rsa_sup_mul.c
#include <openssl/e_os2.h>
#include <stddef.h>
#include <sys/types.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/rsaerr.h>
#include "internal/numbers.h"
#include "internal/constant_time.h"
#include "bn_local.h"
# if BN_BYTES == 8
typedef uint64_t limb_t;
# if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16
/* nonstandard; implemented by gcc on 64-bit platforms */
typedef __uint128_t limb2_t;
# define HAVE_LIMB2_T
# endif
# define LIMB_BIT_SIZE 64
# define LIMB_BYTE_SIZE 8
# elif BN_BYTES == 4
typedef uint32_t limb_t;
typedef uint64_t limb2_t;
# define LIMB_BIT_SIZE 32
# define LIMB_BYTE_SIZE 4
# define HAVE_LIMB2_T
# else
# error "Not supported"
# endif
/*
* For multiplication we're using schoolbook multiplication,
* so if we have two numbers, each with 6 "digits" (words)
* the multiplication is calculated as follows:
* A B C D E F
* x I J K L M N
* --------------
* N*F
* N*E
* N*D
* N*C
* N*B
* N*A
* M*F
* M*E
* M*D
* M*C
* M*B
* M*A
* L*F
* L*E
* L*D
* L*C
* L*B
* L*A
* K*F
* K*E
* K*D
* K*C
* K*B
* K*A
* J*F
* J*E
* J*D
* J*C
* J*B
* J*A
* I*F
* I*E
* I*D
* I*C
* I*B
* + I*A
* ==========================
* N*B N*D N*F
* + N*A N*C N*E
* + M*B M*D M*F
* + M*A M*C M*E
* + L*B L*D L*F
* + L*A L*C L*E
* + K*B K*D K*F
* + K*A K*C K*E
* + J*B J*D J*F
* + J*A J*C J*E
* + I*B I*D I*F
* + I*A I*C I*E
*
* 1+1 1+3 1+5
* 1+0 1+2 1+4
* 0+1 0+3 0+5
* 0+0 0+2 0+4
*
* 0 1 2 3 4 5 6
* which requires n^2 multiplications and 2n full length additions
* as we can keep every other result of limb multiplication in two separate
* limbs
*/
#if defined HAVE_LIMB2_T
static ossl_inline void _mul_limb(limb_t *hi, limb_t *lo, limb_t a, limb_t b)
{
limb2_t t;
/*
* this is idiomatic code to tell compiler to use the native mul
* those three lines will actually compile to single instruction
*/
t = (limb2_t)a * b;
*hi = t >> LIMB_BIT_SIZE;
*lo = (limb_t)t;
}
#elif (BN_BYTES == 8) && (defined _MSC_VER)
/* https://learn.microsoft.com/en-us/cpp/intrinsics/umul128?view=msvc-170 */
#pragma intrinsic(_umul128)
static ossl_inline void _mul_limb(limb_t *hi, limb_t *lo, limb_t a, limb_t b)
{
*lo = _umul128(a, b, hi);
}
#else
/*
* if the compiler doesn't have either a 128bit data type nor a "return
* high 64 bits of multiplication"
*/
static ossl_inline void _mul_limb(limb_t *hi, limb_t *lo, limb_t a, limb_t b)
{
limb_t a_low = (limb_t)(uint32_t)a;
limb_t a_hi = a >> 32;
limb_t b_low = (limb_t)(uint32_t)b;
limb_t b_hi = b >> 32;
limb_t p0 = a_low * b_low;
limb_t p1 = a_low * b_hi;
limb_t p2 = a_hi * b_low;
limb_t p3 = a_hi * b_hi;
uint32_t cy = (uint32_t)(((p0 >> 32) + (uint32_t)p1 + (uint32_t)p2) >> 32);
*lo = p0 + (p1 << 32) + (p2 << 32);
*hi = p3 + (p1 >> 32) + (p2 >> 32) + cy;
}
#endif
/* add two limbs with carry in, return carry out */
static ossl_inline limb_t _add_limb(limb_t *ret, limb_t a, limb_t b, limb_t carry)
{
limb_t carry1, carry2, t;
/*
* `c = a + b; if (c < a)` is idiomatic code that makes compilers
* use add with carry on assembly level
*/
*ret = a + carry;
if (*ret < a)
carry1 = 1;
else
carry1 = 0;
t = *ret;
*ret = t + b;
if (*ret < t)
carry2 = 1;
else
carry2 = 0;
