined(MBEDTLS_MPI_WINDOW_SIZE)
/*
- * Maximum window size used for modular exponentiation. Default: 2
+ * Maximum window size used for modular exponentiation. Default: 3
* Minimum value: 1. Maximum value: 6.
*
* Result is an array of ( 2 ** MBEDTLS_MPI_WINDOW_SIZE ) MPIs used
- * for the sliding window calculation. (So 64 by default)
+ * for the sliding window calculation. (So 8 by default)
*
* Reduction in size, reduces speed.
*/
-#define MBEDTLS_MPI_WINDOW_SIZE 2 /**< Maximum window size used. */
+#define MBEDTLS_MPI_WINDOW_SIZE 3 /**< Maximum window size used. */
#endif /* !MBEDTLS_MPI_WINDOW_SIZE */
#if !defined(MBEDTLS_MPI_MAX_SIZE)
diff --git a/library/bignum.c b/library/bignum.c
index d3d72ab..eecdf1e 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -37,6 +37,19 @@
#include "mbedtls/platform.h"
+
+
+/*
+ * Conditionally select an MPI sign in constant time.
+ * (MPI sign is the field s in mbedtls_mpi. It is unsigned short and only 1 and -1 are valid
+ * values.)
+ */
+static inline signed short mbedtls_ct_mpi_sign_if(mbedtls_ct_condition_t cond,
+ signed short sign1, signed short sign2)
+{
+ return (signed short) mbedtls_ct_uint_if(cond, sign1 + 1, sign2 + 1) - 1;
+}
+
/*
* Compare signed values in constant time
*/
@@ -112,7 +125,7 @@
{
mbedtls_ct_condition_t do_assign = mbedtls_ct_bool(assign);
- X->s = (int) mbedtls_ct_uint_if(do_assign, Y->s, X->s);
+ X->s = mbedtls_ct_mpi_sign_if(do_assign, Y->s, X->s);
mbedtls_mpi_core_cond_assign(X->p, Y->p, Y->n, do_assign);
@@ -149,8 +162,8 @@
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n));
s = X->s;
- X->s = (int) mbedtls_ct_uint_if(do_swap, Y->s, X->s);
- Y->s = (int) mbedtls_ct_uint_if(do_swap, s, Y->s);
+ X->s = mbedtls_ct_mpi_sign_if(do_swap, Y->s, X->s);
+ Y->s = mbedtls_ct_mpi_sign_if(do_swap, s, Y->s);
mbedtls_mpi_core_cond_swap(X->p, Y->p, X->n, do_swap);
@@ -288,8 +301,7 @@
* This function is not constant-time. Leading zeros in Y may be removed.
*
* Ensure that X does not shrink. This is not guaranteed by the public API,
- * but some code in the bignum module relies on this property, for example
- * in mbedtls_mpi_exp_mod().
+ * but some code in the bignum module might still rely on this property.
*/
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
{
@@ -1598,98 +1610,11 @@
return 0;
}
-static void mpi_montg_init(mbedtls_mpi_uint *mm, const mbedtls_mpi *N)
-{
- *mm = mbedtls_mpi_core_montmul_init(N->p);
-}
-
-/** 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 modulus. \p 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 1
- * (T->n >= 2 * N->n + 1).
- * Its initial content is unused and
- * its final content is indeterminate.
- * It does not get reallocated.
- */
-static void mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B,
- const mbedtls_mpi *N, mbedtls_mpi_uint mm,
- mbedtls_mpi *T)
-{
- mbedtls_mpi_core_montmul(A->p, A->p, B->p, B->n, N->p, N->n, mm, T->p);
-}
-
-/*
- * Montgomery reduction: A = A * R^-1 mod N
- *
- * See mpi_montmul() regarding constraints and guarantees on the parameters.
- */
-static void mpi_montred(mbedtls_mpi *A, const mbedtls_mpi *N,
- mbedtls_mpi_uint mm, mbedtls_mpi *T)
-{
- mbedtls_mpi_uint z = 1;
- mbedtls_mpi U;
- U.n = 1;
- U.s = 1;
- U.p = &z;
-
- mpi_montmul(A, &U, N, mm, T);
-}
-
-/**
- * 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_ct_uint_eq(i, idx)));
- }
-cleanup:
- return ret;
-}
-
-/*
- * Sliding-window exponentiation: X = A^E mod N (HAC 14.85)
- */
int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A,
const mbedtls_mpi *E, const mbedtls_mpi *N,
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;
if (mbedtls_mpi_cmp_int(N, 0) <= 0 || (N->p[0] & 1) == 0) {
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
@@ -1705,261 +1630,86 @@
}
/*
- * Init temps and window size
+ * Ensure that the exponent that we are passing to the core is not NULL.
*/
- 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;
+ if (E->n == 0) {
+ ret = mbedtls_mpi_lset(X, 1);
+ return ret;
}
-#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.
