#include <stdio.h>
#include <string.h>
#include <malloc.h>
+#include <limits.h>
+#include <assert.h>
#include "mbedtls/bignum.h"
#include "mbedtls/bn_mul.h"
#include "rom/bigint.h"
+#include "soc/hwcrypto_reg.h"
+#include "esp_system.h"
+#include "esp_log.h"
+
+#include "freertos/FreeRTOS.h"
+#include "freertos/task.h"
+
+static const char *TAG = "bignum";
#if defined(MBEDTLS_MPI_MUL_MPI_ALT) || defined(MBEDTLS_MPI_EXP_MOD_ALT)
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));
+ printf("%s = 0x", name);
+ mbedtls_mpi_write_string(X, 16, buf, sizeof(buf)-1, &n);
+ if(n) {
+ puts(buf);
+ } else {
+ puts("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.
_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.
+*/
+static inline size_t hardware_words_needed(const mbedtls_mpi *mpi)
+{
+ size_t res;
+ for(res = mpi->n; res > 0; res-- ) {
+ if( mpi->p[res - 1] != 0 )
+ break;
+ }
+ res = (res + 0xF) & ~0xF;
+ return res;
+}
+
+/* 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
+ these additional words will be zeroed in the memory buffer.
+*/
+static inline void mpi_to_mem_block(uint32_t mem_base, const mbedtls_mpi *mpi, size_t num_words)
+{
+ for(size_t i = 0; i < mpi->n && i < num_words; i++) {
+ REG_WRITE(mem_base + i * 4, mpi->p[i]);
+ }
+ for(size_t i = mpi->n; i < num_words; i++) {
+ REG_WRITE(mem_base + i * 4, 0);
+ }
+}
+
+/* Read mbedTLS MPI bignum back from hardware memory block.
+
+ Reads num_words words from block.
+
+ Can return a failure result if fails to grow the MPI result.
+*/
+static inline int mem_block_to_mpi(mbedtls_mpi *x, uint32_t mem_base, int num_words)
+{
+ int ret = 0;
+ size_t x_n = x->n;
+
+ /* this code is written in non-intuitive way, to only grow the
+ result if it is absolutely necessary - ie if all the high bits
+ are zero, the bignum won't be grown to fit them. */
+ for(int i = num_words - 1; i >= 0; i--) {
+ uint32_t value = REG_READ(mem_base + i * 4);
+ if(value != 0 && x_n <= i) {
+ MBEDTLS_MPI_CHK( mbedtls_mpi_grow(x, i+1) );
+ x_n = i+1;
+ }
+ if(x_n > i) {
+ x->p[i] = value;
+ }
+ }
+ /* Zero any remaining limbs in the bignum, if the buffer was
+ always bigger than num_words */
+ for(size_t i = num_words; i < x->n; i++) {
+ x->p[i] = 0;
+ }
+
+ cleanup:
+ return ret;
+}
+
/* Given a & b, determine u & v such that
- gcd(a,b) = d = au + bv
+ 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.ucl.ac.uk/~ucahcjm/combopt/ext_gcd_python_programs.pdf
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 ta, tb;
+ mbedtls_mpi a_, ta;
- mbedtls_mpi_init(&ta);
- mbedtls_mpi_copy(&ta, a);
- mbedtls_mpi_init(&tb);
- mbedtls_mpi_copy(&tb, b);
+ /* 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:
- ta = u*2*a - v*b. */
+ 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
/* u = (u + b) >> 1 */
mbedtls_mpi_add_mpi(u, u, b);
mbedtls_mpi_shift_r(u, 1);
- /* v = (v >> 1) + a */
+ /* v = (v - a) >> 1 */
mbedtls_mpi_shift_r(v, 1);
- mbedtls_mpi_add_mpi(v, v, a);
+ mbedtls_mpi_add_mpi(v, v, &a_);
}
}
mbedtls_mpi_free(&ta);
- mbedtls_mpi_free(&tb);
-
- /* u = u * 2, so 1 = u*a - v*b */
- mbedtls_mpi_shift_l(u, 1);
+ mbedtls_mpi_free(&a_);
}
-/* inner part of MPI modular multiply, after Rinv & Mprime are calculated */
-static int mpi_mul_mpi_mod_inner(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *M, mbedtls_mpi *Rinv, uint32_t Mprime, size_t num_words)
+/* Execute RSA operation. op_reg specifies which 'START' register
+ to write to.
