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cosmopolitan/third_party/mbedtls/bignum.c
Jōshin e16a7d8f3b
flip et / noet in modelines 
`et` means `expandtab`.

```sh
rg 'vi: .* :vi' -l -0 | \
  xargs -0 sed -i '' 's/vi: \(.*\) et\(.*\)  :vi/vi: \1 xoet\2:vi/'
rg 'vi: .*  :vi' -l -0 | \
  xargs -0 sed -i '' 's/vi: \(.*\)noet\(.*\):vi/vi: \1et\2  :vi/'
rg 'vi: .*  :vi' -l -0 | \
  xargs -0 sed -i '' 's/vi: \(.*\)xoet\(.*\):vi/vi: \1noet\2:vi/'
```
2023-12-07 22:17:11 -05:00

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/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:4;coding:utf-8 -*-│
│ vi: set et ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi │
╞══════════════════════════════════════════════════════════════════════════════╡
│ Copyright The Mbed TLS Contributors │
│ │
│ Licensed under the Apache License, Version 2.0 (the "License"); │
│ you may not use this file except in compliance with the License. │
│ You may obtain a copy of the License at │
│ │
│ http://www.apache.org/licenses/LICENSE-2.0 │
│ │
│ Unless required by applicable law or agreed to in writing, software │
│ distributed under the License is distributed on an "AS IS" BASIS, │
│ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. │
│ See the License for the specific language governing permissions and │
│ limitations under the License. │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "third_party/mbedtls/bignum.h"
#include "libc/serialize.h"
#include "libc/intrin/bsf.h"
#include "libc/intrin/bswap.h"
#include "libc/macros.internal.h"
#include "libc/nexgen32e/nexgen32e.h"
#include "libc/nexgen32e/x86feature.h"
#include "libc/runtime/runtime.h"
#include "libc/str/str.h"
#include "third_party/mbedtls/bignum_internal.h"
#include "third_party/mbedtls/chk.h"
#include "third_party/mbedtls/common.h"
#include "third_party/mbedtls/error.h"
#include "third_party/mbedtls/fastdiv.h"
#include "third_party/mbedtls/math.h"
#include "third_party/mbedtls/platform.h"
#include "third_party/mbedtls/profile.h"
#include "third_party/mbedtls/select.h"
asm(".ident\t\"\\n\\n\
Mbed TLS (Apache 2.0)\\n\
Copyright ARM Limited\\n\
Copyright Mbed TLS Contributors\"");
asm(".include \"libc/disclaimer.inc\"");
/**
* @fileoverview Big Numbers.
*
* The following sources were referenced in the design of this
* Multi-precision Integer library:
*
* [1] Handbook of Applied Cryptography - 1997
* Menezes, van Oorschot and Vanstone
*
* [2] Multi-Precision Math
* Tom St Denis
* https://github.com/libtom/libtommath/blob/develop/tommath.pdf
*
* [3] GNU Multi-Precision Arithmetic Library
* https://gmplib.org/manual/index.html
*/
#if defined(MBEDTLS_BIGNUM_C)
/* Implementation that should never be optimized out by the compiler */
static inline void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n )
{
mbedtls_platform_zeroize( v, ciL * n );
}
/**
* \brief This function frees the components of an MPI context.
*
* \param X The MPI context to be cleared. This may be \c NULL,
* in which case this function is a no-op. If it is
* not \c NULL, it must point to an initialized MPI.
*/
void mbedtls_mpi_free( mbedtls_mpi *X )
{
if( !X )
return;
if( X->p )
{
mbedtls_mpi_zeroize( X->p, X->n );
mbedtls_free( X->p );
}
X->s = 1;
X->n = 0;
X->p = NULL;
}
/**
* \brief Enlarge an MPI to the specified number of limbs.
*
* \note This function does nothing if the MPI is
* already large enough.
*
* \param X The MPI to grow. It must be initialized.
* \param nblimbs The target number of limbs.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs)
{
mbedtls_mpi_uint *p;
MPI_VALIDATE_RET(X);
if (nblimbs > MBEDTLS_MPI_MAX_LIMBS)
return MBEDTLS_ERR_MPI_ALLOC_FAILED;
if (nblimbs > X->n)
{
if (X->p && (p = realloc_in_place(X->p, nblimbs * ciL)))
{
mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n);
}
else
{
if (!(p = malloc(nblimbs * ciL)))
return MBEDTLS_ERR_MPI_ALLOC_FAILED;
if (X->p)
{
memcpy(p, X->p, X->n * ciL);
mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n);
mbedtls_mpi_zeroize(X->p, X->n);
free(X->p);
}
else
{
mbedtls_mpi_zeroize(p, nblimbs);
}
}
X->n = nblimbs;
X->p = p;
}
return 0;
}
/**
* \brief This function resizes an MPI to a number of limbs.
*
* \param X The MPI to resize. This must point to an initialized MPI.
* \param n The minimum number of limbs to keep.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
* which can only happen when resizing up
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_resize(mbedtls_mpi *X, size_t n)
{
mbedtls_mpi_uint *p;
MPI_VALIDATE_RET(X);
if (X->n == n)
return 0;
if (X->n <= n)
return mbedtls_mpi_grow(X, n);
if (n > MBEDTLS_MPI_MAX_LIMBS)
return MBEDTLS_ERR_MPI_ALLOC_FAILED;
mbedtls_mpi_zeroize(X->p + n, X->n - n);
if (!realloc_in_place(X->p, n * ciL))
{
if (!(p = malloc(n * ciL)))
return MBEDTLS_ERR_MPI_ALLOC_FAILED;
memcpy(p, X->p, n * ciL);
mbedtls_mpi_zeroize(X->p, n);
free(X->p);
X->p = p;
}
X->n = n;
return 0;
}
/**
* \brief This function resizes an MPI downwards, keeping at
* least the specified number of limbs.
*
* If \c X is smaller than \c nblimbs, it is resized up
* instead.
*
* \param X The MPI to shrink. This must point to an initialized MPI.
* \param nblimbs The minimum number of limbs to keep.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
* which can only happen when resizing up
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs)
{
MPI_VALIDATE_RET(X);
if (X->n <= nblimbs) return mbedtls_mpi_grow(X, nblimbs);
return mbedtls_mpi_resize(X, MAX(MAX(1, nblimbs), mbedtls_mpi_limbs(X)));
}
/**
* \brief Make a copy of an MPI.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param Y The source MPI. This must point to an initialized MPI.
*
* \note The limb-buffer in the destination MPI is enlarged
* if necessary to hold the value in the source MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_copy( mbedtls_mpi *X, const mbedtls_mpi *Y )
{
int ret = 0;
size_t i;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( Y );
if( X == Y )
return( 0 );
if( Y->n == 0 )
{
mbedtls_mpi_free( X );
return( 0 );
}
for( i = Y->n - 1; i > 0; i-- )
if( Y->p[i] != 0 )
break;
i++;
X->s = Y->s;
if( X->n < i )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i ) );
}
else
{
mbedtls_platform_zeroize( X->p + i, ( X->n - i ) * ciL );
}
memcpy( X->p, Y->p, i * ciL );
cleanup:
return( ret );
}
/**
* \brief Swap the contents of two MPIs.
*
* \param X The first MPI. It must be initialized.
* \param Y The second MPI. It must be initialized.
*/
void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
{
mbedtls_mpi T;
MPI_VALIDATE( X );
MPI_VALIDATE( Y );
memcpy( &T, X, sizeof( mbedtls_mpi ) );
memcpy( X, Y, sizeof( mbedtls_mpi ) );
memcpy( Y, &T, sizeof( mbedtls_mpi ) );
}
/**
* \brief Perform a safe conditional copy of MPI which doesn't
* reveal whether the condition was true or not.
*
* \param X The MPI to conditionally assign to. This must point
* to an initialized MPI.
* \param Y The MPI to be assigned from. This must point to an
* initialized MPI.
* \param assign The condition deciding whether to perform the
* assignment or not. Possible values:
* * \c 1: Perform the assignment `X = Y`.
* * \c 0: Keep the original value of \p X.
*
* \note This function is equivalent to
* `if( assign ) mbedtls_mpi_copy( X, Y );`
* except that it avoids leaking any information about whether
* the assignment was done or not (the above code may leak
* information through branch prediction and/or memory access
* patterns analysis).
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X,
const mbedtls_mpi *Y,
unsigned char assign)
{
int ret = 0;
size_t i;
MPI_VALIDATE_RET(X);
MPI_VALIDATE_RET(Y);
/* make sure assign is 0 or 1 in a time-constant manner */
if (Y->n > X->n)
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
assign = (assign | (unsigned char)-assign) >> 7;
X->s = Select(Y->s, X->s, -assign);
for (i = 0; i < Y->n; i++)
X->p[i] = Select(Y->p[i], X->p[i], -assign);
for (i = Y->n; i < X->n; i++)
X->p[i] &= __conceal("r", assign - 1);
cleanup:
return( ret );
}
/**
* \brief Perform a safe conditional swap which doesn't
* reveal whether the condition was true or not.
*
* \param X The first MPI. This must be initialized.
* \param Y The second MPI. This must be initialized.
* \param assign The condition deciding whether to perform
* the swap or not. Possible values:
* * \c 1: Swap the values of \p X and \p Y.
* * \c 0: Keep the original values of \p X and \p Y.
*
* \note This function is equivalent to
* if( assign ) mbedtls_mpi_swap( X, Y );
* except that it avoids leaking any information about whether
* the assignment was done or not (the above code may leak
* information through branch prediction and/or memory access
* patterns analysis).
