#include <limits.h>
#include <assert.h>
#include <stdlib.h>
+#include <sys/param.h>
#include "mbedtls/bignum.h"
#include "rom/bigint.h"
#include "soc/hwcrypto_reg.h"
#include "freertos/task.h"
#include "freertos/semphr.h"
+/* Some implementation notes:
+ *
+ * - Naming convention x_words, y_words, z_words for number of words (limbs) used in a particular
+ * bignum. This number may be less than the size of the bignum
+ *
+ * - Naming convention hw_words for the hardware length of the operation. This number is always
+ * rounded up to a 512 bit multiple, and may be larger than any of the numbers involved in the
+ * calculation.
+ *
+ * - Timing behaviour of these functions will depend on the length of the inputs. This is fundamentally
+ * the same constraint as the software mbedTLS implementations, and relies on the same
+ * countermeasures (exponent blinding, etc) which are used in mbedTLS.
+ */
+
static const __attribute__((unused)) char *TAG = "bignum";
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
_lock_release(&mpi_lock);
}
-/* Number of words used to hold 'mpi', rounded up to nearest
- 16 words (512 bits) to match hardware support.
-
- Note that mpi->n (size of memory buffer) may be higher than this
- number, if the high bits are mostly zeroes.
+/* Convert bit count to word count
+ */
+static inline size_t bits_to_words(size_t bits)
+{
+ return (bits + 31) / 32;
+}
- This implementation may cause the caller to leak a small amount of
- timing information when an operation is performed (length of a
- given mpi value, rounded to nearest 512 bits), but not all mbedTLS
- RSA operations succeed if we use mpi->N as-is (buffers are too long).
+/* Round up number of words to nearest
+ 512 bit (16 word) block count.
*/
-static inline size_t hardware_words_needed(const mbedtls_mpi *mpi)
+static inline size_t hardware_words(size_t words)
{
- size_t res = 1;
- for(size_t i = 0; i < mpi->n; i++) {
- if( mpi->p[i] != 0 ) {
- res = i + 1;
- }
- }
- res = (res + 0xF) & ~0xF;
- return res;
+ return (words + 0xF) & ~0xF;
}
-/* Convert number of bits to number of words, rounded up to nearest
- 512 bit (16 word) block count.
+/* Number of words used to hold 'mpi'.
+
+ Equivalent of bits_to_words(mbedtls_mpi_bitlen(mpi)), but uses less cycles if the
+ exact bit count is not needed.
+
+ Note that mpi->n (size of memory buffer) may be higher than this
+ number, if the high bits are mostly zeroes.
*/
-static inline size_t bits_to_hardware_words(size_t num_bits)
+static inline size_t word_length(const mbedtls_mpi *mpi)
{
- return ((num_bits + 511) / 512) * 16;
+ for(size_t i = mpi->n; i > 0; i--) {
+ if( mpi->p[i - 1] != 0 ) {
+ return i;
+ }
+ }
+ return 0;
}
/* Copy mbedTLS MPI bignum 'mpi' to hardware memory block at 'mem_base'.
- If num_words is higher than the number of words in the bignum then
+ If hw_words is higher than the number of words in the bignum then
these additional words will be zeroed in the memory buffer.
- As this function only writes to DPORT memory, no DPORT_STALL_OTHER_CPU_START()
- is required.
*/
-static inline void mpi_to_mem_block(uint32_t mem_base, const mbedtls_mpi *mpi, size_t num_words)
+static inline void mpi_to_mem_block(uint32_t mem_base, const mbedtls_mpi *mpi, size_t hw_words)
{
uint32_t *pbase = (uint32_t *)mem_base;
- uint32_t copy_words = num_words < mpi->n ? num_words : mpi->n;
+ uint32_t copy_words = hw_words < mpi->n ? hw_words : mpi->n;
/* Copy MPI data to memory block registers */
for (int i = 0; i < copy_words; i++) {
}
/* Zero any remaining memory block data */
- for (int i = copy_words; i < num_words; i++) {
+ for (int i = copy_words; i < hw_words; i++) {
pbase[i] = 0;
}
Reads num_words words from block.
- Can return a failure result if fails to grow the MPI result.
-
- Cannot be called inside DPORT_STALL_OTHER_CPU_START() (as may allocate memory).