+*/
+static inline void execute_op(uint32_t op_reg)
{
- int ret;
- mbedtls_mpi TA, TB;
- size_t num_bits = num_words * 32;
-
- mbedtls_mpi_grow(Rinv, num_words);
-
- /* TODO: fill memory blocks directly so this isn't needed */
- mbedtls_mpi_init(&TA);
- mbedtls_mpi_copy(&TA, A);
- mbedtls_mpi_grow(&TA, num_words);
- A = &TA;
- mbedtls_mpi_init(&TB);
- mbedtls_mpi_copy(&TB, B);
- mbedtls_mpi_grow(&TB, num_words);
- B = &TB;
-
- esp_mpi_acquire_hardware();
-
- if(ets_bigint_mod_mult_prepare(A->p, B->p, M->p, Mprime,
- Rinv->p, num_bits, false)) {
- mbedtls_mpi_grow(X, num_words);
- ets_bigint_wait_finish();
- if(ets_bigint_mod_mult_getz(M->p, X->p, num_bits)) {
- X->s = A->s * B->s;
- ret = 0;
- } else {
- printf("ets_bigint_mod_mult_getz failed\n");
- ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
- }
- } else {
- printf("ets_bigint_mod_mult_prepare failed\n");
- ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
- }
- esp_mpi_release_hardware();
-
- /* unclear why this is necessary, but the result seems
- to come back rotated 32 bits to the right... */
- uint32_t last_word = X->p[num_words-1];
- X->p[num_words-1] = 0;
- mbedtls_mpi_shift_l(X, 32);
- X->p[0] = last_word;
+ /* Clear interrupt status, start operation */
+ REG_WRITE(RSA_INTERRUPT_REG, 1);
+ REG_WRITE(op_reg, 1);
- mbedtls_mpi_free(&TA);
- mbedtls_mpi_free(&TB);
+ /* TODO: use interrupt instead of busywaiting */
+ while(REG_READ(RSA_INTERRUPT_REG) != 1)
+ { }
- return ret;
+ /* clear the interrupt */
+ REG_WRITE(RSA_INTERRUPT_REG, 1);
}
-/* X = (A * B) mod M
-
- Not an mbedTLS function
+/* 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);
- num_bits guaranteed to be a multiple of 512 already.
+/* Z = (X * Y) mod M
- TODO: ensure M is odd
+ Not an mbedTLS function
*/
-int esp_mpi_mul_mpi_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *M, size_t num_bits)
+int esp_mpi_mul_mpi_mod(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, const mbedtls_mpi *M)
{
- int ret = 0;
- mbedtls_mpi RR, Rinv, Mprime;
- uint32_t Mprime_int;
- size_t num_words = num_bits / 32;
+ int ret;
+ size_t num_words = hardware_words_needed(M);
- /* 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_set_bit(&RR, num_bits+32, 1);
- mbedtls_mpi_init(&Mprime);
- extended_binary_gcd(&RR, M, &Rinv, &Mprime);
+ /* Calculate and load the first stage montgomery multiplication */
+ MBEDTLS_MPI_CHK( modular_op_prepare(X, M, num_words) );
- /* M' is mod 2^32 */
- Mprime_int = Mprime.p[0];
+ execute_op(RSA_MULT_START_REG);
- ret = mpi_mul_mpi_mod_inner(X, A, B, M, &Rinv, Mprime_int, num_words);
+ MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
- mbedtls_mpi_free(&RR);
- mbedtls_mpi_free(&Mprime);
- mbedtls_mpi_free(&Rinv);
+ esp_mpi_release_hardware();
+ cleanup:
return ret;
}
+#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
/*
- * Helper for mbedtls_mpi multiplication
- * copied/trimmed from mbedtls bignum.c
+ * Sliding-window exponentiation: Z = X^Y mod M (HAC 14.85)
*/
-static void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
+int mbedtls_mpi_exp_mod( mbedtls_mpi* Z, const mbedtls_mpi* X, const mbedtls_mpi* Y, const mbedtls_mpi* M, mbedtls_mpi* _RR )
{
- mbedtls_mpi_uint c = 0, t = 0;
-
- for( ; i >= 16; i -= 16 )
- {
- MULADDC_INIT
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
-
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_STOP
+ 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;
}
-
- for( ; i >= 8; i -= 8 )
- {
- MULADDC_INIT
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
-
- MULADDC_CORE MULADDC_CORE
- MULADDC_CORE MULADDC_CORE
- MULADDC_STOP
+ if (y_words > num_words) {
+ num_words = y_words;
}
-
-
- for( ; i > 0; i-- )