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*
*/
int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap )
{
int ret, s;
size_t i;
mbedtls_mpi_uint tmp;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( Y );
if( X == Y )
return( 0 );
/* make sure swap is 0 or 1 in a time-constant manner */
swap = (swap | (unsigned char)-swap) >> 7;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( Y, X->n ) );
s = X->s;
X->s = X->s * ( 1 - swap ) + Y->s * swap;
Y->s = Y->s * ( 1 - swap ) + s * swap;
for( i = 0; i < X->n; i++ )
{
tmp = X->p[i];
X->p[i] = X->p[i] * ( 1 - swap ) + Y->p[i] * swap;
Y->p[i] = Y->p[i] * ( 1 - swap ) + tmp * swap;
}
cleanup:
return( ret );
}
/**
* \brief Store integer value in MPI.
*
* \param X The MPI to set. This must be initialized.
* \param z The value to use.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
MPI_VALIDATE_RET( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
mbedtls_platform_zeroize( X->p, X->n * ciL );
X->p[0] = ( z < 0 ) ? -z : z;
X->s = ( z < 0 ) ? -1 : 1;
cleanup:
return( ret );
}
/**
* \brief Get a specific bit from an MPI.
*
* \param X The MPI to query. This must be initialized.
* \param pos Zero-based index of the bit to query.
*
* \return \c 0 or \c 1 on success, depending on whether bit \c pos
* of \c X is unset or set.
* \return A negative error code on failure.
*/
int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos )
{
MPI_VALIDATE_RET( X );
if( X->n * biL <= pos )
return( 0 );
return( ( X->p[pos / biL] >> ( pos % biL ) ) & 0x01 );
}
/* Get a specific byte, without range checks. */
#define GET_BYTE( X, i ) \
( ( ( X )->p[( i ) / ciL] >> ( ( ( i ) % ciL ) * 8 ) ) & 0xff )
/**
* \brief Modify a specific bit in an MPI.
*
* \note This function will grow the target MPI if necessary to set a
* bit to \c 1 in a not yet existing limb. It will not grow if
* the bit should be set to \c 0.
*
* \param X The MPI to modify. This must be initialized.
* \param pos Zero-based index of the bit to modify.
* \param val The desired value of bit \c pos: \c 0 or \c 1.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_set_bit( mbedtls_mpi *X, size_t pos, unsigned char val )
{
int ret = 0;
size_t off = pos / biL;
size_t idx = pos % biL;
MPI_VALIDATE_RET( X );
if( val != 0 && val != 1 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
if( X->n * biL <= pos )
{
if( !val )
return( 0 );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, off + 1 ) );
}
X->p[off] &= ~( (mbedtls_mpi_uint) 0x01 << idx );
X->p[off] |= (mbedtls_mpi_uint) val << idx;
cleanup:
return( ret );
}
/**
* \brief Return the number of bits of value \c 0 before the
* least significant bit of value \c 1.
*
* \note This is the same as the zero-based index of
* the least significant bit of value \c 1.
*
* \param X The MPI to query.
*
* \return The number of bits of value \c 0 before the least significant
* bit of value \c 1 in \p X.
*/
size_t mbedtls_mpi_lsb( const mbedtls_mpi *X )
{
size_t i, count = 0;
MBEDTLS_INTERNAL_VALIDATE_RET(X, 0);
for( i = 0; i < X->n; i++ )
{
if ( X->p[i] )
return count + __builtin_ctzll(X->p[i]);
else
count += biL;
}
return 0;
}
/*
* Count leading zero bits in a given integer
*/
static inline size_t mbedtls_clz( const mbedtls_mpi_uint x )
{
return x ? __builtin_clzll(x) : biL;
}
/**
* \brief Return the number of bits up to and including the most
* significant bit of value \c 1.
*
* \note This is same as the one-based index of the most
* significant bit of value \c 1.
*
* \param X The MPI to query. This must point to an initialized MPI.
*
* \return The number of bits up to and including the most
* significant bit of value \c 1.
*/
size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X)
{
size_t n;
n = mbedtls_mpi_limbs(X);
if (!n) return 0;
return biL - __builtin_clzll(X->p[n - 1]) + (n - 1) * biL;
}
/**
* \brief Return the total size of an MPI value in bytes.
*
* \param X The MPI to use. This must point to an initialized MPI.
*
* \note The value returned by this function may be less than
* the number of bytes used to store \p X internally.
* This happens if and only if there are trailing bytes
* of value zero.
*
* \return The least number of bytes capable of storing
* the absolute value of \p X.
*/
size_t mbedtls_mpi_size( const mbedtls_mpi *X )
{
return( ( mbedtls_mpi_bitlen( X ) + 7 ) >> 3 );
}
/*
* Convert an ASCII character to digit value
*/
static int mpi_get_digit( mbedtls_mpi_uint *d, int radix, char c )
{
*d = 255;
if( c >= 0x30 && c <= 0x39 ) *d = c - 0x30;
if( c >= 0x41 && c <= 0x46 ) *d = c - 0x37;
if( c >= 0x61 && c <= 0x66 ) *d = c - 0x57;
if( *d >= (mbedtls_mpi_uint) radix )
return( MBEDTLS_ERR_MPI_INVALID_CHARACTER );
return( 0 );
}
/**
* \brief Import an MPI from an ASCII string.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param radix The numeric base of the input string.
* \param s Null-terminated string buffer.
*
* \return \c 0 if successful.
* \return A negative error code on failure.
*/
int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
size_t i, j, slen, n;
mbedtls_mpi_uint d;
mbedtls_mpi T;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( s );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
mbedtls_mpi_init( &T );
slen = strlen( s );
if( radix == 16 )
{
if( slen > MPI_SIZE_T_MAX >> 2 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
n = BITS_TO_LIMBS( slen << 2 );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, n ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = slen, j = 0; i > 0; i--, j++ )
{
if( i == 1 && s[i - 1] == '-' )
{
X->s = -1;
break;
}
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i - 1] ) );
X->p[j / ( 2 * ciL )] |= d << ( ( j % ( 2 * ciL ) ) << 2 );
}
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = 0; i < slen; i++ )
{
if( i == 0 && s[i] == '-' )
{
X->s = -1;
continue;
}
MBEDTLS_MPI_CHK( mpi_get_digit( &d, radix, s[i] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T, X, radix ) );
if( X->s == 1 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, &T, d ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, &T, d ) );
}
}
}
cleanup:
mbedtls_mpi_free( &T );
return( ret );
}
/*
* Helper to write the digits high-order first.
*/
static int mpi_write_hlp( mbedtls_mpi *X, int radix,
char **p, const size_t buflen )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
mbedtls_mpi_uint r;
size_t length = 0;
char *p_end = *p + buflen;
do
{
if( length >= buflen )
{
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, radix ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_div_int( X, NULL, X, radix ) );
/*
* Write the residue in the current position, as an ASCII character.
*/
if( r < 0xA )
*(--p_end) = (char)( '0' + r );
else
*(--p_end) = (char)( 'A' + ( r - 0xA ) );
length++;
} while( mbedtls_mpi_cmp_int( X, 0 ) != 0 );
memmove( *p, p_end, length );
*p += length;
cleanup:
return( ret );
}
/**
* \brief Export an MPI to an ASCII string.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param radix The numeric base of the output string.
* \param buf The buffer to write the string to. This must be writable
* buffer of length \p buflen Bytes.
* \param buflen The available size in Bytes of \p buf.
* \param olen The address at which to store the length of the string
* written, including the final \c NULL byte. This must
* not be \c NULL.
*
* \note You can call this function with `buflen == 0` to obtain the
* minimum required buffer size in `*olen`.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf
* is too small to hold the value of \p X in the desired base.
* In this case, `*olen` is nonetheless updated to contain the
* size of \p buf required for a successful call.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
char *buf, size_t buflen, size_t *olen )
{
int ret = 0;
size_t n;
char *p;
mbedtls_mpi T;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( olen );
MPI_VALIDATE_RET( buflen == 0 || buf );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
n = mbedtls_mpi_bitlen( X ); /* Number of bits necessary to present `n`. */
if( radix >= 4 ) n >>= 1; /* Number of 4-adic digits necessary to present
* `n`. If radix > 4, this might be a strict
* overapproximation of the number of
* radix-adic digits needed to present `n`. */
if( radix >= 16 ) n >>= 1; /* Number of hexadecimal digits necessary to
* present `n`. */
n += 1; /* Terminating null byte */
n += 1; /* Compensate for the divisions above, which round down `n`
* in case it's not even. */
n += 1; /* Potential '-'-sign. */
n += ( n & 1 ); /* Make n even to have enough space for hexadecimal writing,
* which always uses an even number of hex-digits. */
if( buflen < n )
{
*olen = n;
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
}
p = buf;
mbedtls_mpi_init( &T );
if( X->s == -1 )
{
*p++ = '-';
buflen--;
}
if( radix == 16 )
{
int c;
size_t i, j, k;
for( i = X->n, k = 0; i > 0; i-- )
{
for( j = ciL; j > 0; j-- )
{
c = ( X->p[i - 1] >> ( ( j - 1 ) << 3) ) & 0xFF;
if( c == 0 && k == 0 && ( i + j ) != 2 )
continue;
*(p++) = "0123456789ABCDEF" [c / 16];
*(p++) = "0123456789ABCDEF" [c % 16];
k = 1;
}
}
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T, X ) );
if( T.s == -1 )
T.s = 1;
MBEDTLS_MPI_CHK( mpi_write_hlp( &T, radix, &p, buflen ) );
}
*p++ = '\0';
*olen = p - buf;
cleanup:
mbedtls_mpi_free( &T );
return( ret );
}
#if defined(MBEDTLS_FS_IO)
/**
* \brief Read an MPI from a line in an opened file.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param radix The numeric base of the string representation used
* in the source line.
