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mbedtls hardware RSA: Combine methods for calculating M' & r inverse

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Remove redundant gcd calculation, use consistent terminology.
Also remove leftover debugging code
This commit is contained in:
Angus Gratton 2016-11-18 13:44:37 +11:00
parent 6b687b43f4
commit f87be70d51
1 changed files with 191 additions and 395 deletions
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586
components/mbedtls/port/esp_bignum.c
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@ -39,46 +39,10 @@ static const char *TAG = "bignum";
#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 )
{
@ -116,6 +80,14 @@ static inline size_t hardware_words_needed(const mbedtls_mpi *mpi)
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
@ -156,194 +128,14 @@ static inline int mem_block_to_mpi(mbedtls_mpi *x, uint32_t mem_base, int num_wo
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
*/
static void extended_binary_gcd(const mbedtls_mpi *a, const mbedtls_mpi *b,
mbedtls_mpi *u, mbedtls_mpi *v)
{
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);
/* '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);
mbedtls_mpi_init(&ta);
mbedtls_mpi_copy(&ta, &a_);
//mbedtls_mpi_printf("a", &a_);
//mbedtls_mpi_printf("b", b);
/* Loop invariant:
2*ta = u*2*a - v*b.
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_);
}
/* Execute RSA operation. op_reg specifies which 'START' register
to write to.
*/
static inline void execute_op(uint32_t op_reg)
{
/* Clear interrupt status, start operation */
REG_WRITE(RSA_INTERRUPT_REG, 1);
REG_WRITE(op_reg, 1);
/* TODO: use interrupt instead of busywaiting */
while(REG_READ(RSA_INTERRUPT_REG) != 1)
{ }
/* clear the interrupt */
REG_WRITE(RSA_INTERRUPT_REG, 1);
}
/* 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);
/* Calculate and load the first stage montgomery multiplication */
MBEDTLS_MPI_CHK( modular_op_prepare(X, M, num_words) );
execute_op(RSA_MULT_START_REG);
MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
esp_mpi_release_hardware();
cleanup:
return ret;
}
#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
/*
* Sliding-window exponentiation: Z = X^Y mod M (HAC 14.85)
*/
#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 ret;
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);
/* "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;
}
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
*
* 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)
{
@ -365,59 +157,104 @@ static mbedtls_mpi_uint modular_inverse(const mbedtls_mpi *M)
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)
/* 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 = 0;
size_t num_bits;
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));
/* 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 ) );
} else {
memcpy(r, _RR, sizeof( mbedtls_mpi ) );
}
mbedtls_mpi_printf("r", r);
*Mi = modular_inverse(M);
cleanup:
cleanup:
mbedtls_mpi_free(&RR);
return ret;
}
static void bignum_param_deinit(mbedtls_mpi *_RR, mbedtls_mpi *r)
/* Execute RSA operation. op_reg specifies which 'START' register
to write to.
*/
static inline void execute_op(uint32_t op_reg)
{
if (_RR == NULL || _RR->p == NULL)
mbedtls_mpi_free(r);
/* Clear interrupt status, start operation */
REG_WRITE(RSA_INTERRUPT_REG, 1);
REG_WRITE(op_reg, 1);
/* TODO: use interrupt instead of busywaiting */
while(REG_READ(RSA_INTERRUPT_REG) != 1)
{ }
/* clear the interrupt */
REG_WRITE(RSA_INTERRUPT_REG, 1);
}
/* 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);
/* 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_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;
}
#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
/*
* 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)
*
*/
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 = 0;
size_t z_words = hardware_words_needed(Z);
@ -426,8 +263,9 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi
size_t m_words = hardware_words_needed(M);
size_t num_words;
mbedtls_mpi r;
mbedtls_mpi_uint Mi = 0;
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...
@ -442,19 +280,24 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi
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)
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);
/* Determine RR pointer, either _RR for cached value
or local RR_new */
if (_Rinv == NULL) {
mbedtls_mpi_init(&Rinv_new);
Rinv = &Rinv_new;
} else {
Rinv = _Rinv;
}
if (Rinv->p == NULL) {
MBEDTLS_MPI_CHK(calculate_rinv(Rinv, M, num_words));
}
Mprime = modular_inverse(M);
esp_mpi_acquire_hardware();
@ -465,8 +308,8 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi
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);
@ -474,91 +317,16 @@ int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi
esp_mpi_release_hardware();
mbedtls_mpi_printf("Z",Z);
ESP_LOGI(TAG, "print (Z == (X ** Y) %% M)\n");
bignum_param_deinit(_RR, &r);
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;
cleanup:
if (_Rinv == NULL) {
mbedtls_mpi_free(&Rinv_new);
}
/* 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;
}
#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.
*
@ -594,17 +362,43 @@ static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X,
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.)
@ -612,12 +406,11 @@ int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi
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 {
@ -640,7 +433,7 @@ int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi
/* "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);
@ -656,54 +449,57 @@ int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi
}
/* 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.
This case is simpler than esp_mpi_mul_mpi_mod() as we control the arguments:
Result (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:
* 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 */