#if defined(MBEDTLS_MPI_MUL_MPI_ALT) || defined(MBEDTLS_MPI_EXP_MOD_ALT)
-/* Constants from mbedTLS bignum.c */
-#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
-#define biL (ciL << 3) /* bits in limb */
-
static _lock_t mpi_lock;
-/* Temporary debugging function to print an MPI number to
- stdout. Happens to be in a format compatible with Python.
-*/
-void mbedtls_mpi_printf(const char *name, const mbedtls_mpi *X)
-{
- static char buf[1024];
- size_t n;
- memset(buf, 0, sizeof(buf));
- mbedtls_mpi_write_string(X, 16, buf, sizeof(buf)-1, &n);
- if(n) {
- ESP_LOGI(TAG, "%s = 0x%s", name, buf);
- } else {
- ESP_LOGI(TAG, "TOOLONG");
- }
-}
-
-/* Temporary debug function to dump a memory block's contents to stdout
- TODO remove
- */
-static void __attribute__((unused)) dump_memory_block(const char *label, uint32_t addr)
-{
- printf("Dumping %s @ %08x\n", label, addr);
- for(int i = 0; i < (4096 / 8); i += 4) {
- if(i % 32 == 0) {
- printf("\n %04x:", i);
- }
- printf("%08x ", REG_READ(addr + i));
- }
- printf("Done\n");
-}
-
/* At the moment these hardware locking functions aren't exposed publically
- for MPI. If you want to use the ROM bigint functions and co-exist with mbedTLS,
- please raise a feature request.
+ for MPI. If you want to use the ROM bigint functions and co-exist with mbedTLS, please raise a feature request.
*/
static void esp_mpi_acquire_hardware( void )
{
return res;
}
+/* Convert number of bits to number of words, rounded up to nearest
+ 512 bit (16 word) block count.
+*/
+static inline size_t bits_to_hardware_words(size_t num_bits)
+{
+ return ((num_bits + 511) / 512) * 16;
+}
+
/* 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
return ret;
}
-/* Given a & b, determine u & v such that
-
- gcd(a,b) = d = au - bv
-
- This is suitable for calculating values for montgomery multiplication:
-
- gcd(R, M) = R * Rinv - M * Mprime = 1
-
- Conditions which must be true:
- - argument 'a' (R) is a power of 2.
- - argument 'b' (M) is odd.
- Underlying algorithm comes from:
- http://www.hackersdelight.org/hdcodetxt/mont64.c.txt
- http://www.ucl.ac.uk/~ucahcjm/combopt/ext_gcd_python_programs.pdf
+/**
+ *
+ * There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1,
+ * where B^-1(B-1) mod N=1. Actually, only the least significant part of
+ * N' is needed, hence the definition N0'=N' mod b. We reproduce below the
+ * simple algorithm from an article by Dusse and Kaliski to efficiently
+ * find N0' from N0 and b
*/
-static void extended_binary_gcd(const mbedtls_mpi *a, const mbedtls_mpi *b,
- mbedtls_mpi *u, mbedtls_mpi *v)
+static mbedtls_mpi_uint modular_inverse(const mbedtls_mpi *M)
{
- mbedtls_mpi a_, ta;
-
- /* These checks degrade performance, TODO remove them... */
- assert(b->p[0] & 1);
- assert(mbedtls_mpi_bitlen(a) == mbedtls_mpi_lsb(a)+1);
- assert(mbedtls_mpi_cmp_mpi(a, b) > 0);
-
- mbedtls_mpi_lset(u, 1);
- mbedtls_mpi_lset(v, 0);
+ int i;
+ uint64_t t = 1;
+ uint64_t two_2_i_minus_1 = 2; /* 2^(i-1) */
+ uint64_t two_2_i = 4; /* 2^i */
+ uint64_t N = M->p[0];
- /* 'a' needs to be half its real value for this algorithm
- TODO see if we can halve the number in the caller to avoid
- allocating a bignum here.
- */
- mbedtls_mpi_init(&a_);
- mbedtls_mpi_copy(&a_, a);
- mbedtls_mpi_shift_r(&a_, 1);
+ for (i = 2; i <= 32; i++) {
+ if ((mbedtls_mpi_uint) N * t % two_2_i >= two_2_i_minus_1) {
+ t += two_2_i_minus_1;
+ }
- mbedtls_mpi_init(&ta);
- mbedtls_mpi_copy(&ta, &a_);
+ two_2_i_minus_1 <<= 1;
+ two_2_i <<= 1;
+ }
- //mbedtls_mpi_printf("a", &a_);
- //mbedtls_mpi_printf("b", b);
+ return (mbedtls_mpi_uint)(UINT32_MAX - t + 1);
+}
- /* Loop invariant:
- 2*ta = u*2*a - v*b.
