Botan::BigInt Class Reference

#include <bigint.h>

Public Types
enum	Base { Decimal = 10 , Hexadecimal = 16 , Binary = 256 }
enum	Sign { Negative = 0 , Positive = 1 }

Public Member Functions
BigInt	abs () const
BigInt &	add (const word y[], size_t y_words, Sign sign)
	BigInt ()=default
	BigInt (BigInt &&other)
	BigInt (const BigInt &other)=default
	BigInt (const std::string &str)
template<typename Alloc >
	BigInt (const std::vector< uint8_t, Alloc > &vec)
	BigInt (const uint8_t buf[], size_t length)
	BigInt (const uint8_t buf[], size_t length, Base base)
	BigInt (RandomNumberGenerator &rng, size_t bits, bool set_high_bit=true)
	Create a random BigInt of the specified size.
	BigInt (uint64_t n)
template<typename Alloc >
void	binary_decode (const std::vector< uint8_t, Alloc > &buf)
void	binary_decode (const uint8_t buf[], size_t length)
void	binary_encode (uint8_t buf[]) const
void	binary_encode (uint8_t buf[], size_t len) const
size_t	bits () const
uint8_t	byte_at (size_t n) const
size_t	bytes () const
void	clear ()
void	clear_bit (size_t n)
int32_t	cmp (const BigInt &n, bool check_signs=true) const
int32_t	cmp_word (word n) const
void	cond_flip_sign (bool predicate)
void	conditionally_set_bit (size_t n, bool set_it)
void	const_time_poison () const
void	const_time_unpoison () const
void	ct_cond_add (bool predicate, const BigInt &value)
void	ct_cond_assign (bool predicate, const BigInt &other)
void	ct_cond_swap (bool predicate, BigInt &other)
void	ct_reduce_below (const BigInt &mod, secure_vector< word > &ws, size_t bound)
const word *	data () const
void	encode_words (word out[], size_t size) const
void	flip_sign ()
bool	get_bit (size_t n) const
uint32_t	get_substring (size_t offset, size_t length) const
secure_vector< word > &	get_word_vector ()
const secure_vector< word > &	get_word_vector () const
void	grow_to (size_t n) const
bool	is_equal (const BigInt &n) const
bool	is_even () const
bool	is_less_than (const BigInt &n) const
bool	is_negative () const
bool	is_nonzero () const
bool	is_odd () const
bool	is_positive () const
bool	is_zero () const
void	mask_bits (size_t n)
BigInt &	mod_add (const BigInt &y, const BigInt &mod, secure_vector< word > &ws)
BigInt &	mod_mul (uint8_t y, const BigInt &mod, secure_vector< word > &ws)
BigInt &	mod_sub (const BigInt &y, const BigInt &mod, secure_vector< word > &ws)
BigInt &	mul (const BigInt &y, secure_vector< word > &ws)
word *	mutable_data ()
bool	operator! () const
BigInt &	operator%= (const BigInt &y)
word	operator%= (word y)
BigInt &	operator*= (const BigInt &y)
BigInt &	operator*= (word y)
BigInt &	operator++ ()
BigInt	operator++ (int)
BigInt &	operator+= (const BigInt &y)
BigInt &	operator+= (word y)
BigInt	operator- () const
BigInt &	operator-- ()
BigInt	operator-- (int)
BigInt &	operator-= (const BigInt &y)
BigInt &	operator-= (word y)
BigInt &	operator/= (const BigInt &y)
BigInt &	operator<<= (size_t shift)
BigInt &	operator= (BigInt &&other)
BigInt &	operator= (const BigInt &)=default
BigInt &	operator>>= (size_t shift)
void	randomize (RandomNumberGenerator &rng, size_t bitsize, bool set_high_bit=true)
size_t	reduce_below (const BigInt &mod, secure_vector< word > &ws)
void	resize (size_t s)
BigInt &	rev_sub (const word y[], size_t y_words, secure_vector< word > &ws)
Sign	reverse_sign () const
void	set_bit (size_t n)
void	set_sign (Sign sign)
void	set_word_at (size_t i, word w)
void	set_words (const word w[], size_t len)
size_t	sig_words () const
Sign	sign () const
size_t	size () const
BigInt &	square (secure_vector< word > &ws)
BigInt &	sub (const word y[], size_t y_words, Sign sign)
void	swap (BigInt &other)
void	swap_reg (secure_vector< word > &reg)
std::string	to_dec_string () const
std::string	to_hex_string () const
uint32_t	to_u32bit () const
size_t	top_bits_free () const
word	word_at (size_t n) const
	~BigInt ()