- {
- MULADDC_INIT
- MULADDC_CORE
- MULADDC_STOP
+ 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);
- t++;
+ /* TODO: _RR parameter currently ignored */
- do {
- *d += c; c = ( *d < c ); d++;
+ ret = modular_op_prepare(X, M, num_words);
+ if (ret != 0) {
+ return ret;
}
- while( c != 0 );
-}
+ mpi_to_mem_block(RSA_MEM_Y_BLOCK_BASE, Y, num_words);
-/*
- * Helper for mbedtls_mpi subtraction
- * Copied/adapter from mbedTLS bignum.c
- */
-static void mpi_sub_hlp( size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d )
-{
- size_t i;
- mbedtls_mpi_uint c, z;
+ //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);
- for( i = c = 0; i < n; i++, s++, d++ )
- {
- z = ( *d < c ); *d -= c;
- c = ( *d < *s ) + z; *d -= *s;
- }
+ REG_WRITE(RSA_MODEXP_MODE_REG, (num_words / 16) - 1);
- while( c != 0 )
- {
- z = ( *d < c ); *d -= c;
- c = z; i++; d++;
- }
-}
+ execute_op(RSA_START_MODEXP_REG);
+ //dump_memory_block("Z_BLOCK", RSA_MEM_Z_BLOCK_BASE);
-/* The following 3 Montgomery arithmetic function are
- copied from mbedTLS bigint.c verbatim as they are static.
+ /* 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);
- TODO: find a way to support making the versions in mbedtls
- non-static.
-*/
+ esp_mpi_release_hardware();
-/*
- * Fast Montgomery initialization (thanks to Tom St Denis)
- */
-static void mpi_montg_init( mbedtls_mpi_uint *mm, const mbedtls_mpi *N )
-{
- mbedtls_mpi_uint x, m0 = N->p[0];
- unsigned int i;
+ mbedtls_mpi_printf("Z",Z);
+ printf("print (Z == (X ** Y) %% M)\n");
- x = m0;
- x += ( ( m0 + 2 ) & 4 ) << 1;
+ return ret;
+}
- for( i = biL; i >= 8; i /= 2 )
- x *= ( 2 - ( m0 * x ) );
+#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
- *mm = ~x + 1;
-}
-/*
- * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
+/* 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 mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm,
- const mbedtls_mpi *T )
+static int modular_op_prepare(const mbedtls_mpi *X, const mbedtls_mpi *M, size_t num_words)
{
- size_t i, n, m;
- mbedtls_mpi_uint u0, u1, *d;
+ int ret = 0;
+ mbedtls_mpi RR, Rinv, Mprime;
+ size_t num_bits;
+
+ /* Calculate number of bits */
+ num_bits = num_words * 32;
- if( T->n < N->n + 1 || T->p == NULL )
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+ if(num_bits > 4096) {
+ return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+ }
- memset( T->p, 0, T->n * ciL );
+ /* 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);
- d = T->p;
- n = N->n;
- m = ( B->n < n ) ? B->n : n;
+ 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);
- for( i = 0; i < n; i++ )
- {
- /*
- * T = (T + u0*B + u1*N) / 2^biL
- */
- u0 = A->p[i];
- u1 = ( d[0] + u0 * B->p[0] ) * mm;
+ /* Block of debugging data, output suitable to paste into Python
+ TODO remove
+ */
+ mbedtls_mpi_printf("R", &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");
- mpi_mul_hlp( m, B->p, d, u0 );
- mpi_mul_hlp( n, N->p, d, u1 );
+ esp_mpi_acquire_hardware();
- *d++ = u0; d[n + 1] = 0;
- }
+ /* 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]);
- memcpy( A->p, d, ( n + 1 ) * ciL );
+ /* "mode" register loaded with number of 512-bit blocks, minus 1 */
+ REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
- if( mbedtls_mpi_cmp_abs( A, N ) >= 0 )
- mpi_sub_hlp( n, N->p, A->p );
- else
- /* prevent timing attacks */
- mpi_sub_hlp( n, A->p, T->p );
+ mbedtls_mpi_free(&Rinv);
+ mbedtls_mpi_free(&RR);
+ mbedtls_mpi_free(&Mprime);
- return( 0 );
+ return ret;
}
-/*
- * Montgomery reduction: A = A * R^-1 mod N
+/* Second & final step of a modular multiply - load second multiplication
+ * factor Y, run the multiply, read back the result into Z.
