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cosmopolitan/third_party/mbedtls/bignum.c
Justine Tunney cc1920749e Add SSL to redbean 
Your redbean can now interoperate with clients that require TLS crypto.
This is accomplished using a protocol polyglot that lets us distinguish
between HTTP and HTTPS regardless of the port number. Certificates will
be generated automatically, if none are supplied by the user. Footprint
increases by only a few hundred kb so redbean in MODY=tiny is now 1.0mb

- Add lseek() polyfills for ZIP executable
- Automatically polyfill /tmp/FOO paths on NT
- Fix readdir() / ftw() / nftw() bugs on Windows
- Introduce -B flag for slower SSL that's stronger
- Remove mbedtls features Cosmopolitan doesn't need
- Have base64 decoder support the uri-safe alternative
- Remove Truncated HMAC because it's forbidden by the IETF
- Add all the mbedtls test suites and make them go 3x faster
- Support opendir() / readdir() / closedir() on ZIP executable
- Use Everest for ECDHE-ECDSA because it's so good it's so good
- Add tinier implementation of sha1 since it's not worth the rom
- Add chi-square monte-carlo mean correlation tests for getrandom()
- Source entropy on Windows from the proper interface everyone uses

We're continuing to outperform NGINX and other servers on raw message
throughput. Using SSL means that instead of 1,000,000 qps you can get
around 300,000 qps. However redbean isn't as fast as NGINX yet at SSL
handshakes, since redbean can do 2,627 per second and NGINX does 4.3k

Right now, the SSL UX story works best if you give your redbean a key
signing key since that can be easily generated by openssl using a one
liner then redbean will do all the things that are impossibly hard to
do like signing ecdsa and rsa certificates that'll work in chrome. We
should integrate the let's encrypt acme protocol in the future.

Live Demo: https://redbean.justine.lol/
Root Cert: https://redbean.justine.lol/redbean1.crt
2021-06-24 13:20:50 -07:00

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#include "libc/log/log.h"
#include "third_party/mbedtls/bignum.h"
#include "third_party/mbedtls/bn_mul.h"
#include "third_party/mbedtls/common.h"
#include "third_party/mbedtls/error.h"
#include "third_party/mbedtls/platform.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\"");
/* clang-format off */
/*
* Multi-precision integer library
*
* Copyright The Mbed TLS Contributors
* SPDX-License-Identifier: Apache-2.0
*
* 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.
*/
/*
* 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)
#define MPI_VALIDATE_RET( cond ) \
MBEDTLS_INTERNAL_VALIDATE_RET( cond, MBEDTLS_ERR_MPI_BAD_INPUT_DATA )
#define MPI_VALIDATE( cond ) \
MBEDTLS_INTERNAL_VALIDATE( cond )
#define ciL (sizeof(mbedtls_mpi_uint)) /* chars in limb */
#define biL (ciL << 3) /* bits in limb */
#define biH (ciL << 2) /* half limb size */
#define MPI_SIZE_T_MAX ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
/*
* Convert between bits/chars and number of limbs
* Divide first in order to avoid potential overflows
*/
#define BITS_TO_LIMBS(i) ( (i) / biL + ( (i) % biL != 0 ) )
#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
/* Implementation that should never be optimized out by the compiler */
static void mbedtls_mpi_zeroize( mbedtls_mpi_uint *v, size_t n )
{
mbedtls_platform_zeroize( v, ciL * n );
}
/**
* \brief Initialize an MPI context.
*
* This makes the MPI ready to be set or freed,
* but does not define a value for the MPI.
*
* \param X The MPI context to initialize. This must not be \c NULL.