+/* Calculate Rinv = RR^2 mod M, where:
+ *
+ * R = b^n where b = 2^32, n=num_words,
+ * R = 2^N (where N=num_bits)
+ * RR = R^2 = 2^(2*N) (where N=num_bits=num_words*32)
+ *
+ * This calculation is computationally expensive (mbedtls_mpi_mod_mpi)
+ * so caller should cache the result where possible.
+ *
+ * DO NOT call this function while holding esp_mpi_acquire_hardware().
+ *
+ */
+static int calculate_rinv(mbedtls_mpi *Rinv, const mbedtls_mpi *M, int num_words)
+{
+ int ret;
+ size_t num_bits = num_words * 32;
+ mbedtls_mpi RR;
+ mbedtls_mpi_init(&RR);
+ MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&RR, num_bits * 2, 1));
+ MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(Rinv, &RR, M));
- Loop until ta == 0
- */
- while (mbedtls_mpi_cmp_int(&ta, 0) != 0) {
- //mbedtls_mpi_printf("ta", &ta);
- //mbedtls_mpi_printf("u", u);
- //mbedtls_mpi_printf("v", v);
- //printf("2*ta == u*2*a - v*b\n");
-
- mbedtls_mpi_shift_r(&ta, 1);
- if (mbedtls_mpi_get_bit(u, 0) == 0) {
- // Remove common factor of 2 in u & v
- mbedtls_mpi_shift_r(u, 1);
- mbedtls_mpi_shift_r(v, 1);
- }
- else {
- /* u = (u + b) >> 1 */
- mbedtls_mpi_add_mpi(u, u, b);
- mbedtls_mpi_shift_r(u, 1);
- /* v = (v - a) >> 1 */
- mbedtls_mpi_shift_r(v, 1);
- mbedtls_mpi_add_mpi(v, v, &a_);
- }
- }
- mbedtls_mpi_free(&ta);
- mbedtls_mpi_free(&a_);
+ cleanup:
+ mbedtls_mpi_free(&RR);
+ return ret;
}
+
/* Execute RSA operation. op_reg specifies which 'START' register
to write to.
*/
}
/* Sub-stages of modulo multiplication/exponentiation operations */
-static int modular_op_prepare(const mbedtls_mpi *X, const mbedtls_mpi *M, size_t num_words);
inline static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words);
/* Z = (X * Y) mod M
Not an mbedTLS function
- */
+*/
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);
+ mbedtls_mpi Rinv;
+ mbedtls_mpi_uint Mprime;
/* Calculate and load the first stage montgomery multiplication */
- MBEDTLS_MPI_CHK( modular_op_prepare(X, M, num_words) );
+ mbedtls_mpi_init(&Rinv);
+ MBEDTLS_MPI_CHK(calculate_rinv(&Rinv, M, num_words));
+ Mprime = modular_inverse(M);
+
+ esp_mpi_acquire_hardware();
+
+ /* 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);
+ REG_WRITE(RSA_M_DASH_REG, (uint32_t)Mprime);
+
+ /* "mode" register loaded with number of 512-bit blocks, minus 1 */
+ REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
+ /* Execute first stage montgomery multiplication */
execute_op(RSA_MULT_START_REG);
+ /* execute second stage */
MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
esp_mpi_release_hardware();
cleanup:
+ mbedtls_mpi_free(&Rinv);
return ret;
}
/*
* Sliding-window exponentiation: Z = X^Y mod M (HAC 14.85)
+ *
+ * _Rinv is optional pre-calculated version of Rinv (via calculate_rinv()).