Static Public Member Functions
static BigInt	add2 (const BigInt &x, const word y[], size_t y_words, Sign y_sign)
template<typename Alloc >
static BigInt	decode (const std::vector< uint8_t, Alloc > &buf)
template<typename Alloc >
static BigInt	decode (const std::vector< uint8_t, Alloc > &buf, Base base)
static BigInt	decode (const uint8_t buf[], size_t length)
static BigInt	decode (const uint8_t buf[], size_t length, Base base)
static std::vector< uint8_t >	encode (const BigInt &n)
static secure_vector< uint8_t >	encode_1363 (const BigInt &n, size_t bytes)
static void	encode_1363 (uint8_t out[], size_t bytes, const BigInt &n)
static secure_vector< uint8_t >	encode_fixed_length_int_pair (const BigInt &n1, const BigInt &n2, size_t bytes)
static secure_vector< uint8_t >	encode_locked (const BigInt &n)
static BigInt	from_bytes_with_max_bits (const uint8_t buf[], size_t length, size_t max_bits)
static BigInt	from_s32 (int32_t n)
static BigInt	from_u64 (uint64_t n)
static BigInt	from_word (word n)
static BigInt	one ()
static BigInt	power_of_2 (size_t n)
static BigInt	random_integer (RandomNumberGenerator &rng, const BigInt &min, const BigInt &max)
static BigInt	with_capacity (size_t n)
static BigInt	zero ()

Detailed Description

Arbitrary precision integer

Definition at line 24 of file bigint.h.

Member Enumeration Documentation

Base

enum Botan::BigInt::Base

Base enumerator for encoding and decoding

Enumerator
Decimal
Hexadecimal
Binary

Definition at line 30 of file bigint.h.

{ Decimal = 10, Hexadecimal = 16, Binary = 256 };

Sign

enum Botan::BigInt::Sign

Sign symbol definitions for positive and negative numbers

Enumerator
Negative
Positive

Definition at line 35 of file bigint.h.

{ Negative = 0, Positive = 1 };

Constructor & Destructor Documentation

BigInt() [1/9]

Botan::BigInt::BigInt ( )

default

Create empty (zero) BigInt

BigInt() [2/9]

Botan::BigInt::BigInt

(

uint64_t

n

)

Create BigInt from an unsigned 64 bit integer

Parameters

n	initial value of this BigInt

Definition at line 17 of file bigint.cpp.

   {
#if BOTAN_MP_WORD_BITS == 64
   m_data.set_word_at(0, n);
#else
   m_data.set_word_at(1, static_cast<word>(n >> 32));
   m_data.set_word_at(0, static_cast<word>(n));
#endif
   }

BigInt() [3/9]

Botan::BigInt::BigInt ( const BigInt &  other )

default

Copy Constructor

Parameters

other

the BigInt to copy

BigInt() [4/9]

Botan::BigInt::BigInt ( const std::string &  str )

explicit

Create BigInt from a string. If the string starts with 0x the rest of the string will be interpreted as hexadecimal digits. Otherwise, it will be interpreted as a decimal number.

Parameters

str	the string to parse for an integer value

Definition at line 70 of file bigint.cpp.

   {
   Base base = Decimal;
   size_t markers = 0;
   bool negative = false;
 
   if(str.length() > 0 && str[0] == '-')
      {
      markers += 1;
      negative = true;
      }
 
   if(str.length() > markers + 2 && str[markers    ] == '0' &&
                                    str[markers + 1] == 'x')
      {
      markers += 2;
      base = Hexadecimal;
      }
 
   *this = decode(cast_char_ptr_to_uint8(str.data()) + markers,
                  str.length() - markers, base);
 
   if(negative) set_sign(Negative);
   else         set_sign(Positive);
   }

References Botan::cast_char_ptr_to_uint8(), Decimal, decode(), Hexadecimal, Negative, Positive, and set_sign().

BigInt() [5/9]

Botan::BigInt::BigInt	(	const uint8_t	buf[],
		size_t	length
	)

Create a BigInt from an integer in a byte array

Parameters

buf	the byte array holding the value
length	size of buf

Definition at line 96 of file bigint.cpp.

   {
   binary_decode(input, length);
   }

References binary_decode().