+ Bignum 'x' should already be grown to at least num_words by caller (can be done while
+ calculation is in progress, to save some cycles)
*/
-static inline int mem_block_to_mpi(mbedtls_mpi *x, uint32_t mem_base, int num_words)
+static inline void mem_block_to_mpi(mbedtls_mpi *x, uint32_t mem_base, int num_words)
{
- int ret = 0;
-
- MBEDTLS_MPI_CHK( mbedtls_mpi_grow(x, num_words) );
+ assert(x->n >= num_words);
/* Copy data from memory block registers */
esp_dport_access_read_buffer(x->p, mem_base, num_words);
+
/* Zero any remaining limbs in the bignum, if the buffer is bigger
than num_words */
for(size_t i = num_words; i < x->n; i++) {
x->p[i] = 0;
}
-
- asm volatile ("memw");
- cleanup:
- return ret;
}
/* Begin an RSA operation. op_reg specifies which 'START' register
to write to.
-
- Because the only DPORT operations here are writes,
- does not need protecting via DPORT_STALL_OTHER_CPU_START();
*/
static inline void start_op(uint32_t op_reg)
{
}
/* Wait for an RSA operation to complete.
-
- This should NOT be called inside a DPORT_STALL_OTHER_CPU_START(), as it will stall the other CPU for an unacceptably long
- period (and - depending on config - may require interrupts enabled).
*/
static inline void wait_op_complete(uint32_t op_reg)
{
}
/* Sub-stages of modulo multiplication/exponentiation operations */
-inline static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words);
+inline static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t hw_words, size_t z_words);
/* Z = (X * Y) mod M
int esp_mpi_mul_mpi_mod(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M)
{
int ret;
- size_t num_words = hardware_words_needed(M);
+ size_t x_bits = mbedtls_mpi_bitlen(X);
+ size_t y_bits = mbedtls_mpi_bitlen(Y);
+ size_t m_bits = mbedtls_mpi_bitlen(M);
+ size_t z_bits = MIN(m_bits, x_bits + y_bits);
+ size_t x_words = bits_to_words(x_bits);
+ size_t y_words = bits_to_words(y_bits);
+ size_t m_words = bits_to_words(m_bits);
+ size_t z_words = bits_to_words(z_bits);
+ size_t hw_words = hardware_words(MAX(x_words, MAX(y_words, m_words))); /* longest operand */
mbedtls_mpi Rinv;
mbedtls_mpi_uint Mprime;
/* Calculate and load the first stage montgomery multiplication */
mbedtls_mpi_init(&Rinv);
- MBEDTLS_MPI_CHK(calculate_rinv(&Rinv, M, num_words));
+ MBEDTLS_MPI_CHK(calculate_rinv(&Rinv, M, hw_words));
Mprime = modular_inverse(M);
esp_mpi_acquire_hardware();
- /* (As the following are all writes to DPORT memory, no DPORT_STALL_OTHER_CPU_START is required.) */
-
/* Load M, X, Rinv, Mprime (Mprime is mod 2^32) */
- mpi_to_mem_block(RSA_MEM_M_BLOCK_BASE, M, num_words);
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
- mpi_to_mem_block(RSA_MEM_RB_BLOCK_BASE, &Rinv, num_words);
+ mpi_to_mem_block(RSA_MEM_M_BLOCK_BASE, M, hw_words);
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, hw_words);
+ mpi_to_mem_block(RSA_MEM_RB_BLOCK_BASE, &Rinv, hw_words);
DPORT_REG_WRITE(RSA_M_DASH_REG, (uint32_t)Mprime);
/* "mode" register loaded with number of 512-bit blocks, minus 1 */
- DPORT_REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
+ DPORT_REG_WRITE(RSA_MULT_MODE_REG, (hw_words / 16) - 1);
/* Execute first stage montgomery multiplication */
start_op(RSA_MULT_START_REG);
wait_op_complete(RSA_MULT_START_REG);
/* execute second stage */
- ret = modular_multiply_finish(Z, X, Y, num_words);
+ ret = modular_multiply_finish(Z, X, Y, hw_words, z_words);
esp_mpi_release_hardware();
int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi* Y, const mbedtls_mpi* M, mbedtls_mpi* _Rinv )
{
int ret = 0;
- size_t z_words = hardware_words_needed(Z);
- size_t x_words = hardware_words_needed(X);
- size_t y_words = hardware_words_needed(Y);
- size_t m_words = hardware_words_needed(M);
- size_t num_words;
-
- mbedtls_mpi Rinv_new; /* used if _Rinv == NULL */
- mbedtls_mpi *Rinv; /* points to _Rinv (if not NULL) othwerwise &RR_new */
- mbedtls_mpi_uint Mprime;
+ size_t x_words = word_length(X);
+ size_t y_words = word_length(Y);
+ size_t m_words = word_length(M);
/* "all numbers must be the same length", so choose longest number
as cardinal length of operation...