*/
void mbedtls_mpi_init( mbedtls_mpi *X )
{
MPI_VALIDATE( X != NULL );
X->s = 1;
X->n = 0;
X->p = NULL;
}
/**
* \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 == NULL )
return;
if( X->p != NULL )
{
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 != NULL );
if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
if( X->n < nblimbs )
{
if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( nblimbs, ciL ) ) == NULL )
return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
if( X->p != NULL )
{
memcpy( p, X->p, X->n * ciL );
mbedtls_mpi_zeroize( X->p, X->n );
mbedtls_free( X->p );
}
X->n = nblimbs;
X->p = p;
}
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
* (this 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 )
{
mbedtls_mpi_uint *p;
size_t i;
MPI_VALIDATE_RET( X != NULL );
if( nblimbs > MBEDTLS_MPI_MAX_LIMBS )
return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
/* Actually resize up if there are currently fewer than nblimbs limbs. */
if( X->n <= nblimbs )
return( mbedtls_mpi_grow( X, nblimbs ) );
/* After this point, then X->n > nblimbs and in particular X->n > 0. */
for( i = X->n - 1; i > 0; i-- )
if( X->p[i] != 0 )
break;
i++;
if( i < nblimbs )
i = nblimbs;
if( ( p = (mbedtls_mpi_uint*)mbedtls_calloc( i, ciL ) ) == NULL )
return( MBEDTLS_ERR_MPI_ALLOC_FAILED );
if( X->p != NULL )
{
memcpy( p, X->p, i * ciL );
mbedtls_mpi_zeroize( X->p, X->n );
mbedtls_free( X->p );
}
X->n = i;
X->p = p;
return( 0 );
}
/**
* \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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
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
{
memset( X->p + i, 0, ( 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 != NULL );
MPI_VALIDATE( Y != NULL );
memcpy( &T, X, sizeof( mbedtls_mpi ) );
memcpy( X, Y, sizeof( mbedtls_mpi ) );
memcpy( Y, &T, sizeof( mbedtls_mpi ) );
}
/*
* Conditionally assign dest = src, without leaking information
* about whether the assignment was made or not.
* dest and src must be arrays of limbs of size n.
* assign must be 0 or 1.
*/
static void mpi_safe_cond_assign( size_t n,
mbedtls_mpi_uint *dest,
const mbedtls_mpi_uint *src,
unsigned char assign )
{
size_t i;
for( i = 0; i < n; i++ )
dest[i] = dest[i] * ( 1 - assign ) + src[i] * assign;
}
/**
* \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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
/* make sure assign is 0 or 1 in a time-constant manner */
assign = (assign | (unsigned char)-assign) >> 7;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, Y->n ) );
X->s = X->s * ( 1 - assign ) + Y->s * assign;
mpi_safe_cond_assign( Y->n, X->p, Y->p, assign );
for( i = Y->n; i < X->n; i++ )
X->p[i] *= ( 1 - assign );
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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
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_ERROR_CORRUPTION_DETECTED;
MPI_VALIDATE_RET( X != NULL );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
memset( X->p, 0, 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 != NULL );
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 != NULL );
if( val != 0 && val != 1 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
if( X->n * biL <= pos )
{
if( val == 0 )
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, j, count = 0;
MBEDTLS_INTERNAL_VALIDATE_RET( X != NULL, 0 );
for( i = 0; i < X->n; i++ )
for( j = 0; j < biL; j++, count++ )
if( ( ( X->p[i] >> j ) & 1 ) != 0 )
return( count );
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 i, j;
if( X->n == 0 )
return( 0 );
for( i = X->n - 1; i > 0; i-- )
if( X->p[i] != 0 )
break;
j = biL - mbedtls_clz( X->p[i] );
return( ( i * biL ) + j );
}
/**
* \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_ERROR_CORRUPTION_DETECTED;
size_t i, j, slen, n;
mbedtls_mpi_uint d;
mbedtls_mpi T;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( s != NULL );
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_ERROR_CORRUPTION_DETECTED;
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 != NULL );
MPI_VALIDATE_RET( olen != NULL );
MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
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 != NULL );
MPI_VALIDATE_RET( fin != NULL );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
memset( s, 0, 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_ERROR_CORRUPTION_DETECTED;
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 != NULL );
if( radix < 2 || radix > 16 )
return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
memset( s, 0, 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 != NULL )
{
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 == 0 )
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 buf The input buffer. This must be a readable buffer of length
* \p buflen Bytes.
* \param buflen 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 *buf, size_t buflen )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i;
size_t const limbs = CHARS_TO_LIMBS( buflen );
/* Ensure that target MPI has exactly the necessary number of limbs */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( i = 0; i < buflen; i++ )
X->p[i / ciL] |= ((mbedtls_mpi_uint) buf[i]) << ((i % ciL) << 3);
cleanup:
/*
* This function is also used to import keys. However, wiping the buffers
* upon failure is not necessary because failure only can happen before any
* input is copied.