return carry1 + carry2;
}
/*
* add two numbers of the same size, return overflow
*
* add a to b, place result in ret; all arrays need to be n limbs long
* return overflow from addition (0 or 1)
*/
static ossl_inline limb_t add(limb_t *ret, limb_t *a, limb_t *b, size_t n)
{
limb_t c = 0;
ossl_ssize_t i;
for(i = n - 1; i > -1; i--)
c = _add_limb(&ret[i], a[i], b[i], c);
return c;
}
/*
* return number of limbs necessary for temporary values
* when multiplying numbers n limbs large
*/
static ossl_inline size_t mul_limb_numb(size_t n)
{
return 2 * n * 2;
}
/*
* multiply two numbers of the same size
*
* multiply a by b, place result in ret; a and b need to be n limbs long
* ret needs to be 2*n limbs long, tmp needs to be mul_limb_numb(n) limbs
* long
*/
static void limb_mul(limb_t *ret, limb_t *a, limb_t *b, size_t n, limb_t *tmp)
{
limb_t *r_odd, *r_even;
size_t i, j, k;
r_odd = tmp;
r_even = &tmp[2 * n];
memset(ret, 0, 2 * n * sizeof(limb_t));
for (i = 0; i < n; i++) {
for (k = 0; k < i + n + 1; k++) {
r_even[k] = 0;
r_odd[k] = 0;
}
for (j = 0; j < n; j++) {
/*
* place results from even and odd limbs in separate arrays so that
* we don't have to calculate overflow every time we get individual
* limb multiplication result
*/
if (j % 2 == 0)
_mul_limb(&r_even[i + j], &r_even[i + j + 1], a[i], b[j]);
else
_mul_limb(&r_odd[i + j], &r_odd[i + j + 1], a[i], b[j]);
}
/*
* skip the least significant limbs when adding multiples of
* more significant limbs (they're zero anyway)
*/
add(ret, ret, r_even, n + i + 1);
add(ret, ret, r_odd, n + i + 1);
}
}
/* modifies the value in place by performing a right shift by one bit */
static ossl_inline void rshift1(limb_t *val, size_t n)
{
limb_t shift_in = 0, shift_out = 0;
size_t i;
for (i = 0; i < n; i++) {
shift_out = val[i] & 1;
val[i] = shift_in << (LIMB_BIT_SIZE - 1) | (val[i] >> 1);
shift_in = shift_out;
}
}
/* extend the LSB of flag to all bits of limb */
static ossl_inline limb_t mk_mask(limb_t flag)
{
flag |= flag << 1;
flag |= flag << 2;
flag |= flag << 4;
flag |= flag << 8;
flag |= flag << 16;
#if (LIMB_BYTE_SIZE == 8)
flag |= flag << 32;
#endif
return flag;
}
/*
* copy from either a or b to ret based on flag
* when flag == 0, then copies from b
* when flag == 1, then copies from a
*/
static ossl_inline void cselect(limb_t flag, limb_t *ret, limb_t *a, limb_t *b, size_t n)
{
/*
* would be more efficient with non volatile mask, but then gcc
* generates code with jumps
*/
volatile limb_t mask;
size_t i;
mask = mk_mask(flag);
for (i = 0; i < n; i++) {
#if (LIMB_BYTE_SIZE == 8)
ret[i] = constant_time_select_64(mask, a[i], b[i]);
#else
ret[i] = constant_time_select_32(mask, a[i], b[i]);
#endif
}
}
static limb_t _sub_limb(limb_t *ret, limb_t a, limb_t b, limb_t borrow)
{
limb_t borrow1, borrow2, t;
/*
* while it doesn't look constant-time, this is idiomatic code
* to tell compilers to use the carry bit from subtraction
*/
*ret = a - borrow;
if (*ret > a)
borrow1 = 1;
else
borrow1 = 0;
t = *ret;
*ret = t - b;
if (*ret > t)
borrow2 = 1;
else
borrow2 = 0;
return borrow1 + borrow2;
}
/*
* place the result of a - b into ret, return the borrow bit.