*/
- num_words = z_words;
- if (x_words > num_words) {
- num_words = x_words;
- }
- if (y_words > num_words) {
- num_words = y_words;
- }
- if (m_words > num_words) {
- num_words = m_words;
- }
+ size_t hw_words = hardware_words(MAX(m_words, MAX(x_words, y_words)));
+
+ mbedtls_mpi Rinv_new; /* used if _Rinv == NULL */
+ mbedtls_mpi *Rinv; /* points to _Rinv (if not NULL) othwerwise &RR_new */
+ mbedtls_mpi_uint Mprime;
- if (num_words * 32 > 4096) {
+ if (hw_words * 32 > 4096) {
return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
Rinv = _Rinv;
}
if (Rinv->p == NULL) {
- MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, num_words));
+ MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, hw_words));
}
Mprime = modular_inverse(M);
esp_mpi_acquire_hardware();
- /* (As the following are all writes to DPORT memory, no DPORT_STALL_OTHER_CPU_START is required.) */
-
/* "mode" register loaded with number of 512-bit blocks, minus 1 */
- DPORT_REG_WRITE(RSA_MODEXP_MODE_REG, (num_words / 16) - 1);
+ DPORT_REG_WRITE(RSA_MODEXP_MODE_REG, (hw_words / 16) - 1);
/* Load M, X, Rinv, M-prime (M-prime is mod 2^32) */
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
- mpi_to_mem_block(RSA_MEM_Y_BLOCK_BASE, Y, num_words);
- mpi_to_mem_block(RSA_MEM_M_BLOCK_BASE, M, num_words);
- mpi_to_mem_block(RSA_MEM_RB_BLOCK_BASE, Rinv, num_words);
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, hw_words);
+ mpi_to_mem_block(RSA_MEM_Y_BLOCK_BASE, Y, hw_words);
+ mpi_to_mem_block(RSA_MEM_M_BLOCK_BASE, M, hw_words);
+ mpi_to_mem_block(RSA_MEM_RB_BLOCK_BASE, Rinv, hw_words);
DPORT_REG_WRITE(RSA_M_DASH_REG, Mprime);
start_op(RSA_START_MODEXP_REG);
+ /* X ^ Y may actually be shorter than M, but unlikely when used for crypto */
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, m_words) );
+
wait_op_complete(RSA_START_MODEXP_REG);
- ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, num_words);
+ mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, m_words);
esp_mpi_release_hardware();
cleanup:
#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
/* Second & final step of a modular multiply - load second multiplication
- * factor Y, run the multiply, read back the result into Z.
+ * factor Y, run the operation (modular inverse), read back the result
+ * into Z.
*
* Called from both mbedtls_mpi_exp_mod and mbedtls_mpi_mod_mpi.
*
* @param Z result value
* @param X first multiplication factor (used to set sign of result).
* @param Y second multiplication factor.
- * @param num_words size of modulo operation, in words (limbs).
- * Should already be rounded up to a multiple of 16 words (512 bits) & range checked.
+ * @param hw_words Size of the hardware operation, in words
+ * @param z_words Size of the expected result, in words (may be less than hw_words).
+ * Z will be grown to at least this length.
*
* Caller must have already called esp_mpi_acquire_hardware().