*/
return( ret );
}
/**
* \brief Import an MPI from unsigned big endian binary data.
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param buf The input buffer. This must be a readable buffer of length
* \p buflen Bytes.
* \param buflen 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 *buf, size_t buflen )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t const limbs = CHARS_TO_LIMBS( buflen );
size_t const overhead = ( limbs * ciL ) - buflen;
unsigned char *Xp;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
/* Ensure that target MPI has exactly the necessary number of limbs */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
/* Avoid calling `memcpy` with NULL source argument,
* even if buflen is 0. */
if( buf != NULL )
{
Xp = (unsigned char*) X->p;
memcpy( Xp + overhead, buf, buflen );
mpi_bigendian_to_host( X->p, limbs );
}
cleanup:
/*
* This function is also used to import keys. However, wiping the buffers
* upon failure is not necessary because failure only can happen before any
* input is copied.
*/
return( ret );
}
/**
* \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 */
memset( buf + stored_bytes, 0, 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 != NULL );
MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
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;
memset( buf, 0, 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 Perform a left-shift on an MPI: X <<= count
*
* \param X The MPI to shift. This must point to an initialized MPI.
* \param count The number of bits to shift by.
*
* \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_shift_l( mbedtls_mpi *X, size_t count )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, v0, t1;
mbedtls_mpi_uint r0 = 0, r1;
MPI_VALIDATE_RET( X != NULL );
v0 = count / (biL );
t1 = count & (biL - 1);
i = mbedtls_mpi_bitlen( X ) + count;
if( X->n * biL < i )
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, BITS_TO_LIMBS( i ) ) );
ret = 0;
/*
* shift by count / limb_size
*/
if( v0 > 0 )
{
for( i = X->n; i > v0; i-- )
X->p[i - 1] = X->p[i - v0 - 1];
for( ; i > 0; i-- )
X->p[i - 1] = 0;
}
/*
* shift by count % limb_size
*/
if( t1 > 0 )
{
for( i = v0; i < X->n; i++ )
{
r1 = X->p[i] >> (biL - t1);
X->p[i] <<= t1;
X->p[i] |= r0;
r0 = r1;
}
}
cleanup:
return( ret );
}
/**
* \brief Perform a right-shift on an MPI: X >>= count
*
* \param X The MPI to shift. This must point to an initialized MPI.
* \param count The number of bits to shift by.
*
* \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_shift_r( mbedtls_mpi *X, size_t count )
{
size_t i, v0, v1;
mbedtls_mpi_uint r0 = 0, r1;
MPI_VALIDATE_RET( X != NULL );
v0 = count / biL;
v1 = count & (biL - 1);
if( v0 > X->n || ( v0 == X->n && v1 > 0 ) )
return mbedtls_mpi_lset( X, 0 );
/*
* shift by count / limb_size
*/
if( v0 > 0 )
{
for( i = 0; i < X->n - v0; i++ )
X->p[i] = X->p[i + v0];
for( ; i < X->n; i++ )
X->p[i] = 0;
}
/*
* shift by count % limb_size
*/
if( v1 > 0 )
{
for( i = X->n; i > 0; i-- )
{
r1 = X->p[i - 1] << (biL - v1);
X->p[i - 1] >>= v1;
X->p[i - 1] |= r0;
r0 = r1;
}
}
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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
for( i = X->n; i > 0; i-- )
if( X->p[i - 1] != 0 )
break;
for( j = Y->n; j > 0; j-- )
if( Y->p[j - 1] != 0 )
break;
if( i == 0 && j == 0 )
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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
for( i = X->n; i > 0; i-- )
if( X->p[i - 1] != 0 )
break;
for( j = Y->n; j > 0; j-- )
if( Y->p[j - 1] != 0 )
break;
if( i == 0 && j == 0 )
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 != NULL );
MPI_VALIDATE_RET( Y != NULL );
MPI_VALIDATE_RET( ret != NULL );
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 != NULL );
*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_ERROR_CORRUPTION_DETECTED;
size_t i, j;
mbedtls_mpi_uint *o, *p, c, tmp;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
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 - s where d and s have the same size.
* This function operates modulo (2^ciL)^n and returns the carry
* (1 if there was a wraparound, i.e. if `d < s`, and 0 otherwise).