* All arrays need to be n limbs long
*/
static limb_t sub(limb_t *ret, limb_t *a, limb_t *b, size_t n)
{
limb_t borrow = 0;
ossl_ssize_t i;
for (i = n - 1; i > -1; i--)
borrow = _sub_limb(&ret[i], a[i], b[i], borrow);
return borrow;
}
/* return the number of limbs necessary to allocate for the mod() tmp operand */
static ossl_inline size_t mod_limb_numb(size_t anum, size_t modnum)
{
return (anum + modnum) * 3;
}
/*
* calculate a % mod, place the result in ret
* size of a is defined by anum, size of ret and mod is modnum,
* size of tmp is returned by mod_limb_numb()
*/
static void mod(limb_t *ret, limb_t *a, size_t anum, limb_t *mod,
size_t modnum, limb_t *tmp)
{
limb_t *atmp, *modtmp, *rettmp;
limb_t res;
size_t i;
memset(tmp, 0, mod_limb_numb(anum, modnum) * LIMB_BYTE_SIZE);
atmp = tmp;
modtmp = &tmp[anum + modnum];
rettmp = &tmp[(anum + modnum) * 2];
for (i = modnum; i <modnum + anum; i++)
atmp[i] = a[i-modnum];
for (i = 0; i < modnum; i++)
modtmp[i] = mod[i];
for (i = 0; i < anum * LIMB_BIT_SIZE; i++) {
rshift1(modtmp, anum + modnum);
res = sub(rettmp, atmp, modtmp, anum+modnum);
cselect(res, atmp, atmp, rettmp, anum+modnum);
}
memcpy(ret, &atmp[anum], sizeof(limb_t) * modnum);
}
/* necessary size of tmp for a _mul_add_limb() call with provided anum */
static ossl_inline size_t _mul_add_limb_numb(size_t anum)
{
return 2 * (anum + 1);
}
/* multiply a by m, add to ret, return carry */
static limb_t _mul_add_limb(limb_t *ret, limb_t *a, size_t anum,
limb_t m, limb_t *tmp)
{
limb_t carry = 0;
limb_t *r_odd, *r_even;
size_t i;
memset(tmp, 0, sizeof(limb_t) * (anum + 1) * 2);
r_odd = tmp;
r_even = &tmp[anum + 1];
for (i = 0; i < anum; i++) {
/*
* place the results from even and odd limbs in separate arrays
* so that we have to worry about carry just once
*/
if (i % 2 == 0)
_mul_limb(&r_even[i], &r_even[i + 1], a[i], m);
else
_mul_limb(&r_odd[i], &r_odd[i + 1], a[i], m);
}
/* assert: add() carry here will be equal zero */
add(r_even, r_even, r_odd, anum + 1);
/*
* while here it will not overflow as the max value from multiplication
* is -2 while max overflow from addition is 1, so the max value of
* carry is -1 (i.e. max int)
*/
carry = add(ret, ret, &r_even[1], anum) + r_even[0];
return carry;
}
static ossl_inline size_t mod_montgomery_limb_numb(size_t modnum)
{
return modnum * 2 + _mul_add_limb_numb(modnum);
}
/*
* calculate a % mod, place result in ret
* assumes that a is in Montgomery form with the R (Montgomery modulus) being
* smallest power of two big enough to fit mod and that's also a power
* of the count of number of bits in limb_t (B).