+ *
+ * @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.
+ *
+ * Caller must have already called esp_mpi_acquire_hardware().
*/
-static int mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T )
+inline static int modular_multiply_finish(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words)
{
- mbedtls_mpi_uint z = 1;
- mbedtls_mpi U;
+ int ret;
+ /* Load Y to X input memory block, rerun */
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, Y, num_words);
- U.n = U.s = (int) z;
- U.p = &z;
+ execute_op(RSA_MULT_START_REG);
- return( mpi_montmul( A, &U, N, mm, T ) );
-}
+ /* Read result into Z */
+ ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, num_words);
-#if defined(MBEDTLS_MPI_MUL_MPI_ALT) /* MBEDTLS_MPI_MUL_MPI_ALT */
+ Z->s = X->s * Y->s;
-/* Number of words used to hold 'mpi', rounded up to nearest
- 16 words (512 bits) to match hardware support
-*/
-static inline size_t hardware_words_needed(const mbedtls_mpi *mpi)
-{
- size_t res;
- for(res = mpi->n; res > 0; res-- ) {
- if( mpi->p[res - 1] != 0 )
- break;
- }
- res = (res + 0xF) & ~0xF;
- return res;
+ return ret;
}
+#if defined(MBEDTLS_MPI_MUL_MPI_ALT) /* MBEDTLS_MPI_MUL_MPI_ALT */
-/* Special-case multiply, where we use hardware montgomery mod
- multiplication to solve the case where A or B are >2048 bits so
- can't do standard multiplication.
-
- the modulus here is chosen with M=(2^num_bits-1)
- to guarantee the output isn't actually modulo anything. This means
- we don't need to calculate M' and Rinv, they are predictable
- as follows:
- M' = 1
- Rinv = (1 << (num_bits - 32)
-
- (See RSA Accelerator section in Technical Reference for derivation
- of M', Rinv)
-*/
-static int esp_mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, size_t num_words)
- {
- mbedtls_mpi M, Rinv;
- int ret;
- size_t mprime;
- size_t num_bits = num_words * 32;
-
- mbedtls_mpi_init(&M);
- mbedtls_mpi_init(&Rinv);
-
- /* TODO: it may be faster to just use 4096-bit arithmetic every time,
- and make these constants rather than runtime derived
- derived. */
- /* M = (2^num_words)-1 */
- mbedtls_mpi_grow(&M, num_words);
- for(int i = 0; i < num_words*32; i++) {
- mbedtls_mpi_set_bit(&M, i, 1);
- }
-
- /* Rinv = (2^num_words-32) */
- mbedtls_mpi_grow(&Rinv, num_words);
- mbedtls_mpi_set_bit(&Rinv, num_bits - 32, 1);
-
- mprime = 1;
-
- ret = mpi_mul_mpi_mod_inner(X, A, B, &M, &Rinv, mprime, num_words);
-
- mbedtls_mpi_free(&M);
- mbedtls_mpi_free(&Rinv);
- return ret;
- }
+static int mpi_mult_mpi_failover_mod_mult(mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t num_words);
-int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
+/* Z = X * Y */
+int mbedtls_mpi_mul_mpi( mbedtls_mpi *Z, const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
- int ret = -1;
- size_t words_a, words_b, words_x, words_mult;
-
- mbedtls_mpi TA, TB;
-
- mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
-
- /* Count words needed for A & B in hardware */
- words_a = hardware_words_needed(A);
- words_b = hardware_words_needed(B);
+ int ret;
+ size_t words_x, words_y, words_mult, words_z;
- words_mult = (words_a > words_b ? words_a : words_b);
+ /* Count words needed for X & Y in hardware */
+ words_x = hardware_words_needed(X);
+ words_y = hardware_words_needed(Y);
- /* Take a copy of A if either X == A OR if A isn't long enough
- to hold the number of words needed for hardware.