* \param fin The input file handle to use. This must not be \c NULL.
*
* \note On success, this function advances the file stream
* to the end of the current line or to EOF.
*
* The function returns \c 0 on an empty line.
*
* Leading whitespaces are ignored, as is a
* '0x' prefix for radix \c 16.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer
* is too small.
* \return Another negative error code on failure.
*/
int mbedtls_mpi_read_file( mbedtls_mpi *X, int radix, FILE *fin )
{
mbedtls_mpi_uint d;
size_t slen;
char *p;
/*
* Buffer should have space for (short) label and decimal formatted MPI,
* newline characters and '\0'
*/
char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( fin );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
mbedtls_platform_zeroize( s, sizeof( s ) );
if( fgets( s, sizeof( s ) - 1, fin ) == NULL )
return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
slen = strlen( s );
if( slen == sizeof( s ) - 2 )
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
if( slen > 0 && s[slen - 1] == '\n' ) { slen--; s[slen] = '\0'; }
if( slen > 0 && s[slen - 1] == '\r' ) { slen--; s[slen] = '\0'; }
p = s + slen;
while( p-- > s )
if( mpi_get_digit( &d, radix, *p ) != 0 )
break;
return( mbedtls_mpi_read_string( X, radix, p + 1 ) );
}
/**
* \brief Export an MPI into an opened file.
*
* \param p A string prefix to emit prior to the MPI data.
* For example, this might be a label, or "0x" when
* printing in base \c 16. This may be \c NULL if no prefix
* is needed.
* \param X The source MPI. This must point to an initialized MPI.
* \param radix The numeric base to be used in the emitted string.
* \param fout The output file handle. This may be \c NULL, in which case
* the output is written to \c stdout.
*
* \return \c 0 if successful.
* \return A negative error code on failure.
*/
int mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X, int radix, FILE *fout )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
size_t n, slen, plen;
/*
* Buffer should have space for (short) label and decimal formatted MPI,
* newline characters and '\0'
*/
char s[ MBEDTLS_MPI_RW_BUFFER_SIZE ];
MPI_VALIDATE_RET( X );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
mbedtls_platform_zeroize( s, sizeof( s ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_write_string( X, radix, s, sizeof( s ) - 2, &n ) );
if( p == NULL ) p = "";
plen = strlen( p );
slen = strlen( s );
s[slen++] = '\r';
s[slen++] = '\n';
if( fout )
{
if( fwrite( p, 1, plen, fout ) != plen ||
fwrite( s, 1, slen, fout ) != slen )
return( MBEDTLS_ERR_MPI_FILE_IO_ERROR );
}
else
mbedtls_printf( "%s%s", p, s );
cleanup:
return( ret );
}
#endif /* MBEDTLS_FS_IO */
#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
#define mpi_uint_bigendian_to_host(x) (x)
#elif __SIZEOF_LONG__ == 8
#define mpi_uint_bigendian_to_host(x) __builtin_bswap64(x)
#elif __SIZEOF_LONG__ == 4
#define mpi_uint_bigendian_to_host(x) __builtin_bswap32(x)
#endif
static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs )
{
mbedtls_mpi_uint *cur_limb_left;
mbedtls_mpi_uint *cur_limb_right;
if( !limbs )
return;
/*
* Traverse limbs and
* - adapt byte-order in each limb
* - swap the limbs themselves.
* For that, simultaneously traverse the limbs from left to right
* and from right to left, as long as the left index is not bigger
* than the right index (it's not a problem if limbs is odd and the
* indices coincide in the last iteration).
*/
for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 );
cur_limb_left <= cur_limb_right;
cur_limb_left++, cur_limb_right-- )
{
mbedtls_mpi_uint tmp;
/* Note that if cur_limb_left == cur_limb_right,
* this code effectively swaps the bytes only once. */
tmp = mpi_uint_bigendian_to_host( *cur_limb_left );
*cur_limb_left = mpi_uint_bigendian_to_host( *cur_limb_right );
*cur_limb_right = tmp;
}
}
/**
* \brief Import X from unsigned binary data, little endian
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param p The input buffer with \p n bytes.
* \param n The length of the input buffer \p p in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, const unsigned char *p, size_t n)
{
int ret;
size_t i;
mbedtls_mpi_uint w;
MPI_VALIDATE_RET(X);
MPI_VALIDATE_RET(!n || p);
if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n))))) return ret;
if (n) {
for (i = 0; i + 8 <= n; i += 8)
X->p[i / ciL] = READ64LE(p + i);
if (i < n) {
w = 0;
do {
w <<= 8;
w |= p[i];
} while (++i < n);
X->p[i / ciL] = w;
}
} else {
X->p[0] = 0;
}
X->s = 1;
return 0;
}
/**
* \brief Import an MPI from unsigned big endian binary data.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param p The input buffer. This must be a readable buffer of length
* \p n Bytes.
* \param n The length of the input buffer \p p in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *p, size_t n)
{
int ret;
size_t i, j, k;
mbedtls_mpi_uint w;
MPI_VALIDATE_RET(X);
MPI_VALIDATE_RET(!n || p);
if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n)))))
return ret;
if (n)
{
for (j = 0, i = n; i >= 8; i -= 8)
X->p[j++] = READ64BE(p + i - ciL);
if (i)
{
k = 0;
w = 0;
do
{
--i;
w <<= 8;
w |= p[k++];
} while (i);
X->p[j] = w;
}
}
else
{
X->p[0] = 0;
}
X->s = 1;
return 0;
}
/**
* \brief Export X into unsigned binary data, little endian.
* Always fills the whole buffer, which will end with zeros
* if the number is smaller.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param buf The output buffer. This must be a writable buffer of length
* \p buflen Bytes.
* \param buflen The size of the output buffer \p buf in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
* large enough to hold the value of \p X.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_binary_le( const mbedtls_mpi *X,
unsigned char *buf, size_t buflen )
{
size_t stored_bytes = X->n * ciL;
size_t bytes_to_copy;
size_t i;
if( stored_bytes < buflen )
{
bytes_to_copy = stored_bytes;
}
else
{
bytes_to_copy = buflen;
/* The output buffer is smaller than the allocated size of X.
* However X may fit if its leading bytes are zero. */
for( i = bytes_to_copy; i < stored_bytes; i++ )
{
if( GET_BYTE( X, i ) != 0 )
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
}
}
for( i = 0; i < bytes_to_copy; i++ )
buf[i] = GET_BYTE( X, i );
if( stored_bytes < buflen )
{
/* Write trailing 0 bytes */
mbedtls_platform_zeroize( buf + stored_bytes, buflen - stored_bytes );
}
return( 0 );
}
/**
* \brief Export X into unsigned binary data, big endian.
* Always fills the whole buffer, which will start with zeros
* if the number is smaller.
*
* \param X The source MPI. This must point to an initialized MPI.
* \param buf The output buffer. This must be a writable buffer of length
* \p buflen Bytes.
* \param buflen The size of the output buffer \p buf in Bytes.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
* large enough to hold the value of \p X.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_write_binary( const mbedtls_mpi *X,
unsigned char *buf, size_t buflen )
{
size_t stored_bytes;
size_t bytes_to_copy;
unsigned char *p;
size_t i;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( buflen == 0 || buf );
stored_bytes = X->n * ciL;
if( stored_bytes < buflen )
{
/* There is enough space in the output buffer. Write initial
* null bytes and record the position at which to start
* writing the significant bytes. In this case, the execution
* trace of this function does not depend on the value of the
* number. */
bytes_to_copy = stored_bytes;
p = buf + buflen - stored_bytes;
mbedtls_platform_zeroize( buf, buflen - stored_bytes );
}
else
{
/* The output buffer is smaller than the allocated size of X.
* However X may fit if its leading bytes are zero. */
bytes_to_copy = buflen;
p = buf;
for( i = bytes_to_copy; i < stored_bytes; i++ )
{
if( GET_BYTE( X, i ) != 0 )
return( MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL );
}
}
for( i = 0; i < bytes_to_copy; i++ )
p[bytes_to_copy - i - 1] = GET_BYTE( X, i );
return( 0 );
}
/**
* \brief Compare the absolute values of two MPIs.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param Y The right-hand MPI. This must point to an initialized MPI.
*
* \return \c 1 if `|X|` is greater than `|Y|`.
* \return \c -1 if `|X|` is lesser than `|Y|`.
* \return \c 0 if `|X|` is equal to `|Y|`.
*/
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
size_t i, j;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( Y );
i = mbedtls_mpi_limbs(X);
j = mbedtls_mpi_limbs(Y);
if( !i && !j )
return( 0 );
if( i > j ) return( 1 );
if( j > i ) return( -1 );
for( ; i > 0; i-- )
{
if( X->p[i - 1] > Y->p[i - 1] ) return( 1 );
if( X->p[i - 1] < Y->p[i - 1] ) return( -1 );
}
return( 0 );
}
/**
* \brief Compare two MPIs.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param Y The right-hand MPI. This must point to an initialized MPI.