* For calculation, we also need n', such that mod * n' == -1 mod B.
* anum must be <= 2 * modnum
* ret needs to be modnum words long
* tmp needs to be mod_montgomery_limb_numb(modnum) limbs long
*/
static void mod_montgomery(limb_t *ret, limb_t *a, size_t anum, limb_t *mod,
size_t modnum, limb_t ni0, limb_t *tmp)
{
limb_t carry, v;
limb_t *res, *rp, *tmp2;
ossl_ssize_t i;
res = tmp;
/*
* for intermediate result we need an integer twice as long as modulus
* but keep the input in the least significant limbs
*/
memset(res, 0, sizeof(limb_t) * (modnum * 2));
memcpy(&res[modnum * 2 - anum], a, sizeof(limb_t) * anum);
rp = &res[modnum];
tmp2 = &res[modnum * 2];
carry = 0;
/* add multiples of the modulus to the value until R divides it cleanly */
for (i = modnum; i > 0; i--, rp--) {
v = _mul_add_limb(rp, mod, modnum, rp[modnum - 1] * ni0, tmp2);
v = v + carry + rp[-1];
carry |= (v != rp[-1]);
carry &= (v <= rp[-1]);
rp[-1] = v;
}
/* perform the final reduction by mod... */
carry -= sub(ret, rp, mod, modnum);
/* ...conditionally */
cselect(carry, ret, rp, ret, modnum);
}
/* allocated buffer should be freed afterwards */
static void BN_to_limb(const BIGNUM *bn, limb_t *buf, size_t limbs)
{
int i;
int real_limbs = (BN_num_bytes(bn) + LIMB_BYTE_SIZE - 1) / LIMB_BYTE_SIZE;
limb_t *ptr = buf + (limbs - real_limbs);
for (i = 0; i < real_limbs; i++)
ptr[i] = bn->d[real_limbs - i - 1];
}
#if LIMB_BYTE_SIZE == 8
static ossl_inline uint64_t be64(uint64_t host)
{
const union {
long one;
char little;
} is_endian = { 1 };
if (is_endian.little) {
uint64_t big = 0;
big |= (host & 0xff00000000000000) >> 56;
big |= (host & 0x00ff000000000000) >> 40;
big |= (host & 0x0000ff0000000000) >> 24;
big |= (host & 0x000000ff00000000) >> 8;
big |= (host & 0x00000000ff000000) << 8;
big |= (host & 0x0000000000ff0000) << 24;
big |= (host & 0x000000000000ff00) << 40;
big |= (host & 0x00000000000000ff) << 56;
return big;
} else {
return host;
}
}
#else
/* Not all platforms have htobe32(). */
static ossl_inline uint32_t be32(uint32_t host)
{
const union {
long one;
char little;
} is_endian = { 1 };
if (is_endian.little) {
uint32_t big = 0;
big |= (host & 0xff000000) >> 24;
big |= (host & 0x00ff0000) >> 8;
big |= (host & 0x0000ff00) << 8;
big |= (host & 0x000000ff) << 24;
return big;
} else {
return host;
}
}
#endif
/*
* We assume that intermediate, possible_arg2, blinding, and ctx are used
* similar to BN_BLINDING_invert_ex() arguments.
* to_mod is RSA modulus.
* buf and num is the serialization buffer and its length.
*
* Here we use classic/Montgomery multiplication and modulo. After the calculation finished
* we serialize the new structure instead of BIGNUMs taking endianness into account.