+ * Allocate working memory for mbedtls_mpi_core_exp_mod()
*/
- 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;
+ size_t T_limbs = mbedtls_mpi_core_exp_mod_working_limbs(N->n, E->n);
+ mbedtls_mpi_uint *T = (mbedtls_mpi_uint *) mbedtls_calloc(T_limbs, sizeof(mbedtls_mpi_uint));
+ if (T == NULL) {
+ return MBEDTLS_ERR_MPI_ALLOC_FAILED;
}
+ mbedtls_mpi RR;
+ mbedtls_mpi_init(&RR);
+
/*
* 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));
+ *prec_RR = RR;
}
} else {
- memcpy(&RR, prec_RR, sizeof(mbedtls_mpi));
+ MBEDTLS_MPI_CHK(mbedtls_mpi_grow(prec_RR, N->n));
+ RR = *prec_RR;
}
/*
- * W[1] = A * R^2 * R^-1 mod N = A * R mod N
+ * To preserve constness we need to make a copy of A. Using X for this to
+ * save memory.
*/
- 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));
- } 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);
+ MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
/*
- * W[x_index] = R^2 * R^-1 mod N = R mod N
+ * Compensate for negative A (and correct at the end).
*/
- 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;
- }
- }
+ X->s = 1;
/*
- * process the remaining bits
+ * Make sure that X is in a form that is safe for consumption by
+ * the core functions.
+ *
+ * - The core functions will not touch the limbs of X above N->n. The
+ * result will be correct if those limbs are 0, which the mod call
+ * ensures.
+ * - Also, X must have at least as many limbs as N for the calls to the
+ * core functions.
*/
- 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);
- }
+ 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));
/*
- * W[x_index] = A^E * R * R^-1 mod N = A^E mod N
+ * Convert to and from Montgomery around mbedtls_mpi_core_exp_mod().
*/
- 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]));
- }
+ 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);
+ mbedtls_mpi_core_exp_mod(X->p, X->p, N->p, N->n, E->p, E->n, RR.p, T);
+ mbedtls_mpi_core_from_mont_rep(X->p, X->p, N->p, N->n, mm, T);
/*
- * Load the result in the output variable.
+ * Correct for negative A.
*/
- MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &W[x_index]));
+ if (A->s == -1 && (E->p[0] & 1) != 0) {
+ mbedtls_ct_condition_t is_x_non_zero = mbedtls_mpi_core_check_zero_ct(X->p, X->n);
+ X->s = mbedtls_ct_mpi_sign_if(is_x_non_zero, -1, 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);
+ mbedtls_mpi_zeroize_and_free(T, T_limbs);
if (prec_RR == NULL || prec_RR->p == NULL) {
mbedtls_mpi_free(&RR);
diff --git a/library/bignum_core.c b/library/bignum_core.c
index dfed60d..1a3e0b9 100644
--- a/library/bignum_core.c
+++ b/library/bignum_core.c
@@ -856,16 +856,17 @@
return c;
}
-mbedtls_mpi_uint mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
- size_t limbs)
+mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
+ size_t limbs)
{
+ volatile const mbedtls_mpi_uint *force_read_A = A;
mbedtls_mpi_uint bits = 0;
for (size_t i = 0; i < limbs; i++) {
- bits |= A[i];
+ bits |= force_read_A[i];
}
- return bits;
+ return mbedtls_ct_bool(bits);
}
void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
diff --git a/library/bignum_core.h b/library/bignum_core.h
index b56be0a..92c8d47 100644
--- a/library/bignum_core.h
+++ b/library/bignum_core.h
@@ -662,11 +662,11 @@
* \param[in] A The MPI to test.
* \param limbs Number of limbs in \p A.
*
- * \return 0 if `A == 0`
- * non-0 (may be any value) if `A != 0`.
+ * \return MBEDTLS_CT_FALSE if `A == 0`
+ * MBEDTLS_CT_TRUE if `A != 0`.
*/
-mbedtls_mpi_uint mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
- size_t limbs);
+mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
+ size_t limbs);
/**
* \brief Returns the number of limbs of working memory required for
diff --git a/tests/suites/test_suite_bignum.function b/tests/suites/test_suite_bignum.function
index 50be2d2..f3a64e1 100644
--- a/tests/suites/test_suite_bignum.function
+++ b/tests/suites/test_suite_bignum.function
@@ -966,6 +966,45 @@
/* END_CASE */
/* BEGIN_CASE */
+void mpi_exp_mod_min_RR(char *input_A, char *input_E,
+ char *input_N, char *input_X,
+ int exp_result)
+{
+ mbedtls_mpi A, E, N, RR, Z, X;
+ int res;
+ mbedtls_mpi_init(&A); mbedtls_mpi_init(&E); mbedtls_mpi_init(&N);
+ mbedtls_mpi_init(&RR); mbedtls_mpi_init(&Z); mbedtls_mpi_init(&X);
+
+ TEST_EQUAL(mbedtls_test_read_mpi(&A, input_A), 0);
+ TEST_EQUAL(mbedtls_test_read_mpi(&E, input_E), 0);
+ TEST_EQUAL(mbedtls_test_read_mpi(&N, input_N), 0);
+ TEST_EQUAL(mbedtls_test_read_mpi(&X, input_X), 0);
+
+ TEST_EQUAL(mbedtls_mpi_core_get_mont_r2_unsafe(&RR, &N), 0);
+ TEST_EQUAL(mbedtls_mpi_shrink(&RR, 0), 0);
+ /* The objective of this test is to check that exp_mod defends
+ * against a smaller RR. */
+ TEST_LE_U(RR.n, N.n - 1);
+
+ res = mbedtls_mpi_exp_mod(&Z, &A, &E, &N, &RR);
+ /* We know that exp_mod internally needs RR to be as large as N.