+ *
+ * (See RSA Accelerator section in Technical Reference for more about Mprime, Rinv)
+ *
*/
- #if 0
-int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi* Y, const mbedtls_mpi* M, mbedtls_mpi* _RR )
+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;
+ 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_printf("X",X);
- mbedtls_mpi_printf("Y",Y);
- mbedtls_mpi_printf("M",M);
+ mbedtls_mpi Rinv_new; /* used if _Rinv == NULL */
+ mbedtls_mpi *Rinv; /* points to _Rinv (if not NULL) othwerwise &RR_new */
+ mbedtls_mpi_uint Mprime;
/* "all numbers must be the same length", so choose longest number
as cardinal length of operation...
if (m_words > num_words) {
num_words = m_words;
}
- printf("num_words = %d # %d, %d, %d\n", num_words, x_words, y_words, m_words);
-
- /* TODO: _RR parameter currently ignored */
-
- ret = modular_op_prepare(X, M, num_words);
- if (ret != 0) {
- return ret;
- }
-
- mpi_to_mem_block(RSA_MEM_Y_BLOCK_BASE, Y, num_words);
-
- //dump_memory_block("X_BLOCK", RSA_MEM_X_BLOCK_BASE);
- //dump_memory_block("Y_BLOCK", RSA_MEM_Y_BLOCK_BASE);
- //dump_memory_block("M_BLOCK", RSA_MEM_M_BLOCK_BASE);
-
- REG_WRITE(RSA_MODEXP_MODE_REG, (num_words / 16) - 1);
-
- execute_op(RSA_START_MODEXP_REG);
-
- //dump_memory_block("Z_BLOCK", RSA_MEM_Z_BLOCK_BASE);
-
- /* TODO: only need to read m_words not num_words, provided result is correct... */
- ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, num_words);
-
- esp_mpi_release_hardware();
-
- mbedtls_mpi_printf("Z",Z);
- printf("print (Z == (X ** Y) %% M)\n");
-
- return ret;
-}
-
-#else
-
-/**
- * There is a need for the value of integer N' such that B^-1(B-1)-N^-1N'=1,
- * where B^-1(B-1) mod N=1. Actually, only the least significant part of
- * N' is needed, hence the definition N0'=N' mod b. We reproduce below the
- * simple algorithm from an article by Dusse and Kaliski to efficiently
- * find N0' from N0 and b
- */
-static mbedtls_mpi_uint modular_inverse(const mbedtls_mpi *M)
-{
- int i;
- uint64_t t = 1;
- uint64_t two_2_i_minus_1 = 2; /* 2^(i-1) */
- uint64_t two_2_i = 4; /* 2^i */
- uint64_t N = M->p[0];
-
- for (i = 2; i <= 32; i++) {
- if ((mbedtls_mpi_uint) N * t % two_2_i >= two_2_i_minus_1) {
- t += two_2_i_minus_1;
- }
- two_2_i_minus_1 <<= 1;
- two_2_i <<= 1;
+ if (num_words * 32 > 4096) {
+ return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
- return (mbedtls_mpi_uint)(UINT32_MAX - t + 1);
-}
-
-static int bignum_param_init(const mbedtls_mpi *M, mbedtls_mpi *_RR, mbedtls_mpi *r, mbedtls_mpi_uint *Mi, size_t num_words)
-{
- int ret = 0;
- size_t num_bits;
- mbedtls_mpi RR;
-
- /* Calculate number of bits */
- num_bits = num_words * 32;
- ESP_LOGI(TAG, "num_bits = %d\n", num_bits);
-
- /*
- * R = b^n where b = 2^32, n=num_words,
- * R = 2^N (where N=num_bits)
- * RR(R^2) = 2^(2*N) (where N=num_bits)
- *
- * r = RR(R^2) mod M
- *
- * Get the RR(RR == r) value from up level if RR and RR->p is not NULL
- */
- ESP_LOGI(TAG, "r = RR(R^2) mod M\n");
- if (_RR == NULL || _RR->p == NULL) {
- ESP_LOGI(TAG, "RR(R^2) = 2^(2*N) (where N=num_bits)\n");
- mbedtls_mpi_init(&RR);
- MBEDTLS_MPI_CHK(mbedtls_mpi_set_bit(&RR, num_bits * 2, 1));
- mbedtls_mpi_printf("RR", &RR);
-
- MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(r, &RR, M));
-
- if (_RR != NULL)
- memcpy(_RR, r, sizeof( mbedtls_mpi ) );
+ /* Determine RR pointer, either _RR for cached value
+ or local RR_new */
+ if (_Rinv == NULL) {
+ mbedtls_mpi_init(&Rinv_new);
+ Rinv = &Rinv_new;
} else {
- memcpy(r, _RR, sizeof( mbedtls_mpi ) );
+ Rinv = _Rinv;
}
- mbedtls_mpi_printf("r", r);
-
- *Mi = modular_inverse(M);
-
-cleanup:
- mbedtls_mpi_free(&RR);
-
- return ret;
-}
-
-static void bignum_param_deinit(mbedtls_mpi *_RR, mbedtls_mpi *r)