*
* \param n Number of limbs of \p d and \p s.
* \param[in,out] d On input, the left operand.
* On output, the result of the subtraction:
* \param[in] s The right operand.
*
* \return 1 if `d < s`.
* 0 if `d >= s`.
*/
static mbedtls_mpi_uint mpi_sub_hlp( size_t n,
mbedtls_mpi_uint *d,
const mbedtls_mpi_uint *s )
{
size_t i;
mbedtls_mpi_uint c, z;
for( i = c = 0; i < n; i++, s++, d++ )
{
z = ( *d < c ); *d -= c;
c = ( *d < *s ) + z; *d -= *s;
}
return( c );
}
/**
* \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 )
{
mbedtls_mpi TB;
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t n;
mbedtls_mpi_uint carry;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
mbedtls_mpi_init( &TB );
if( X == B )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) );
B = &TB;
}
if( X != A )
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
/*
* X should always be positive as a result of unsigned subtractions.
*/
X->s = 1;
ret = 0;
for( n = B->n; n > 0; n-- )
if( B->p[n - 1] != 0 )
break;
if( n > A->n )
{
/* B >= (2^ciL)^n > A */
ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
goto cleanup;
}
carry = mpi_sub_hlp( n, X->p, B->p );
if( carry != 0 )
{
/* Propagate the carry to the first nonzero limb of X. */
for( ; n < X->n && X->p[n] == 0; n++ )
--X->p[n];
/* If we ran out of space for the carry, it means that the result
* is negative. */
if( n == X->n )
{
ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE;
goto cleanup;
}
--X->p[n];
}
cleanup:
mbedtls_mpi_free( &TB );
return( ret );
}
/**
* \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;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
s = A->s;
if( A->s * B->s < 0 )
{
if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
X->s = s;
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
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;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
s = A->s;
if( A->s * B->s > 0 )
{
if( mbedtls_mpi_cmp_abs( A, B ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, A, B ) );
X->s = s;
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( X, B, A ) );
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 != NULL );
MPI_VALIDATE_RET( A != NULL );
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 != NULL );
MPI_VALIDATE_RET( A != NULL );
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 ) );
}
/*
* Helper for mbedtls_mpi multiplication
*/
static void mpi_mul_hlp( size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b )
{
uint128_t axdx;
mbedtls_mpi_uint c = 0, t = 0, ax, dx, z;
#if defined(MULADDC_HUIT)
for( ; i >= 8; i -= 8 )
{
MULADDC_INIT
MULADDC_HUIT
MULADDC_STOP
}
for( ; i > 0; i-- )
{
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#else /* MULADDC_HUIT */
for( ; i >= 16; i -= 16 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i >= 8; i -= 8 )
{
MULADDC_INIT
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_CORE MULADDC_CORE
MULADDC_STOP
}
for( ; i > 0; i-- )
{
MULADDC_INIT
MULADDC_CORE
MULADDC_STOP
}
#endif /* MULADDC_HUIT */
t++;
do {
*d += c; c = ( *d < c ); d++;
}
while( c != 0 );
}
/**
* \brief Perform a multiplication of two MPIs: X = A * B
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first factor. This must point to an initialized MPI.
* \param B The second factor. 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_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i, j;
mbedtls_mpi TA, TB;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
mbedtls_mpi_init( &TA ); mbedtls_mpi_init( &TB );
if( X == A ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TA, A ) ); A = &TA; }
if( X == B ) { MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &TB, B ) ); B = &TB; }
for( i = A->n; i > 0; i-- )
if( A->p[i - 1] != 0 )
break;
for( j = B->n; j > 0; j-- )
if( B->p[j - 1] != 0 )
break;
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + j ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
for( ; j > 0; j-- )
mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
X->s = A->s * B->s;
cleanup:
mbedtls_mpi_free( &TB ); mbedtls_mpi_free( &TA );
return( ret );
}
/**
* \brief Perform a multiplication of an MPI with an unsigned integer:
* X = A * b
*
* \param X The destination MPI. This must point to an initialized MPI.
* \param A The first factor. This must point to an initialized MPI.
* \param b The second factor.