+ * Validate that it is the case now, otherwise there was probably
+ * a buffer overread. */
+ TEST_EQUAL(RR.n, N.n);
+
+ TEST_EQUAL(res, exp_result);
+ if (res == 0) {
+ TEST_EQUAL(sign_is_valid(&Z), 1);
+ TEST_EQUAL(mbedtls_mpi_cmp_mpi(&Z, &X), 0);
+ }
+
+exit:
+ mbedtls_mpi_free(&A); mbedtls_mpi_free(&E); mbedtls_mpi_free(&N);
+ mbedtls_mpi_free(&RR); mbedtls_mpi_free(&Z); mbedtls_mpi_free(&X);
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
void mpi_exp_mod(char *input_A, char *input_E,
char *input_N, char *input_X,
int exp_result)
diff --git a/tests/suites/test_suite_bignum.misc.data b/tests/suites/test_suite_bignum.misc.data
index c53e42a..eb55dbe 100644
--- a/tests/suites/test_suite_bignum.misc.data
+++ b/tests/suites/test_suite_bignum.misc.data
@@ -1362,6 +1362,9 @@
Test mbedtls_mpi_exp_mod: 10 ^ 0 (1 limb) mod 9
mpi_exp_mod:"0a":"00":"09":"1":0
+Test mbedtls_mpi_exp_mod: -3 ^ 3 mod 27
+mpi_exp_mod:"-3":"3":"1b":"1b":0
+
Test mbedtls_mpi_exp_mod: MAX_SIZE exponent
mpi_exp_mod_size:2:MBEDTLS_MPI_MAX_SIZE:10:"":0
@@ -1391,6 +1394,14 @@
depends_on:MPI_MAX_BITS_LARGER_THAN_792
mpi_exp_mod:"-9f13012cd92aa72fb86ac8879d2fde4f7fd661aaae43a00971f081cc60ca277059d5c37e89652e2af2585d281d66ef6a9d38a117e9608e9e7574cd142dc55278838a2161dd56db9470d4c1da2d5df15a908ee2eb886aaa890f23be16de59386663a12f1afbb325431a3e835e3fd89b98b96a6f77382f458ef9a37e1f84a03045c8676ab55291a94c2228ea15448ee96b626b998":"40a54d1b9e86789f06d9607fb158672d64867665c73ee9abb545fc7a785634b354c7bae5b962ce8040cf45f2c1f3d3659b2ee5ede17534c8fc2ec85c815e8df1fe7048d12c90ee31b88a68a081f17f0d8ce5f4030521e9400083bcea73a429031d4ca7949c2000d597088e0c39a6014d8bf962b73bb2e8083bd0390a4e00b9b3":"eeaf0ab9adb38dd69c33f80afa8fc5e86072618775ff3c0b9ea2314c9c256576d674df7496ea81d3383b4813d692c6e0e0d5d8e250b98be48e495c1d6089dad15dc7d7b46154d6b6ce8ef4ad69b15d4982559b297bcf1885c529f566660e57ec68edbc3c05726cc02fd4cbf4976eaa9afd5138fe8376435b9fc61d2fc0eb06e3":"21acc7199e1b90f9b4844ffe12c19f00ec548c5d32b21c647d48b6015d8eb9ec9db05b4f3d44db4227a2b5659c1a7cceb9d5fa8fa60376047953ce7397d90aaeb7465e14e820734f84aa52ad0fc66701bcbb991d57715806a11531268e1e83dd48288c72b424a6287e9ce4e5cc4db0dd67614aecc23b0124a5776d36e5c89483":0
+Test mbedtls_mpi_exp_mod (N.n=3, RR.n=1 on 32 bit)
+depends_on:MBEDTLS_HAVE_INT32
+mpi_exp_mod_min_RR:"10":"2":"10000000100000001":"100":0
+
+Test mbedtls_mpi_exp_mod (N.n=3, RR.n=1 on 64 bit)
+depends_on:MBEDTLS_HAVE_INT64
+mpi_exp_mod_min_RR:"10":"2":"100000000000000010000000000000001":"100":0
+
Base test GCD #1
mpi_gcd:"2b5":"261":"15"