-{
- if (_RR == NULL || _RR->p == NULL)
- mbedtls_mpi_free(r);
-}
-
-/*
- * Sliding-window exponentiation: Z = X^Y mod M (HAC 14.85)
- */
-int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi* Y, const mbedtls_mpi* M, mbedtls_mpi* _RR )
-{
- 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 r;
- mbedtls_mpi_uint Mi = 0;
-
- /* "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 (Rinv->p == NULL) {
+ MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, num_words));
}
- if (m_words > num_words) {
- num_words = m_words;
- }
- ESP_LOGI(TAG, "num_words = %d # %d, %d, %d\n", num_words, x_words, y_words, m_words);
- if (num_words * 32 > 4096)
- return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
-
- mbedtls_mpi_init(&r);
- ret = bignum_param_init(M, _RR, &r, &Mi, num_words);
- if (ret != 0) {
- return ret;
- }
-
- mbedtls_mpi_printf("X",X);
- mbedtls_mpi_printf("Y",Y);
+ Mprime = modular_inverse(M);
esp_mpi_acquire_hardware();
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, &r, num_words);
- REG_WRITE(RSA_M_DASH_REG, Mi);
+ mpi_to_mem_block(RSA_MEM_RB_BLOCK_BASE, Rinv, num_words);
+ REG_WRITE(RSA_M_DASH_REG, Mprime);
execute_op(RSA_START_MODEXP_REG);
esp_mpi_release_hardware();
- mbedtls_mpi_printf("Z",Z);
- ESP_LOGI(TAG, "print (Z == (X ** Y) %% M)\n");
-
- bignum_param_deinit(_RR, &r);
+ cleanup:
+ if (_Rinv == NULL) {
+ mbedtls_mpi_free(&Rinv_new);
+ }
return ret;
}
-
-#endif
-
#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
-
-/* The common parts of modulo multiplication and modular sliding
- * window exponentiation:
- *
- * @param X first multiplication factor and/or base of exponent.
- * @param M modulo value for result
- * @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.
- *
- * Steps:
- * Calculate Rinv & Mprime based on M & num_words
- * Load all coefficients to memory
- * Set mode register
- *
- * @note This function calls esp_mpi_acquire_hardware. If successful,
- * returns 0 and it becomes the callers responsibility to call
- * esp_mpi_release_hardware(). If failure is returned, the caller does
- * not need to call esp_mpi_release_hardware().
- */
-static int modular_op_prepare(const mbedtls_mpi *X, const mbedtls_mpi *M, size_t num_words)
-{
- int ret = 0;
- mbedtls_mpi RR, Rinv, Mprime;
- size_t num_bits;
-
- /* Calculate number of bits */
- num_bits = num_words * 32;
-
- if(num_bits > 4096) {
- return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
- }
-
- /* Rinv & Mprime are calculated via extended binary gcd
- algorithm, see references on extended_binary_gcd() above.
- */
- mbedtls_mpi_init(&Rinv);
- mbedtls_mpi_init(&RR);
- mbedtls_mpi_init(&Mprime);
-
- mbedtls_mpi_set_bit(&RR, num_bits, 1); /* R = b^n where b = 2^32, n=num_words,
- ie R = 2^N (where N=num_bits) */
- /* calculate Rinv & Mprime */
- extended_binary_gcd(&RR, M, &Rinv, &Mprime);
-
- /* Block of debugging data, output suitable to paste into Python
- TODO remove
- */
- mbedtls_mpi_printf("RR", &RR);
- mbedtls_mpi_printf("M", M);
- mbedtls_mpi_printf("Rinv", &Rinv);
- mbedtls_mpi_printf("Mprime", &Mprime);
- printf("print (R * Rinv - M * Mprime == 1)\n");
- printf("print (Rinv == (R * R) %% M)\n");
-
- esp_mpi_acquire_hardware();
-
- /* Load M, X, Rinv, M-prime (M-prime 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);
- REG_WRITE(RSA_M_DASH_REG, Mprime.p[0]);
-
- /* "mode" register loaded with number of 512-bit blocks, minus 1 */
- REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
-
- mbedtls_mpi_free(&Rinv);
- mbedtls_mpi_free(&RR);
- mbedtls_mpi_free(&Mprime);
-
- return ret;
-}
-
/* Second & final step of a modular multiply - load second multiplication
* factor Y, run the multiply, read back the result into Z.