*
* \return \c 1 if \p X is greater than \p Y.
* \return \c -1 if \p X is lesser than \p Y.
* \return \c 0 if \p X is equal to \p Y.
*/
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y )
{
size_t i, j;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( Y );
i = mbedtls_mpi_limbs(X);
j = mbedtls_mpi_limbs(Y);
if( !i && !j )
return( 0 );
if( i > j ) return( X->s );
if( j > i ) return( -Y->s );
if( X->s > 0 && Y->s < 0 ) return( 1 );
if( Y->s > 0 && X->s < 0 ) return( -1 );
for( ; i > 0; i-- )
{
if( X->p[i - 1] > Y->p[i - 1] ) return( X->s );
if( X->p[i - 1] < Y->p[i - 1] ) return( -X->s );
}
return( 0 );
}
/**
* Decide if an integer is less than the other, without branches.
*
* \param x First integer.
* \param y Second integer.
*
* \return 1 if \p x is less than \p y, 0 otherwise
*/
static unsigned ct_lt_mpi_uint( const mbedtls_mpi_uint x,
const mbedtls_mpi_uint y )
{
mbedtls_mpi_uint ret;
mbedtls_mpi_uint cond;
/*
* Check if the most significant bits (MSB) of the operands are different.
*/
cond = ( x ^ y );
/*
* If the MSB are the same then the difference x-y will be negative (and
* have its MSB set to 1 during conversion to unsigned) if and only if x<y.
*/
ret = ( x - y ) & ~cond;
/*
* If the MSB are different, then the operand with the MSB of 1 is the
* bigger. (That is if y has MSB of 1, then x<y is true and it is false if
* the MSB of y is 0.)
*/
ret |= y & cond;
ret = ret >> ( biL - 1 );
return (unsigned) ret;
}
/**
* \brief Check if an MPI is less than the other in constant time.
*
* \param X The left-hand MPI. This must point to an initialized MPI
* with the same allocated length as Y.
* \param Y The right-hand MPI. This must point to an initialized MPI
* with the same allocated length as X.
* \param ret The result of the comparison:
* \c 1 if \p X is less than \p Y.
* \c 0 if \p X is greater than or equal to \p Y.
*
* \return 0 on success.
* \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of
* the two input MPIs is not the same.
*/
int mbedtls_mpi_lt_mpi_ct( const mbedtls_mpi *X, const mbedtls_mpi *Y,
unsigned *ret )
{
size_t i;
/* The value of any of these variables is either 0 or 1 at all times. */
unsigned cond, done, X_is_negative, Y_is_negative;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( Y );
MPI_VALIDATE_RET( ret );
if( X->n != Y->n )
return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
/*
* Set sign_N to 1 if N >= 0, 0 if N < 0.
* We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0.
*/
X_is_negative = ( X->s & 2 ) >> 1;
Y_is_negative = ( Y->s & 2 ) >> 1;
/*
* If the signs are different, then the positive operand is the bigger.
* That is if X is negative (X_is_negative == 1), then X < Y is true and it
* is false if X is positive (X_is_negative == 0).
*/
cond = ( X_is_negative ^ Y_is_negative );
*ret = cond & X_is_negative;
/*
* This is a constant-time function. We might have the result, but we still
* need to go through the loop. Record if we have the result already.
*/
done = cond;
for( i = X->n; i > 0; i-- )
{
/*
* If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both
* X and Y are negative.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = ct_lt_mpi_uint( Y->p[i - 1], X->p[i - 1] );
*ret |= cond & ( 1 - done ) & X_is_negative;
done |= cond;
/*
* If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both
* X and Y are positive.
*
* Again even if we can make a decision, we just mark the result and
* the fact that we are done and continue looping.
*/
cond = ct_lt_mpi_uint( X->p[i - 1], Y->p[i - 1] );
*ret |= cond & ( 1 - done ) & ( 1 - X_is_negative );
done |= cond;
}
return( 0 );
}
/**
* \brief Compare an MPI with an integer.
*
* \param X The left-hand MPI. This must point to an initialized MPI.
* \param z The integer value to compare \p X to.
*
* \return \c 1 if \p X is greater than \p z.
* \return \c -1 if \p X is lesser than \p z.
* \return \c 0 if \p X is equal to \p z.
*/
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
{
mbedtls_mpi Y;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( X );
*p = ( z < 0 ) ? -z : z;
Y.s = ( z < 0 ) ? -1 : 1;
Y.n = 1;
Y.p = p;
return( mbedtls_mpi_cmp_mpi( X, &Y ) );
}
/**
* \brief Perform an unsigned addition of MPIs: X = |A| + |B|
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param B The second summand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
size_t i, j;
mbedtls_mpi_uint *o, *p, c, tmp;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
if( X == B )
{
const mbedtls_mpi *T = A; A = X; B = T;
}
if( X != A )
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
/*
* X should always be positive as a result of unsigned additions.
*/
X->s = 1;
for( j = B->n; j > 0; j-- )
if( B->p[j - 1] != 0 )
break;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
o = B->p; p = X->p; c = 0;
/*
* tmp is used because it might happen that p == o
*/
for( i = 0; i < j; i++, o++, p++ )
{
tmp= *o;
*p += c; c = ( *p < c );
*p += tmp; c += ( *p < tmp );
}
while( c != 0 )
{
if( i >= X->n )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
p = X->p + i;
}
*p += c; c = ( *p < c ); i++; p++;
}
cleanup:
return( ret );
}
/**
* Helper for mbedtls_mpi subtraction.
*
* Calculate d = a - b where d, a, and b have the same size.
* This function operates modulo (2^ciL)^n and returns the carry
* (1 if there was a wraparound, i.e. if `a < b`, and 0 otherwise).
*
* \param[out] d Result of subtraction.
* \param[in] a Left operand.
* \param[in] b Right operand.
* \param n Number of limbs of \p a and \p b.
* \return 1 if `d < s`.
* 0 if `d >= s`.
*/
forceinline mbedtls_mpi_uint mpi_sub_hlp(mbedtls_mpi_uint *d,
const mbedtls_mpi_uint *a,
const mbedtls_mpi_uint *b,
size_t n)
{
size_t i;
unsigned char cf;
mbedtls_mpi_uint c, x;
(void)x;
(void)cf;
cf = c = i = 0;
#if defined(__x86_64__) && !defined(__STRICT_ANSI__)
if (!n) return 0;
asm volatile("xor\t%1,%1\n\t"
".align\t16\n1:\t"
"mov\t(%5,%3,8),%1\n\t"
"sbb\t(%6,%3,8),%1\n\t"
"mov\t%1,(%4,%3,8)\n\t"
"lea\t1(%3),%3\n\t"
"dec\t%2\n\t"
"jnz\t1b"
: "=@ccb"(cf), "=&r"(x), "+&c"(n), "=&r"(i)
: "r"(d), "r"(a), "r"(b), "3"(0)
: "cc", "memory");
return cf;
#else
for (; i < n; ++i)
SBB(d[i], a[i], b[i], c, c);
return c;
#endif
}
/**
* \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param B The subtrahend. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
size_t n, m, r;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
if( X != A && !B->n )
return mbedtls_mpi_copy( X, A ); /* wut */
for( n = B->n; n > 0; n-- )
if( B->p[n - 1] != 0 )
break;
if( n > A->n )
return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* B >= (2^ciL)^n > A */
if (X != A)
{
if (X->n < A->n) {
if ((r = mbedtls_mpi_grow(X, A->n))) return r;
} else if (X->n > A->n) {
mbedtls_mpi_zeroize(X->p + A->n, X->n - A->n);
}
if ((m = A->n - n))
memcpy(X->p + n, A->p + n, m * ciL);
}
/*
* X should always be positive as a result of unsigned subtractions.
*/
X->s = 1;
if( mpi_sub_hlp( X->p, A->p, B->p, n ) ){
/* Propagate the carry to the first nonzero limb of X. */
for( ; n < A->n && A->p[n] == 0; n++ )
/* --X->p[n]; */
X->p[n] = A->p[n] - 1;
/* If we ran out of space for the carry, it means that the result
* is negative. */
if( n == X->n )
return MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
--X->p[n];
}
return( 0 );
}
static int mpi_cmp_abs(const mbedtls_mpi *X,
const mbedtls_mpi *Y,
size_t *Xn,
size_t *Yn)
{
size_t i, j;
i = mbedtls_mpi_limbs(X);
j = mbedtls_mpi_limbs(Y);
*Xn = i;
*Yn = j;
if (!i && !j) return 0;
if (i > j) return 1;
if (j > i) return -1;
for (; i > 0; i--)
{
if (X->p[i - 1] > Y->p[i - 1]) return 1;
if (X->p[i - 1] < Y->p[i - 1]) return -1;
}
return 0;
}
static int mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, size_t n )
{
size_t m, r;
if( X != A && !B->n )
return mbedtls_mpi_copy( X, A ); /* wut */
if( n > A->n )
return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* B >= (2^ciL)^n > A */
if (X != A)
{
if (X->n < A->n) {
if ((r = mbedtls_mpi_grow(X, A->n))) return r;
} else if (X->n > A->n) {
mbedtls_mpi_zeroize(X->p + A->n, X->n - A->n);
}
if ((m = A->n - n))
memcpy(X->p + n, A->p + n, m * ciL);
}
/*
* X should always be positive as a result of unsigned subtractions.