*/
-static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words)
+static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t hw_words, size_t z_words)
{
int ret = 0;
/* Load Y to X input memory block, rerun */
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, Y, num_words);
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, Y, hw_words);
start_op(RSA_MULT_START_REG);
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, z_words) );
+
wait_op_complete(RSA_MULT_START_REG);
- /* Read result into Z */
- ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, num_words);
+ mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, z_words);
Z->s = X->s * Y->s;
+ cleanup:
return ret;
}
#if defined(MBEDTLS_MPI_MUL_MPI_ALT) /* MBEDTLS_MPI_MUL_MPI_ALT */
-static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words);
-static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t Y_bits, size_t words_result);
+static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words);
+static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t Y_bits, size_t z_words);
/* Z = X * Y */
int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
int ret = 0;
- size_t bits_x, bits_y, words_x, words_y, words_mult, words_z;
-
- /* Count words needed for X & Y in hardware */
- bits_x = mbedtls_mpi_bitlen(X);
- bits_y = mbedtls_mpi_bitlen(Y);
- /* Convert bit counts to words, rounded up to 512-bit
- (16 word) blocks */
- words_x = bits_to_hardware_words(bits_x);
- words_y = bits_to_hardware_words(bits_y);
+ size_t x_bits = mbedtls_mpi_bitlen(X);
+ size_t y_bits = mbedtls_mpi_bitlen(Y);
+ size_t x_words = bits_to_words(x_bits);
+ size_t y_words = bits_to_words(y_bits);
+ size_t z_words = bits_to_words(x_bits + y_bits);
+ size_t hw_words = hardware_words(MAX(x_words, y_words)); // length of one operand in hardware
/* Short-circuit eval if either argument is 0 or 1.
argument will sometimes call in here when one
argument is too large for the hardware unit, but the other
argument is zero or one.
-
- This leaks some timing information, although overall there is a
- lot less timing variation than a software MPI approach.
*/
- if (bits_x == 0 || bits_y == 0) {
+ if (x_bits == 0 || y_bits == 0) {
mbedtls_mpi_lset(Z, 0);
return 0;
}
- if (bits_x == 1) {
+ if (x_bits == 1) {
ret = mbedtls_mpi_copy(Z, Y);
Z->s *= X->s;
return ret;
}
- if (bits_y == 1) {
+ if (y_bits == 1) {
ret = mbedtls_mpi_copy(Z, X);
Z->s *= Y->s;
return ret;
}
- words_mult = (words_x > words_y ? words_x : words_y);
-
- /* Result Z has to have room for double the larger factor */
- words_z = words_mult * 2;
-
-
/* If either factor is over 2048 bits, we can't use the standard hardware multiplier
(it assumes result is double longest factor, and result is max 4096 bits.)
multiplication doesn't have the same restriction, so result is simply the
number of bits in X plus number of bits in in Y.)
*/
- if (words_mult * 32 > 2048) {
- /* Calculate new length of Z */
- words_z = bits_to_hardware_words(bits_x + bits_y);
- if (words_z * 32 <= 4096) {
+ if (hw_words * 32 > 2048) {
+ if (z_words * 32 <= 4096) {
/* Note: it's possible to use mpi_mult_mpi_overlong
for this case as well, but it's very slightly
slower and requires a memory allocation.
*/
- return mpi_mult_mpi_failover_mod_mult(Z, X, Y, words_z);
+ return mpi_mult_mpi_failover_mod_mult(Z, X, Y, z_words);
} else {
/* Still too long for the hardware unit... */
- if(bits_y > bits_x) {
- return mpi_mult_mpi_overlong(Z, X, Y, bits_y, words_z);
+ if(y_words > x_words) {
+ return mpi_mult_mpi_overlong(Z, X, Y, y_words, z_words);
} else {
- return mpi_mult_mpi_overlong(Z, Y, X, bits_x, words_z);
+ return mpi_mult_mpi_overlong(Z, Y, X, x_words, z_words);
}
}
}
esp_mpi_acquire_hardware();
/* Copy X (right-extended) & Y (left-extended) to memory block */
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, words_mult);
- mpi_to_mem_block(RSA_MEM_Z_BLOCK_BASE + words_mult * 4, Y, words_mult);
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, hw_words);
+ mpi_to_mem_block(RSA_MEM_Z_BLOCK_BASE + hw_words * 4, Y, hw_words);
/* NB: as Y is left-extended, we don't zero the bottom words_mult words of Y block.
This is OK for now because zeroing is done by hardware when we do esp_mpi_acquire_hardware().