*
int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
int ret;
- size_t words_x, words_y, words_mult, words_z;
+ size_t bits_x, bits_y, words_x, words_y, words_mult, words_z;
/* Count words needed for X & Y in hardware */
- words_x = hardware_words_needed(X);
- words_y = hardware_words_needed(Y);
+ 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);
+
+ /* Short-circuit eval if either argument is 0 or 1.
+
+ This is needed as the mpi modular division
+ 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) {
+ mbedtls_mpi_lset(Z, 0);
+ return 0;
+ }
+ if (bits_x == 1) {
+ return mbedtls_mpi_copy(Z, Y);
+ }
+ if (bits_y == 1) {
+ return mbedtls_mpi_copy(Z, X);
+ }
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.)
*/
- //ESP_LOGE(TAG, "INFO: %d bit result (%d bits * %d bits)\n", words_z * 32, mbedtls_mpi_bitlen(X), mbedtls_mpi_bitlen(Y));
if (words_mult * 32 > 2048) {
/* Calculate new length of Z */
- words_z = words_x + words_y;
+ words_z = bits_to_hardware_words(bits_x + bits_y);
if (words_z * 32 > 4096) {
- ESP_LOGE(TAG, "ERROR: %d bit result (%d bits * %d bits) too large for hardware unit\n", words_z * 32, mbedtls_mpi_bitlen(X), mbedtls_mpi_bitlen(Y));
+ ESP_LOGE(TAG, "ERROR: %d bit result %d bits * %d bits too large for hardware unit\n", words_z * 32, bits_x, bits_y);
return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
else {
/* "mode" register loaded with number of 512-bit blocks in result,
plus 7 (for range 9-12). (this is ((N~ / 32) - 1) + 8))
- */
+ */
REG_WRITE(RSA_MULT_MODE_REG, (words_z / 16) + 7);
execute_op(RSA_MULT_START_REG);
}
/* Special-case of mbedtls_mpi_mult_mpi(), where we use hardware montgomery mod
- multiplication to solve the case where A or B are >2048 bits so
- can't use the standard multiplication method.
+ 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.
- This case is simpler than esp_mpi_mul_mpi_mod() as we control the arguments:
+ This case is simpler than the general case modulo multiply of
+ esp_mpi_mul_mpi_mod() because we can control the other arguments:
* Modulus is chosen with M=(2^num_bits - 1) (ie M=R-1), so output
- isn't actually modulo anything.
- * Therefore of of M' and Rinv are predictable as follows:
- M' = 1
- Rinv = 1
+ isn't actually modulo anything.
+ * Mprime and Rinv are therefore predictable as follows:
+ Mprime = 1
+ Rinv = 1
- (See RSA Accelerator section in Technical Reference *
- extended_binary_gcd() function above for more about M', Rinv)
+ (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)
- {
- int ret = 0;
+{
+ int ret = 0;
- /* Load coefficients to hardware */
- esp_mpi_acquire_hardware();
+ /* 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++) {
- REG_WRITE(RSA_MEM_M_BLOCK_BASE + i * 4, UINT32_MAX);
- }
- /* Mprime = 1 */
- REG_WRITE(RSA_M_DASH_REG, 1);
+ /* M = 2^num_words - 1, so block is entirely FF */
+ for(int i = 0; i < num_words; i++) {
+ REG_WRITE(RSA_MEM_M_BLOCK_BASE + i * 4, UINT32_MAX);
+ }
+ /* Mprime = 1 */
+ REG_WRITE(RSA_M_DASH_REG, 1);
- /* "mode" register loaded with number of 512-bit blocks, minus 1 */
- REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
+ /* "mode" register loaded with number of 512-bit blocks, minus 1 */
+ REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
- /* Load X */
- mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
+ /* Load X */
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
- /* Rinv = 1 */
- REG_WRITE(RSA_MEM_RB_BLOCK_BASE, 1);
- for(int i = 1; i < num_words; i++) {
- REG_WRITE(RSA_MEM_RB_BLOCK_BASE + i * 4, 0);
- }
+ /* Rinv = 1 */
+ REG_WRITE(RSA_MEM_RB_BLOCK_BASE, 1);
+ for(int i = 1; i < num_words; i++) {
+ REG_WRITE(RSA_MEM_RB_BLOCK_BASE + i * 4, 0);
+ }
- execute_op(RSA_MULT_START_REG);
+ execute_op(RSA_MULT_START_REG);
- MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
+ /* finish the modular multiplication */
+ MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
- esp_mpi_release_hardware();
+ esp_mpi_release_hardware();
cleanup:
- return ret;
+ return ret;
}
#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
projects / esp-idf / commitdiff