*/
int ossl_bn_rsa_do_unblind(const BIGNUM *intermediate,
const BN_BLINDING *blinding,
const BIGNUM *possible_arg2,
const BIGNUM *to_mod, BN_CTX *ctx,
unsigned char *buf, int num)
{
limb_t *l_im = NULL, *l_mul = NULL, *l_mod = NULL;
limb_t *l_ret = NULL, *l_tmp = NULL, l_buf;
size_t l_im_count = 0, l_mul_count = 0, l_size = 0, l_mod_count = 0;
size_t l_tmp_count = 0;
int ret = 0;
size_t i;
unsigned char *tmp;
const BIGNUM *arg1 = intermediate;
const BIGNUM *arg2 = (possible_arg2 == NULL) ? blinding->Ai : possible_arg2;
l_im_count = (BN_num_bytes(arg1) + LIMB_BYTE_SIZE - 1) / LIMB_BYTE_SIZE;
l_mul_count = (BN_num_bytes(arg2) + LIMB_BYTE_SIZE - 1) / LIMB_BYTE_SIZE;
l_mod_count = (BN_num_bytes(to_mod) + LIMB_BYTE_SIZE - 1) / LIMB_BYTE_SIZE;
l_size = l_im_count > l_mul_count ? l_im_count : l_mul_count;
l_im = OPENSSL_zalloc(l_size * LIMB_BYTE_SIZE);
l_mul = OPENSSL_zalloc(l_size * LIMB_BYTE_SIZE);
l_mod = OPENSSL_zalloc(l_mod_count * LIMB_BYTE_SIZE);
if ((l_im == NULL) || (l_mul == NULL) || (l_mod == NULL))
goto err;
BN_to_limb(arg1, l_im, l_size);
BN_to_limb(arg2, l_mul, l_size);
BN_to_limb(to_mod, l_mod, l_mod_count);
l_ret = OPENSSL_malloc(2 * l_size * LIMB_BYTE_SIZE);
if (blinding->m_ctx != NULL) {
l_tmp_count = mul_limb_numb(l_size) > mod_montgomery_limb_numb(l_mod_count) ?
mul_limb_numb(l_size) : mod_montgomery_limb_numb(l_mod_count);
l_tmp = OPENSSL_malloc(l_tmp_count * LIMB_BYTE_SIZE);
} else {
l_tmp_count = mul_limb_numb(l_size) > mod_limb_numb(2 * l_size, l_mod_count) ?
mul_limb_numb(l_size) : mod_limb_numb(2 * l_size, l_mod_count);
l_tmp = OPENSSL_malloc(l_tmp_count * LIMB_BYTE_SIZE);
}
if ((l_ret == NULL) || (l_tmp == NULL))
goto err;
if (blinding->m_ctx != NULL) {
limb_mul(l_ret, l_im, l_mul, l_size, l_tmp);
mod_montgomery(l_ret, l_ret, 2 * l_size, l_mod, l_mod_count,
blinding->m_ctx->n0[0], l_tmp);
} else {
limb_mul(l_ret, l_im, l_mul, l_size, l_tmp);
mod(l_ret, l_ret, 2 * l_size, l_mod, l_mod_count, l_tmp);
}
/* modulus size in bytes can be equal to num but after limbs conversion it becomes bigger */
if (num < BN_num_bytes(to_mod)) {
BNerr(BN_F_OSSL_BN_RSA_DO_UNBLIND, ERR_R_PASSED_INVALID_ARGUMENT);
goto err;
}
memset(buf, 0, num);
tmp = buf + num - BN_num_bytes(to_mod);
for (i = 0; i < l_mod_count; i++) {
#if LIMB_BYTE_SIZE == 8
l_buf = be64(l_ret[i]);
#else
l_buf = be32(l_ret[i]);
#endif
if (i == 0) {
int delta = LIMB_BYTE_SIZE - ((l_mod_count * LIMB_BYTE_SIZE) - num);
memcpy(tmp, ((char *)&l_buf) + LIMB_BYTE_SIZE - delta, delta);
tmp += delta;
} else {
memcpy(tmp, &l_buf, LIMB_BYTE_SIZE);
tmp += LIMB_BYTE_SIZE;
}
}
ret = num;
err:
OPENSSL_free(l_im);
OPENSSL_free(l_mul);
OPENSSL_free(l_mod);
OPENSSL_free(l_tmp);
OPENSSL_free(l_ret);
return ret;
}