+ words_mult = (words_x > words_y ? words_x : words_y);
- (can't grow A directly as it is const)
+ /* Result Z has to have room for double the larger factor */
+ words_z = words_mult * 2;
- TODO: growing the input operands is only necessary because the
- ROM functions only take one length argument. It should be
- possible for us to just copy the used data only into the
- hardware buffers, and set the remaining bits to zero - saving
- RAM. But we need to reimplement ets_bigint_mult_prepare() in
- software for this.
- */
- if( X == A || A->n < words_mult) {
- MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &TA, words_mult) );
- A = &TA;
- }
- /* Same for B */
- if( X == B || B->n < words_mult ) {
- MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
- MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &TB, words_mult) );
- B = &TB;
- }
+ /* 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.)
- /* Result X has to have room for double the larger operand */
- words_x = words_mult * 2;
- MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, words_x ) );
- /* TODO: check if lset here is necessary, hardware should zero */
- MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
-
- /* If either operand is over 2048 bits, we can't use the standard hardware multiplier
- (it assumes result is double longest operand, and result is max 4096 bits.)
-
- However, we can fail over to mod_mult for up to 4096 bits.
+ However, we can fail over to mod_mult for up to 4096 bits of result (modulo
+ 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) {
- /* TODO: check if there's an overflow condition if words_a & words_b are both
- the bit lengths of the operands, result could be 1 bit longer
- */
- if((words_a + words_b) * 32 > 4096) {
- printf("ERROR: %d bit operands (%d bits * %d bits) too large for hardware unit\n", words_mult * 32, mbedtls_mpi_bitlen(A), mbedtls_mpi_bitlen(B));
- ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+ if (words_mult * 32 > 2048) {
+ /* Calculate new length of Z */
+ words_z = words_x + words_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));
+ return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
}
else {
- ret = esp_mpi_mult_mpi_failover_mod_mult(X, A, B, words_a + words_b);
- }
- }
- else {
-
- /* normal mpi multiplication */
- esp_mpi_acquire_hardware();
- if (ets_bigint_mult_prepare(A->p, B->p, words_mult * 32)) {
- ets_bigint_wait_finish();
- /* NB: argument to bigint_mult_getz is length of inputs, double this number (words_x) is
- copied to output X->p.
- */
- if (ets_bigint_mult_getz(X->p, words_mult * 32) == true) {
- X->s = A->s * B->s;
- ret = 0;
- } else {
- printf("ets_bigint_mult_getz failed\n");
- ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
- }
- } else{
- printf("Baseline multiplication failed\n");
- ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+ return mpi_mult_mpi_failover_mod_mult(Z, X, Y, words_z);
}
- esp_mpi_release_hardware();
}
-cleanup:
-
- mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
-
- return( ret );
-}
-
-#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
-
-#if defined(MBEDTLS_MPI_EXP_MOD_ALT)
-/*
- * 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* _RR )
-{
- int ret;
- size_t wbits, wsize, one = 1;
- size_t i, j, nblimbs;
- size_t bufsize, nbits;
- mbedtls_mpi_uint ei, mm, state;
- mbedtls_mpi RR, T, W[ 2 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
- int neg;
-
- if( mbedtls_mpi_cmp_int( N, 0 ) < 0 || ( N->p[0] & 1 ) == 0 )
- return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
-
- if( mbedtls_mpi_cmp_int( E, 0 ) < 0 )
- 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 );
- memset( W, 0, sizeof( W ) );
-
- i = mbedtls_mpi_bitlen( E );
-
- wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
- ( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
-
- if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
- wsize = MBEDTLS_MPI_WINDOW_SIZE;
-
- j = N->n + 1;
- MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 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;
- }
+ /* Otherwise, we can use the (faster) multiply hardware unit */
- /*
- * If 1st call, pre-compute R^2 mod N
- */
- if( _RR == NULL || _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 ) );
-
- if( _RR != NULL )
- memcpy( _RR, &RR, sizeof( mbedtls_mpi) );
- }
- else
- memcpy( &RR, _RR, sizeof( mbedtls_mpi) );
+ esp_mpi_acquire_hardware();
- /*
- * W[1] = A * R^2 * R^-1 mod N = A * R mod N
- */
- if( mbedtls_mpi_cmp_mpi( A, N ) >= 0 )
- MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &W[1], A, N ) );
- else
- MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &W[1], A ) );
+ /* 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);
+ /* 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().