*/
X->s = 1;
if( mpi_sub_hlp( X->p, A->p, B->p, n ) ){
/* Propagate the carry to the first nonzero limb of X. */
for( ; n < A->n && A->p[n] == 0; n++ )
/* --X->p[n]; */
X->p[n] = A->p[n] - 1;
/* If we ran out of space for the carry, it means that the result
* is negative. */
if( n == X->n )
return MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
--X->p[n];
}
return( 0 );
}
/**
* \brief Perform a signed addition of MPIs: X = A + B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param B The second summand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret, s;
size_t i, j;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
s = A->s;
if( A->s * B->s < 0 )
{
if( mpi_cmp_abs( A, B, &i, &j ) >= 0 )
{
MBEDTLS_MPI_CHK( mpi_sub_abs( X, A, B, j ) );
X->s = s;
}
else
{
MBEDTLS_MPI_CHK( mpi_sub_abs( X, B, A, i ) );
X->s = -s;
}
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
X->s = s;
}
cleanup:
return( ret );
}
/**
* \brief Perform a signed subtraction of MPIs: X = A - B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param B The subtrahend. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret, s;
size_t i, j;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
s = A->s;
if( A->s * B->s > 0 )
{
if( mpi_cmp_abs( A, B, &i, &j ) >= 0 )
{
MBEDTLS_MPI_CHK( mpi_sub_abs( X, A, B, j ) );
X->s = s;
}
else
{
MBEDTLS_MPI_CHK( mpi_sub_abs( X, B, A, i ) );
X->s = -s;
}
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_abs( X, A, B ) );
X->s = s;
}
cleanup:
return( ret );
}
/**
* \brief Perform a signed addition of an MPI and an integer: X = A + b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first summand. This must point to an initialized MPI.
* \param b The second summand.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mbedtls_mpi_add_mpi( X, A, &_B ) );
}
/**
* \brief Perform a signed subtraction of an MPI and an integer:
* X = A - b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The minuend. This must point to an initialized MPI.
* \param b The subtrahend.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mbedtls_mpi_sub_mpi( X, A, &_B ) );
}
/*
* Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
* mbedtls_mpi_uint divisor, d
*/
static mbedtls_mpi_uint mbedtls_int_div_int( mbedtls_mpi_uint u1,
mbedtls_mpi_uint u0,
mbedtls_mpi_uint d,
mbedtls_mpi_uint *r )
{
#if defined(__x86_64__) && !defined(__STRICT_ANSI__)
if (d && u1 < d)
{
mbedtls_mpi_uint quo, rem;
asm("div\t%2" : "=a"(quo), "=d"(rem) : "r"(d), "0"(u0), "1"(u1) : "cc");
if (r) *r = rem;
return quo;
}
else
{
if (r) *r = ~0;
return ~0;
}
#else
#if defined(MBEDTLS_HAVE_UDBL)
mbedtls_t_udbl dividend, quotient;
#else
const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
const mbedtls_mpi_uint uint_halfword_mask = ( (mbedtls_mpi_uint) 1 << biH ) - 1;
mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
mbedtls_mpi_uint u0_msw, u0_lsw;
size_t s;
#endif
/*
* Check for overflow
*/
if( 0 == d || u1 >= d )
{
if (r) *r = ~0;
return ( ~0 );
}
#if defined(MBEDTLS_HAVE_UDBL)
dividend = (mbedtls_t_udbl) u1 << biL;
dividend |= (mbedtls_t_udbl) u0;
quotient = dividend / d;
if( quotient > ( (mbedtls_t_udbl) 1 << biL ) - 1 )
quotient = ( (mbedtls_t_udbl) 1 << biL ) - 1;
if( r )
*r = (mbedtls_mpi_uint)( dividend - (quotient * d ) );
return (mbedtls_mpi_uint) quotient;
#else
/*
* Algorithm D, Section 4.3.1 - The Art of Computer Programming
* Vol. 2 - Seminumerical Algorithms, Knuth
*/
/*
* Normalize the divisor, d, and dividend, u0, u1
*/
s = mbedtls_clz( d );
d = d << s;
u1 = u1 << s;
u1 |= ( u0 >> ( biL - s ) ) & ( -(mbedtls_mpi_sint)s >> ( biL - 1 ) );
u0 = u0 << s;
d1 = d >> biH;
d0 = d & uint_halfword_mask;
u0_msw = u0 >> biH;
u0_lsw = u0 & uint_halfword_mask;
/*
* Find the first quotient and remainder
*/
q1 = u1 / d1;
r0 = u1 - d1 * q1;
while( q1 >= radix || ( q1 * d0 > radix * r0 + u0_msw ) )
{
q1 -= 1;
r0 += d1;
if ( r0 >= radix ) break;
}
rAX = ( u1 * radix ) + ( u0_msw - q1 * d );
q0 = rAX / d1;
r0 = rAX - q0 * d1;
while( q0 >= radix || ( q0 * d0 > radix * r0 + u0_lsw ) )
{
q0 -= 1;
r0 += d1;
if ( r0 >= radix ) break;
}
if (r)
*r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
quotient = q1 * radix + q0;
return quotient;
#endif
#endif
}
static inline void Multiply2x1(uint64_t a[3], uint64_t b) {
uint128_t x;
uint64_t l, h;
x = a[0];
x *= b;
l = x;
h = x >> 64;
x = a[1];
x *= b;
x += h + ((a[0] = l) < 0);
l = x;
h = x >> 64;
a[2] = h + ((a[1] = l) < 0);
}
static inline bool GreaterThan3x3(uint64_t a[3], uint64_t b[3]) {
if (a[2] > b[2]) return true;
if (a[2] < b[2]) return false;
if (a[1] > b[1]) return true;
if (a[1] < b[1]) return false;
return a[0] > b[0];
}
/**
* \brief Perform a division with remainder of two MPIs:
* A = Q * B + R
*
* \param Q The destination MPI for the quotient.
* This may be \c NULL if the value of the
* quotient is not needed.
* \param R The destination MPI for the remainder value.
* This may be \c NULL if the value of the
* remainder is not needed.
* \param A The dividend. This must point to an initialized MPi.
* \param B The divisor. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
const mbedtls_mpi *B)
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
size_t i, n, t, k;
mbedtls_mpi X, Y, Z, T1, T2;
mbedtls_mpi_uint TP2[3];
MPI_VALIDATE_RET(A);
MPI_VALIDATE_RET(B);
if (mbedtls_mpi_is_zero(B))
return MBEDTLS_ERR_MPI_DIVISION_BY_ZERO;
mbedtls_mpi_init(&X);
mbedtls_mpi_init(&Y);
mbedtls_mpi_init(&Z);
mbedtls_mpi_init(&T1);
/*
* Avoid dynamic memory allocations for constant-size T2.
*
* T2 is used for comparison only and the 3 limbs are assigned explicitly,
* so nobody increase the size of the MPI and we're safe to use an on-stack
* buffer.
*/
T2.s = 1;
T2.n = sizeof(TP2) / sizeof(*TP2);
T2.p = TP2;
if (mbedtls_mpi_cmp_abs(A, B) < 0)
{
if (Q) MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0));
if (R) MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, A));
return 0;
}
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&X, A));
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, B));
X.s = Y.s = 1;
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&Z, A->n + 2));
MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Z, 0));
MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T1, 80)); /* we need left pad hard below */
k = mbedtls_mpi_bitlen(&Y) % biL;
if (k < biL - 1)
{
k = biL - 1 - k;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&X, k));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, k));
}
else
{
k = 0;
}
n = X.n - 1;
t = Y.n - 1;
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, biL * (n - t)));
while (mbedtls_mpi_cmp_abs(&X, &Y) >= 0)
{
Z.p[n - t]++;
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&X, &X, &Y));
}
mbedtls_mpi_shift_r(&Y, biL * (n - t));
for (i = n; i > t; i--)
{
if (X.p[i] >= Y.p[t])
Z.p[i - t - 1] = ~0;
else
Z.p[i - t - 1] = mbedtls_int_div_int(X.p[i], X.p[i - 1], Y.p[t], NULL);
T2.p[0] = (i < 2) ? 0 : X.p[i - 2];
T2.p[1] = (i < 1) ? 0 : X.p[i - 1];
T2.p[2] = X.p[i];
Z.p[i - t - 1]++;
do {
Z.p[i - t - 1]--;
T1.p[0] = (t < 1) ? 0 : Y.p[t - 1];
T1.p[1] = Y.p[t];
Multiply2x1(T1.p, Z.p[i - t - 1]);
} while (GreaterThan3x3(T1.p, T2.p));
MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &Y, Z.p[i - t - 1]));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &T1));
if (X.s < 0)
{
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &Y));
MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&X, &X, &T1));
Z.p[i - t - 1]--;
}
}
if (Q)
{
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z));
Q->s = A->s * B->s;
}
if (R)
{
mbedtls_mpi_shift_r(&X, k);
X.s = A->s;
MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X));
if (mbedtls_mpi_is_zero(R)) R->s = 1;
}
cleanup:
mbedtls_mpi_free(&X);
mbedtls_mpi_free(&Y);
mbedtls_mpi_free(&Z);
mbedtls_mpi_free(&T1);
mbedtls_platform_zeroize(TP2, sizeof(TP2));
return ret;
}
/**
* \brief Perform a division with remainder of an MPI by an integer:
* A = Q * b + R
*
* \param Q The destination MPI for the quotient.
* This may be \c NULL if the value of the
* quotient is not needed.
* \param R The destination MPI for the remainder value.
* This may be \c NULL if the value of the
* remainder is not needed.