*/
/* "mode" register loaded with number of 512-bit blocks in result,
plus 7 (for range 9-12). (this is ((N~ / 32) - 1) + 8))
*/
- DPORT_REG_WRITE(RSA_MULT_MODE_REG, (words_z / 16) + 7);
+ DPORT_REG_WRITE(RSA_MULT_MODE_REG, ((hw_words * 2) / 16) + 7);
start_op(RSA_MULT_START_REG);
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow(Z, z_words) );
+
wait_op_complete(RSA_MULT_START_REG);
/* Read back the result */
- ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, words_z);
+ mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, z_words);
Z->s = X->s * Y->s;
+ cleanup:
esp_mpi_release_hardware();
return ret;
multiplication to calculate an mbedtls_mpi_mult_mpi result where either
A or B are >2048 bits so can't use the standard multiplication method.
- Result (A bits + B bits) must still be less than 4096 bits.
+ Result (z_words, based on A bits + B bits) must still be less than 4096 bits.
This case is simpler than the general case modulo multiply of
esp_mpi_mul_mpi_mod() because we can control the other arguments:
(See RSA Accelerator section in Technical Reference for more about Mprime, Rinv)
*/
-static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words)
+static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t z_words)
{
int ret = 0;
+ size_t hw_words = hardware_words(z_words);
/* Load coefficients to hardware */
esp_mpi_acquire_hardware();
/* M = 2^num_words - 1, so block is entirely FF */
- for(int i = 0; i < num_words; i++) {
+ for(int i = 0; i < hw_words; i++) {
DPORT_REG_WRITE(RSA_MEM_M_BLOCK_BASE + i * 4, UINT32_MAX);
}
/* Mprime = 1 */
DPORT_REG_WRITE(RSA_M_DASH_REG, 1);
/* "mode" register loaded with number of 512-bit blocks, minus 1 */
- DPORT_REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
+ DPORT_REG_WRITE(RSA_MULT_MODE_REG, (hw_words / 16) - 1);
/* Load X */
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, hw_words);
/* Rinv = 1 */
DPORT_REG_WRITE(RSA_MEM_RB_BLOCK_BASE, 1);
- for(int i = 1; i < num_words; i++) {
+ for(int i = 1; i < hw_words; i++) {
DPORT_REG_WRITE(RSA_MEM_RB_BLOCK_BASE + i * 4, 0);
}
wait_op_complete(RSA_MULT_START_REG);
/* finish the modular multiplication */
- ret = modular_multiply_finish(Z, X, Y, num_words);
+ ret = modular_multiply_finish(Z, X, Y, hw_words, z_words);
esp_mpi_release_hardware();
Note that this function may recurse multiple times, if both X & Y
are too long for the hardware multiplication unit.
*/
-static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t bits_y, size_t words_result)
+static int mpi_mult_mpi_overlong(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t y_words, size_t z_words)
{
int ret = 0;
mbedtls_mpi Ztemp;
- const size_t limbs_y = (bits_y + biL - 1) / biL;
/* Rather than slicing in two on bits we slice on limbs (32 bit words) */
- const size_t limbs_slice = limbs_y / 2;
+ const size_t words_slice = y_words / 2;
/* Yp holds lower bits of Y (declared to reuse Y's array contents to save on copying) */
const mbedtls_mpi Yp = {
.p = Y->p,
- .n = limbs_slice,
+ .n = words_slice,
.s = Y->s
};
/* Ypp holds upper bits of Y, right shifted (also reuses Y's array contents) */
const mbedtls_mpi Ypp = {
- .p = Y->p + limbs_slice,
- .n = limbs_y - limbs_slice,
+ .p = Y->p + words_slice,
+ .n = y_words - words_slice,
.s = Y->s
};
mbedtls_mpi_init(&Ztemp);
/* Grow Z to result size early, avoid interim allocations */
- mbedtls_mpi_grow(Z, words_result);
+ mbedtls_mpi_grow(Z, z_words);
/* Get result Ztemp = Yp * X (need temporary variable Ztemp) */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(&Ztemp, X, &Yp) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi(Z, X, &Ypp) );
/* Z = Z << b */
- MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l(Z, limbs_slice * biL) );
+ MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l(Z, words_slice * 32) );
/* Z += Ztemp */
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi(Z, Z, &Ztemp) );
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