+ */
- mpi_montmul( &W[1], &RR, N, mm, &T );
+ REG_WRITE(RSA_M_DASH_REG, 0);
- /*
- * X = R^2 * R^-1 mod N = R mod N
+ /* "mode" register loaded with number of 512-bit blocks in result,
+ plus 7 (for range 9-12). (this is ((N~ / 32) - 1) + 8))
*/
- MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &RR ) );
- mpi_montred( X, N, mm, &T );
-
- if( wsize > 1 )
- {
- /*
- * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
- */
- j = one << ( wsize - 1 );
-
- 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 < wsize - 1; i++ )
- mpi_montmul( &W[j], &W[j], N, mm, &T );
-
- /*
- * W[i] = W[i - 1] * W[1]
- */
- for( i = j + 1; i < ( one << wsize ); 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;
- wbits = 0;
- state = 0;
+ REG_WRITE(RSA_MULT_MODE_REG, (words_z / 16) + 7);
- while( 1 )
- {
- if( bufsize == 0 )
- {
- if( nblimbs == 0 )
- break;
+ execute_op(RSA_MULT_START_REG);
- nblimbs--;
+ /* Read back the result */
+ ret = mem_block_to_mpi(Z, RSA_MEM_Z_BLOCK_BASE, words_z);
- bufsize = sizeof( mbedtls_mpi_uint ) << 3;
- }
+ Z->s = X->s * Y->s;
- bufsize--;
+ esp_mpi_release_hardware();
- ei = (E->p[nblimbs] >> bufsize) & 1;
+ return ret;
+}
- /*
- * skip leading 0s
- */
- if( ei == 0 && state == 0 )
- continue;
+/* 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.
- if( ei == 0 && state == 1 )
- {
- /*
- * out of window, square X
- */
- mpi_montmul( X, X, N, mm, &T );
- continue;
- }
+ This case is simpler than esp_mpi_mul_mpi_mod() as we control the arguments:
- /*
- * add ei to current window
- */
- state = 2;
-
- nbits++;
- wbits |= ( ei << ( wsize - nbits ) );
-
- if( nbits == wsize )
- {
- /*
- * X = X^wsize R^-1 mod N
- */
- for( i = 0; i < wsize; i++ )
- mpi_montmul( X, X, N, mm, &T );
-
- /*
- * X = X * W[wbits] R^-1 mod N
- */
- mpi_montmul( X, &W[wbits], N, mm, &T );
-
- state--;
- nbits = 0;
- wbits = 0;
- }
- }
+ * 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
- /*
- * process the remaining bits
- */
- for( i = 0; i < nbits; i++ )
- {
- mpi_montmul( X, X, N, mm, &T );
+ (See RSA Accelerator section in Technical Reference *
+ extended_binary_gcd() function above for more about M', 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;
- wbits <<= 1;
+ /* Load coefficients to hardware */
+ esp_mpi_acquire_hardware();
- if( ( wbits & ( one << wsize ) ) != 0 )
- mpi_montmul( X, &W[1], N, mm, &T );
- }
+ /* 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);
- /*
- * X = A^E * R * R^-1 mod N = A^E mod N
- */
- mpi_montred( X, N, mm, &T );
+ /* "mode" register loaded with number of 512-bit blocks, minus 1 */
+ REG_WRITE(RSA_MULT_MODE_REG, (num_words / 16) - 1);
- if( neg )
- {
- X->s = -1;
- MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
- }
+ /* Load X */
+ mpi_to_mem_block(RSA_MEM_X_BLOCK_BASE, X, num_words);
-cleanup:
+ /* 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);
+ }
- for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
- mbedtls_mpi_free( &W[i] );
+ execute_op(RSA_MULT_START_REG);
- mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
+ MBEDTLS_MPI_CHK( modular_multiply_finish(Z, X, Y, num_words) );
- if( _RR == NULL || _RR->p == NULL )
- mbedtls_mpi_free( &RR );
+ esp_mpi_release_hardware();
- return( ret );
+ cleanup:
+ return ret;
}
-#endif /* MBEDTLS_MPI_EXP_MOD_ALT */
+#endif /* MBEDTLS_MPI_MUL_MPI_ALT */
#endif /* MBEDTLS_MPI_MUL_MPI_ALT || MBEDTLS_MPI_EXP_MOD_ALT */
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