* \param A The dividend. This must point to an initialized MPi.
* \param b The divisor.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R,
const mbedtls_mpi *A,
mbedtls_mpi_sint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( A );
p[0] = ( b < 0 ) ? -b : b;
_B.s = ( b < 0 ) ? -1 : 1;
_B.n = 1;
_B.p = p;
return( mbedtls_mpi_div_mpi( Q, R, A, &_B ) );
}
/**
* \brief Perform a modular reduction. R = A mod B
*
* \param R The destination MPI for the residue value.
* This must point to an initialized MPI.
* \param A The MPI to compute the residue of.
* This must point to an initialized MPI.
* \param B The base of the modular reduction.
* This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative.
* \return Another negative error code on different kinds of failure.
*
*/
int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
MPI_VALIDATE_RET( R );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
if( mbedtls_mpi_cmp_int( B, 0 ) < 0 )
return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( NULL, R, A, B ) );
while( mbedtls_mpi_cmp_int( R, 0 ) < 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( R, R, B ) );
while( mbedtls_mpi_cmp_mpi( R, B ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( R, R, B ) );
cleanup:
return( ret );
}
/**
* \brief Perform a modular reduction with respect to an integer.
* r = A mod b
*
* \param r The address at which to store the residue.
* This must not be \c NULL.
* \param A The MPI to compute the residue of.
* This must point to an initialized MPi.
* \param b The integer base of the modular reduction.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero.
* \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b )
{
size_t i;
mbedtls_mpi_uint x, y, z;
MPI_VALIDATE_RET( r );
MPI_VALIDATE_RET( A );
if( b == 0 )
return( MBEDTLS_ERR_MPI_DIVISION_BY_ZERO );
if( b < 0 )
return( MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
/*
* handle trivial cases
*/
if( b == 1 )
{
*r = 0;
return( 0 );
}
if( b == 2 )
{
*r = A->p[0] & 1;
return( 0 );
}
/*
* general case
*/
for( i = A->n, y = 0; i > 0; i-- )
{
x = A->p[i - 1];
y = ( y << biH ) | ( x >> biH );
z = y / b;
y -= z * b;
x <<= biH;
y = ( y << biH ) | ( x >> biH );
z = y / b;
y -= z * b;
}
/*
* If A is negative, then the current y represents a negative value.
* Flipping it to the positive side.
*/
if( A->s < 0 && y != 0 )
y = b - y;
*r = y;
return( 0 );
}
/*
* 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;
x = m0;
x += ( ( m0 + 2 ) & 4 ) << 1;
for( i = biL; i >= 8; i /= 2 )
x *= ( 2 - ( m0 * x ) );
*mm = -x;
}
/**
* Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
*
* \param[in,out] A One of the numbers to multiply.
* It must have at least as many limbs as N
* (A->n >= N->n), and any limbs beyond n are ignored.
* On successful completion, A contains the result of
* the multiplication A * B * R^-1 mod N where
* R = (2^ciL)^n.
* \param[in] B One of the numbers to multiply.
* It must be nonzero and must not have more limbs than N
* (B->n <= N->n).
* \param[in] N The modulo. N must be odd.
* \param mm The value calculated by `mpi_montg_init(&mm, N)`.
* This is -N^-1 mod 2^ciL.
* \param[in,out] T A bignum for temporary storage.
* It must be at least twice the limb size of N plus 2
* (T->n >= 2 * (N->n + 1)).
* Its initial content is unused and
* its final content is indeterminate.
* Note that unlike the usual convention in the library
* for `const mbedtls_mpi*`, the content of T can change.
*/
static void mpi_montmul( mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T )
{
size_t i, n, m;
mbedtls_mpi_uint u0, u1, *d, *Ap, *Bp, *Np;
mbedtls_platform_zeroize( T->p, T->n * ciL );
d = T->p;
n = N->n;
m = ( B->n < n ) ? B->n : n;
Ap = A->p;
Bp = B->p;
Np = N->p;
for( i = 0; i < n; i++ )
{
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = Ap[i];
u1 = ( d[0] + u0 * Bp[0] ) * mm;
mbedtls_mpi_mul_hlp( m, Bp, d, u0 );
mbedtls_mpi_mul_hlp( n, Np, d, u1 );
*d++ = u0; d[n + 1] = 0;
}
/* At this point, d is either the desired result or the desired result
* plus N. We now potentially subtract N, avoiding leaking whether the
* subtraction is performed through side channels. */
/* Copy the n least significant limbs of d to A, so that
* A = d if d < N (recall that N has n limbs). */
memcpy( Ap, d, n * ciL );
/* If d >= N then we want to set A to d - N. To prevent timing attacks,
* do the calculation without using conditional tests. */
/* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */
d[n] += 1;
d[n] -= mpi_sub_hlp( d, d, Np, n );
/* If d0 < N then d < (2^biL)^n
* so d[n] == 0 and we want to keep A as it is.
* If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n
* so d[n] == 1 and we want to set A to the result of the subtraction
* which is d - (2^biL)^n, i.e. the n least significant limbs of d.
* This exactly corresponds to a conditional assignment. */
for (i = 0; i < n; ++i) {
Ap[i] = Select(d[i], Ap[i], -d[n]);
}
}
/*
* Montgomery reduction: A = A * R^-1 mod N
*
* See mpi_montmul() regarding constraints and guarantees on the parameters.
*/
static void mpi_montred( mbedtls_mpi *A, const mbedtls_mpi *N,
mbedtls_mpi_uint mm, const mbedtls_mpi *T )
{
mbedtls_mpi_uint z = 1;
mbedtls_mpi U;
U.n = U.s = (int) z;
U.p = &z;
mpi_montmul( A, &U, N, mm, T );
}
/**
* \brief Perform a sliding-window exponentiation: X = A^E mod N
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The base of the exponentiation.
* This must point to an initialized MPI.
* \param E The exponent MPI. This must point to an initialized MPI.
* \param N The base for the modular reduction. This must point to an
* initialized MPI.
* \param _RR A helper MPI depending solely on \p N which can be used to
* speed-up multiple modular exponentiations for the same value
* of \p N. This may be \c NULL. If it is not \c NULL, it must
* point to an initialized MPI. If it hasn't been used after
* the call to mbedtls_mpi_init(), this function will compute
* the helper value and store it in \p _RR for reuse on
* subsequent calls to this function. Otherwise, the function
* will assume that \p _RR holds the helper value set by a
* previous call to mbedtls_mpi_exp_mod(), and reuse it.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or
* even, or if \c E is negative.
* \return Another negative error code on different kinds of failures.
*
*/
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 = MBEDTLS_ERR_THIS_CORRUPTION;
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[ 1 << MBEDTLS_MPI_WINDOW_SIZE ], Apos;
int neg;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( E );
MPI_VALIDATE_RET( N );
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 );
if( mbedtls_mpi_bitlen( E ) > MBEDTLS_MPI_MAX_BITS ||
mbedtls_mpi_bitlen( N ) > MBEDTLS_MPI_MAX_BITS )
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 );
mbedtls_platform_zeroize( W, sizeof( W ) );
i = mbedtls_mpi_bitlen( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
#if( MBEDTLS_MPI_WINDOW_SIZE < 6 )
if( wsize > MBEDTLS_MPI_WINDOW_SIZE )
wsize = MBEDTLS_MPI_WINDOW_SIZE;
#endif
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;
}
/*
* 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 )
memcpy( _RR, &RR, sizeof( mbedtls_mpi ) );
}
else
memcpy( &RR, _RR, sizeof( mbedtls_mpi ) );
/*
* 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 ) );
mpi_montmul( &W[1], &RR, N, mm, &T );
/*
* X = R^2 * R^-1 mod N = R mod N
*/
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;
while( 1 )
{
if( bufsize == 0 )
{
if( nblimbs == 0 )
break;
nblimbs--;
bufsize = sizeof( mbedtls_mpi_uint ) << 3;
}
bufsize--;
ei = (E->p[nblimbs] >> bufsize) & 1;
/*
* skip leading 0s
*/
if( ei == 0 && state == 0 )
continue;
if( ei == 0 && state == 1 )
{
/*
* out of window, square X
*/
mpi_montmul( X, X, N, mm, &T );
continue;
}
/*
* 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;
}
}
/*
* process the remaining bits
*/
for( i = 0; i < nbits; i++ )
{
mpi_montmul( X, X, N, mm, &T );
wbits <<= 1;
if( ( wbits & ( one << wsize ) ) != 0 )
mpi_montmul( X, &W[1], N, mm, &T );
}
/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
mpi_montred( X, N, mm, &T );
if( neg && E->n != 0 && ( E->p[0] & 1 ) != 0 )
{
X->s = -1;
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, N, X ) );
}
cleanup:
for( i = ( one << ( wsize - 1 ) ); i < ( one << wsize ); i++ )
mbedtls_mpi_free( &W[i] );
mbedtls_mpi_free( &W[1] ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &Apos );
if( _RR == NULL || _RR->p == NULL )
mbedtls_mpi_free( &RR );
return( ret );
}
/**
* \brief Compute the greatest common divisor: G = gcd(A, B)
*
* \param G The destination MPI. This must point to an initialized MPI.
* \param A The first operand. This must point to an initialized MPI.
* \param B The second operand. This must point to an initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on different kinds of failure.