*
* \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_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b )
{
mbedtls_mpi _B;
mbedtls_mpi_uint p[1];
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
_B.s = 1;
_B.n = 1;
_B.p = p;
p[0] = b;
return( mbedtls_mpi_mul_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(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 != NULL) *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 != NULL )
*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 != NULL)
*r = ( rAX * radix + u0_lsw - q0 * d ) >> s;
quotient = q1 * radix + q0;
return quotient;
#endif
}
/**
* \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_ERROR_CORRUPTION_DETECTED;
size_t i, n, t, k;
mbedtls_mpi X, Y, Z, T1, T2;
mbedtls_mpi_uint TP2[3];
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
if( mbedtls_mpi_cmp_int( B, 0 ) == 0 )
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 != NULL ) MBEDTLS_MPI_CHK( mbedtls_mpi_lset( Q, 0 ) );
if( R != NULL ) 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, 2 ) );
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_mpi( &X, &Y ) >= 0 )
{
Z.p[n - t]++;
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &X, &X, &Y ) );
}
MBEDTLS_MPI_CHK( 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]--;
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &T1, 0 ) );
T1.p[0] = ( t < 1 ) ? 0 : Y.p[t - 1];
T1.p[1] = Y.p[t];
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &T1, &T1, Z.p[i - t - 1] ) );
}
while( mbedtls_mpi_cmp_mpi( &T1, &T2 ) > 0 );
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( mbedtls_mpi_cmp_int( &X, 0 ) < 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 != NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( Q, &Z ) );
Q->s = A->s * B->s;
}
if( R != NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &X, k ) );
X.s = A->s;
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( R, &X ) );
if( mbedtls_mpi_cmp_int( R, 0 ) == 0 )
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 != NULL );
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_ERROR_CORRUPTION_DETECTED;
MPI_VALIDATE_RET( R != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
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 != NULL );
MPI_VALIDATE_RET( A != NULL );
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 + 1;
}
/**
* 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;
memset( T->p, 0, T->n * ciL );
d = T->p;
n = N->n;
m = ( B->n < n ) ? B->n : n;
for( i = 0; i < n; i++ )
{
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = A->p[i];
u1 = ( d[0] + u0 * B->p[0] ) * mm;
mpi_mul_hlp( m, B->p, d, u0 );
mpi_mul_hlp( n, N->p, 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( A->p, 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( n, d, N->p );
/* 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. */
mpi_safe_cond_assign( n, A->p, d, (unsigned char) 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_ERROR_CORRUPTION_DETECTED;
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 != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( E != NULL );
MPI_VALIDATE_RET( N != NULL );
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 );
memset( W, 0, sizeof( W ) );
i = mbedtls_mpi_bitlen( E );
wsize = ( i > 671 ) ? 6 : ( i > 239 ) ? 5 :
( i > 79 ) ? 4 : ( i > 23 ) ? 3 : 1;
#if( 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 != NULL )
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_ERROR_CORRUPTION_DETECTED;
size_t lz, lzt;
mbedtls_mpi TA, TB;
MPI_VALIDATE_RET( G != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( B != NULL );
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_cmp_int( &TA, 0 ) != 0 )
{
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( mbedtls_mpi_cmp_mpi( &TA, &TB ) >= 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TA, &TA, &TB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TA, 1 ) );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &TB, &TB, &TA ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TB, 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_ERROR_CORRUPTION_DETECTED;
size_t const limbs = CHARS_TO_LIMBS( size );
size_t const overhead = ( limbs * ciL ) - size;
unsigned char *Xp;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( f_rng != NULL );
/* Ensure that target MPI has exactly the necessary number of limbs */
if( X->n != limbs )
{
mbedtls_mpi_free( X );
mbedtls_mpi_init( X );
MBEDTLS_MPI_CHK( mbedtls_mpi_grow( 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_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( A != NULL );
MPI_VALIDATE_RET( N != NULL );
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 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TU, 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 ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U1, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &U2, 1 ) );
}
while( ( TV.p[0] & 1 ) == 0 )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &TV, 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 ) );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V1, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &V2, 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_cmp_int( &TU, 0 ) != 0 );
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 != NULL );
MPI_VALIDATE_RET( f_rng != NULL );
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_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi XX;
MPI_VALIDATE_RET( X != NULL );
MPI_VALIDATE_RET( f_rng != NULL );
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 != NULL );
MPI_VALIDATE_RET( f_rng != NULL );
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 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &Y, 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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