*/
int mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
mbedtls_mpi TA, TB;
size_t lz, lzt, i, j;
MPI_VALIDATE_RET( G );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( B );
mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
lz = mbedtls_mpi_lsb( &TA );
lzt = mbedtls_mpi_lsb( &TB );
if( lzt < lz )
lz = lzt;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, lz ) );
TA.s = TB.s = 1;
while( !mbedtls_mpi_is_zero( &TA ) )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, mbedtls_mpi_lsb( &TA ) ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, mbedtls_mpi_lsb( &TB ) ) );
if( mpi_cmp_abs( &TA, &TB, &i, &j ) >= 0 )
{
MBEDTLS_MPI_CHK( mpi_sub_abs( &TA, &TA, &TB, j ) );
ShiftRight( TA.p, TA.n, 1 );
}
else
{
MBEDTLS_MPI_CHK( mpi_sub_abs( &TB, &TB, &TA, i ) );
ShiftRight( TB.p, TB.n, 1 );
}
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( &TB, lz ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( G, &TB ) );
cleanup:
mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TB );
return( ret );
}
/**
* \brief Fill an MPI with a number of random bytes.
*
* Use a temporary bytes representation to make sure the result is the
* same regardless of the platform endianness (useful when f_rng is
* actually deterministic, eg for tests).
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param size The number of random bytes to generate.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng. This may be
* \c NULL if \p f_rng doesn't need a context argument.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return Another negative error code on failure.
*
* \note The bytes obtained from the RNG are interpreted
* as a big-endian representation of an MPI; this can
* be relevant in applications like deterministic ECDSA.
*/
int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
size_t const limbs = CHARS_TO_LIMBS( size );
size_t const overhead = ( limbs * ciL ) - size;
unsigned char *Xp;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( f_rng );
MBEDTLS_MPI_CHK(mbedtls_mpi_resize( X, limbs ));
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
Xp = (unsigned char*) X->p;
MBEDTLS_MPI_CHK( f_rng( p_rng, Xp + overhead, size ) );
mpi_bigendian_to_host( X->p, limbs );
cleanup:
return( ret );
}
/**
* \brief Compute the modular inverse: X = A^-1 mod N
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The MPI to calculate the modular inverse of. This must point
* to an initialized MPI.
* \param N The base of the modular inversion. This must point to an
* initialized MPI.
*
* \return \c 0 if successful.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than
* or equal to one.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse
* with respect to \p N.
*/
int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( A );
MPI_VALIDATE_RET( N );
if( mbedtls_mpi_cmp_int( N, 1 ) <= 0 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TU ); mbedtls_mpi_init( &U1 ); mbedtls_mpi_init( &U2 );
mbedtls_mpi_init( &G ); mbedtls_mpi_init( &TB ); mbedtls_mpi_init( &TV );
mbedtls_mpi_init( &V1 ); mbedtls_mpi_init( &V2 );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, A, N ) );
if( mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
{
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
goto cleanup;
}
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &TA, A, N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TU, &TA ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TV, N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U1, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &U2, 0 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V1, 0 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &V2, 1 ) );
do
{
while( ( TU.p[0] & 1 ) == 0 )
{
ShiftRight( TU.p, TU.n, 1 );
if( ( U1.p[0] & 1 ) != 0 || ( U2.p[0] & 1 ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &U1, &U1, &TB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &TA ) );
}
ShiftRight( U1.p, U1.n, 1 );
ShiftRight( U2.p, U2.n, 1 );
}
while( ( TV.p[0] & 1 ) == 0 )
{
ShiftRight( TV.p, TV.n, 1 );
if( ( V1.p[0] & 1 ) != 0 || ( V2.p[0] & 1 ) != 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, &TB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &TA ) );
}
ShiftRight( V1.p, V1.n, 1 );
ShiftRight( V2.p, V2.n, 1 );
}
if( mbedtls_mpi_cmp_mpi( &TU, &TV ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TU, &TU, &TV ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U1, &U1, &V1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &U2, &U2, &V2 ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &TV, &TV, &TU ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, &U1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V2, &V2, &U2 ) );
}
}
while( !mbedtls_mpi_is_zero(&TU) );
while( mbedtls_mpi_cmp_int( &V1, 0 ) < 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &V1, &V1, N ) );
while( mbedtls_mpi_cmp_mpi( &V1, N ) >= 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &V1, &V1, N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, &V1 ) );
cleanup:
mbedtls_mpi_free( &TA ); mbedtls_mpi_free( &TU ); mbedtls_mpi_free( &U1 ); mbedtls_mpi_free( &U2 );
mbedtls_mpi_free( &G ); mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TV );
mbedtls_mpi_free( &V1 ); mbedtls_mpi_free( &V2 );
return( ret );
}
#if defined(MBEDTLS_GENPRIME)
static const short small_prime[] =
{
3, 5, 7, 11, 13, 17, 19, 23,
29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97,
101, 103, 107, 109, 113, 127, 131, 137,
139, 149, 151, 157, 163, 167, 173, 179,
181, 191, 193, 197, 199, 211, 223, 227,
229, 233, 239, 241, 251, 257, 263, 269,
271, 277, 281, 283, 293, 307, 311, 313,
317, 331, 337, 347, 349, 353, 359, 367,
373, 379, 383, 389, 397, 401, 409, 419,
421, 431, 433, 439, 443, 449, 457, 461,
463, 467, 479, 487, 491, 499, 503, 509,
521, 523, 541, 547, 557, 563, 569, 571,
577, 587, 593, 599, 601, 607, 613, 617,
619, 631, 641, 643, 647, 653, 659, 661,
673, 677, 683, 691, 701, 709, 719, 727,
733, 739, 743, 751, 757, 761, 769, 773,
787, 797, 809, 811, 821, 823, 827, 829,
839, 853, 857, 859, 863, 877, 881, 883,
887, 907, 911, 919, 929, 937, 941, 947,
953, 967, 971, 977, 983, 991, 997, -103
};
/*
* Small divisors test (X must be positive)
*
* Return values:
* 0: no small factor (possible prime, more tests needed)
* 1: certain prime
* MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
* other negative: error
*/
static int mpi_check_small_factors( const mbedtls_mpi *X )
{
int ret = 0;
size_t i;
mbedtls_mpi_uint r;
if( ( X->p[0] & 1 ) == 0 )
return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
for( i = 0; small_prime[i] > 0; i++ )
{
if( mbedtls_mpi_cmp_int( X, small_prime[i] ) <= 0 )
return( 1 );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, small_prime[i] ) );
if( r == 0 )
return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
}
cleanup:
return( ret );
}
/*
* Miller-Rabin pseudo-primality test (HAC 4.24)
*/
static int mpi_miller_rabin( const mbedtls_mpi *X, size_t rounds,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret, count;
size_t i, j, k, s;
mbedtls_mpi W, R, T, A, RR;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( f_rng );
mbedtls_mpi_init( &W ); mbedtls_mpi_init( &R );
mbedtls_mpi_init( &T ); mbedtls_mpi_init( &A );
mbedtls_mpi_init( &RR );
/*
* W = |X| - 1
* R = W >> lsb( W )
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &W, X, 1 ) );
s = mbedtls_mpi_lsb( &W );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R, &W ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &R, s ) );
for( i = 0; i < rounds; i++ )
{
/*
* pick a random A, 1 < A < |X| - 1
*/
count = 0;
do {
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &A, X->n * ciL, f_rng, p_rng ) );
j = mbedtls_mpi_bitlen( &A );
k = mbedtls_mpi_bitlen( &W );
if (j > k) {
A.p[A.n - 1] &= ( (mbedtls_mpi_uint) 1 << ( k - ( A.n - 1 ) * biL - 1 ) ) - 1;
}
if (count++ > 30) {
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
goto cleanup;
}
} while ( mbedtls_mpi_cmp_mpi( &A, &W ) >= 0 ||
mbedtls_mpi_cmp_int( &A, 1 ) <= 0 );
/*
* A = A^R mod |X|
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &A, &A, &R, X, &RR ) );
if( mbedtls_mpi_cmp_mpi( &A, &W ) == 0 ||
mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
continue;
j = 1;
while( j < s && mbedtls_mpi_cmp_mpi( &A, &W ) != 0 )
{
/*
* A = A * A mod |X|
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, &A, &A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &A, &T, X ) );
if( mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
break;
j++;
}
/*
* not prime if A != |X| - 1 or A == 1
*/
if( mbedtls_mpi_cmp_mpi( &A, &W ) != 0 ||
mbedtls_mpi_cmp_int( &A, 1 ) == 0 )
{
ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
break;
}
}
cleanup:
mbedtls_mpi_free( &W ); mbedtls_mpi_free( &R );
mbedtls_mpi_free( &T ); mbedtls_mpi_free( &A );
mbedtls_mpi_free( &RR );
return( ret );
}
/**
* \brief Miller-Rabin primality test.
*
* \warning If \p X is potentially generated by an adversary, for example
* when validating cryptographic parameters that you didn't
* generate yourself and that are supposed to be prime, then
* \p rounds should be at least the half of the security
* strength of the cryptographic algorithm. On the other hand,
* if \p X is chosen uniformly or non-adversially (as is the
* case when mbedtls_mpi_gen_prime calls this function), then
* \p rounds can be much lower.
*
* \param X The MPI to check for primality.
* This must point to an initialized MPI.
* \param rounds The number of bases to perform the Miller-Rabin primality
* test for. The probability of returning 0 on a composite is
* at most 2<sup>-2*\p rounds</sup>.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
* This may be \c NULL if \p f_rng doesn't use
* a context parameter.
*
* \return \c 0 if successful, i.e. \p X is probably prime.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
* \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret = MBEDTLS_ERR_THIS_CORRUPTION;
mbedtls_mpi XX;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( f_rng );
XX.s = 1;
XX.n = X->n;
XX.p = X->p;
if( mbedtls_mpi_cmp_int( &XX, 0 ) == 0 ||
mbedtls_mpi_cmp_int( &XX, 1 ) == 0 )
return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
if( mbedtls_mpi_cmp_int( &XX, 2 ) == 0 )
return( 0 );
if( ( ret = mpi_check_small_factors( &XX ) ) != 0 )
{
if( ret == 1 )
return( 0 );
return( ret );
}
return( mpi_miller_rabin( &XX, rounds, f_rng, p_rng ) );
}
/**
* \brief Generate a prime number.
*
* To generate an RSA key in a way recommended by FIPS
* 186-4, both primes must be either 1024 bits or 1536
* bits long, and flags must contain
* MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR.
*
* \param X The destination MPI to store the generated prime in.
* This must point to an initialized MPi.
* \param nbits The required size of the destination MPI in bits.
* This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS.
* \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t.
* \param f_rng The RNG function to use. This must not be \c NULL.
* \param p_rng The RNG parameter to be passed to \p f_rng.
* This may be \c NULL if \p f_rng doesn't use
* a context parameter.
*
* \return \c 0 if successful, in which case \p X holds a
* probably prime number.
* \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
* \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not between
* \c 3 and #MBEDTLS_MPI_MAX_BITS.
*/
int mbedtls_mpi_gen_prime( mbedtls_mpi *X, size_t nbits, int flags,
int (*f_rng)(void *, unsigned char *, size_t),
void *p_rng )
{
int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
size_t k, n;
int rounds;
mbedtls_mpi_uint r;
mbedtls_mpi Y;
MPI_VALIDATE_RET( X );
MPI_VALIDATE_RET( f_rng );
if( nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
mbedtls_mpi_init( &Y );
n = BITS_TO_LIMBS( nbits );
if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR ) == 0 )
{
/*
* 2^-80 error probability, number of rounds chosen per HAC, table 4.4
*/
rounds = ( ( nbits >= 1300 ) ? 2 : ( nbits >= 850 ) ? 3 :
( nbits >= 650 ) ? 4 : ( nbits >= 350 ) ? 8 :
( nbits >= 250 ) ? 12 : ( nbits >= 150 ) ? 18 : 27 );
}
else
{
/*
* 2^-100 error probability, number of rounds computed based on HAC,
* fact 4.48
*/
rounds = ( ( nbits >= 1450 ) ? 4 : ( nbits >= 1150 ) ? 5 :
( nbits >= 1000 ) ? 6 : ( nbits >= 850 ) ? 7 :
( nbits >= 750 ) ? 8 : ( nbits >= 500 ) ? 13 :
( nbits >= 250 ) ? 28 : ( nbits >= 150 ) ? 40 : 51 );
}
while( 1 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( X, n * ciL, f_rng, p_rng ) );
/* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */
if( X->p[n-1] < 0xb504f333f9de6485ULL /* ceil(2^63.5) */ ) continue;
k = n * biL;
if( k > nbits ) MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, k - nbits ) );
X->p[0] |= 1;
if( ( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH ) == 0 )
{
ret = mbedtls_mpi_is_prime_ext( X, rounds, f_rng, p_rng );
if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
goto cleanup;
}
else
{
/*
* An necessary condition for Y and X = 2Y + 1 to be prime
* is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
* Make sure it is satisfied, while keeping X = 3 mod 4
*/
X->p[0] |= 2;
MBEDTLS_MPI_CHK( mbedtls_mpi_mod_int( &r, X, 3 ) );
if( r == 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 8 ) );
else if( r == 1 )
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 4 ) );
/* Set Y = (X-1) / 2, which is X / 2 because X is odd */
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Y, X ) );
ShiftRight( Y.p, Y.n, 1 );
while( 1 )
{
/*
* First, check small factors for X and Y
* before doing Miller-Rabin on any of them
*/
if( ( ret = mpi_check_small_factors( X ) ) == 0 &&
( ret = mpi_check_small_factors( &Y ) ) == 0 &&
( ret = mpi_miller_rabin( X, rounds, f_rng, p_rng ) )
== 0 &&
( ret = mpi_miller_rabin( &Y, rounds, f_rng, p_rng ) )
== 0 )
goto cleanup;
if( ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
goto cleanup;
/*
* Next candidates. We want to preserve Y = (X-1) / 2 and
* Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
* so up Y by 6 and X by 12.
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( X, X, 12 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &Y, &Y, 6 ) );
}
}
}
cleanup:
mbedtls_mpi_free( &Y );
return( ret );
}
#endif /* MBEDTLS_GENPRIME */
#if defined(MBEDTLS_SELF_TEST)
#define GCD_PAIR_COUNT 3
static const int gcd_pairs[GCD_PAIR_COUNT][3] =
{
{ 693, 609, 21 },
{ 1764, 868, 28 },
{ 768454923, 542167814, 1 }
};
/**
* \brief Checkup routine
*
* \return 0 if successful, or 1 if the test failed
*/
int mbedtls_mpi_self_test( int verbose )
{
int ret, i;
mbedtls_mpi A, E, N, X, Y, U, V;
mbedtls_mpi_init( &A ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N ); mbedtls_mpi_init( &X );
mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &U ); mbedtls_mpi_init( &V );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &A, 16,
"EFE021C2645FD1DC586E69184AF4A31E" \
"D5F53E93B5F123FA41680867BA110131" \
"944FE7952E2517337780CB0DB80E61AA" \
"E7C8DDC6C5C6AADEB34EB38A2F40D5E6" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &E, 16,
"B2E7EFD37075B9F03FF989C7C5051C20" \
"34D2A323810251127E7BF8625A4F49A5" \
"F3E27F4DA8BD59C47D6DAABA4C8127BD" \
"5B5C25763222FEFCCFC38B832366C29E" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &N, 16,
"0066A198186C18C10B2F5ED9B522752A" \
"9830B69916E535C8F047518A889A43A5" \
"94B6BED27A168D31D4A52F88925AA8F5" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &X, &A, &N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
"602AB7ECA597A3D6B56FF9829A5E8B85" \
"9E857EA95A03512E2BAE7391688D264A" \
"A5663B0341DB9CCFD2C4C5F421FEC814" \
"8001B72E848A38CAE1C65F78E56ABDEF" \
"E12D3C039B8A02D6BE593F0BBBDA56F1" \
"ECF677152EF804370C1A305CAF3B5BF1" \
"30879B56C61DE584A0F53A2447A51E" ) );
if( verbose != 0 )
mbedtls_printf( " MPI test #1 (mul_mpi): " );
if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
mbedtls_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
mbedtls_printf( "passed\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &X, &Y, &A, &N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
"256567336059E52CAE22925474705F39A94" ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &V, 16,
"6613F26162223DF488E9CD48CC132C7A" \
"0AC93C701B001B092E4E5B9F73BCD27B" \
"9EE50D0657C77F374E903CDFA4C642" ) );
if( verbose != 0 )
mbedtls_printf( " MPI test #2 (div_mpi): " );
if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 ||
mbedtls_mpi_cmp_mpi( &Y, &V ) != 0 )
{
if( verbose != 0 )
mbedtls_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
mbedtls_printf( "passed\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &X, &A, &E, &N, NULL ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
"36E139AEA55215609D2816998ED020BB" \
"BD96C37890F65171D948E9BC7CBAA4D9" \
"325D24D6A3C12710F10A09FA08AB87" ) );
if( verbose != 0 )
mbedtls_printf( " MPI test #3 (exp_mod): " );
if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
mbedtls_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
mbedtls_printf( "passed\n" );
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &X, &A, &N ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &U, 16,
"003A0AAEDD7E784FC07D8F9EC6E3BFD5" \
"C3DBA76456363A10869622EAC2DD84EC" \
"C5B8A74DAC4D09E03B5E0BE779F2DF61" ) );
if( verbose != 0 )
mbedtls_printf( " MPI test #4 (inv_mod): " );
if( mbedtls_mpi_cmp_mpi( &X, &U ) != 0 )
{
if( verbose != 0 )
mbedtls_printf( "failed\n" );
ret = 1;
goto cleanup;
}
if( verbose != 0 )
mbedtls_printf( "passed\n" );
if( verbose != 0 )
mbedtls_printf( " MPI test #5 (simple gcd): " );
for( i = 0; i < GCD_PAIR_COUNT; i++ )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &X, gcd_pairs[i][0] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &Y, gcd_pairs[i][1] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &A, &X, &Y ) );
if( mbedtls_mpi_cmp_int( &A, gcd_pairs[i][2] ) != 0 )
{
if( verbose != 0 )
mbedtls_printf( "failed at %d\n", i );
ret = 1;
goto cleanup;
}
}
if( verbose != 0 )
mbedtls_printf( "passed\n" );
cleanup:
if( ret != 0 && verbose != 0 )
mbedtls_printf( "Unexpected error, return code = %08X\n", (unsigned int) ret );
mbedtls_mpi_free( &A ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N ); mbedtls_mpi_free( &X );
mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &U ); mbedtls_mpi_free( &V );
if( verbose != 0 )
mbedtls_printf( "\n" );
return( ret );
}
#endif /* MBEDTLS_SELF_TEST */
#endif /* MBEDTLS_BIGNUM_C */
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