BigInt() [6/9]

template<typename Alloc >

Botan::BigInt::BigInt ( const std::vector< uint8_t, Alloc > &  vec )

inlineexplicit

Create a BigInt from an integer in a byte array

Parameters

vec	the byte vector holding the value

Definition at line 103 of file bigint.h.

: BigInt(vec.data(), vec.size()) {}

BigInt() [7/9]

Botan::BigInt::BigInt	(	const uint8_t	buf[],
		size_t	length,
		Base	base
	)

Create a BigInt from an integer in a byte array

Parameters

buf	the byte array holding the value
length	size of buf
base	is the number base of the integer in buf

Definition at line 104 of file bigint.cpp.

   {
   *this = decode(input, length, base);
   }

References decode().

BigInt() [8/9]

Botan::BigInt::BigInt	(	RandomNumberGenerator &	rng,
		size_t	bits,
		bool	set_high_bit = true
	)

Create a random BigInt of the specified size.

Parameters

rng	random number generator
bits	size in bits
set_high_bit	if true, the highest bit is always set

See also

randomize

Definition at line 130 of file bigint.cpp.

   {
   randomize(rng, bits, set_high_bit);
   }

References bits(), and randomize().

BigInt() [9/9]

Botan::BigInt::BigInt ( BigInt &&  other )

inline

Move constructor

Definition at line 147 of file bigint.h.

        {
        this->swap(other);
        }

~BigInt()

Botan::BigInt::~BigInt ( )

inline

Definition at line 152 of file bigint.h.

{ const_time_unpoison(); }

Member Function Documentation

abs()

BigInt Botan::BigInt::abs

(

)

const

Returns

absolute (positive) value of this

Definition at line 391 of file bigint.cpp.

   {
   BigInt x = (*this);
   x.set_sign(Positive);
   return x;
   }

References Positive, and set_sign().

Referenced by Botan::abs().

add()

BigInt & Botan::BigInt::add	(	const word	y[],
		size_t	y_words,
		Sign	sign
	)

Definition at line 15 of file big_ops2.cpp.

   {
   const size_t x_sw = sig_words();
 
   grow_to(std::max(x_sw, y_words) + 1);
 
   if(sign() == y_sign)
      {
      bigint_add2(mutable_data(), size() - 1, y, y_words);
      }
   else
      {
      const int32_t relative_size = bigint_cmp(data(), x_sw, y, y_words);
 
      if(relative_size >= 0)
         {
         // *this >= y
         bigint_sub2(mutable_data(), x_sw, y, y_words);
         }
      else
         {
         // *this < y
         bigint_sub2_rev(mutable_data(), y, y_words);
         }
 
      //this->sign_fixup(relative_size, y_sign);
      if(relative_size < 0)
         set_sign(y_sign);
      else if(relative_size == 0)
         set_sign(Positive);
      }
 
   return (*this);
   }

References Botan::bigint_add2(), Botan::bigint_cmp(), Botan::bigint_sub2(), Botan::bigint_sub2_rev(), data(), grow_to(), mutable_data(), Positive, set_sign(), sig_words(), sign(), size(), and y.

Referenced by Botan::Modular_Reducer::reduce().

add2()

BigInt Botan::BigInt::add2 ( const BigInt &  x, const word  y[], size_t  y_words, BigInt::Sign  y_sign  )

static

Definition at line 18 of file big_ops3.cpp.

   {
   const size_t x_sw = x.sig_words();
 
   BigInt z = BigInt::with_capacity(std::max(x_sw, y_words) + 1);
 
   if(x.sign() == y_sign)
      {
      bigint_add3(z.mutable_data(), x.data(), x_sw, y, y_words);
      z.set_sign(x.sign());
      }
   else
      {
      const int32_t relative_size = bigint_sub_abs(z.mutable_data(), x.data(), x_sw, y, y_words);
 
      //z.sign_fixup(relative_size, y_sign);
      if(relative_size < 0)
         z.set_sign(y_sign);
      else if(relative_size == 0)
         z.set_sign(BigInt::Positive);
      else
         z.set_sign(x.sign());
      }
 
   return z;
   }

References Botan::bigint_add3(), Botan::bigint_sub_abs(), data(), mutable_data(), Positive, set_sign(), sig_words(), sign(), with_capacity(), and y.

Referenced by Botan::operator+(), and Botan::operator-().

binary_decode() [1/2]

template<typename Alloc >

void Botan::BigInt::binary_decode ( const std::vector< uint8_t, Alloc > &  buf )

inline

Read integer value from a byte vector

Parameters

buf	the vector to load from

Definition at line 712 of file bigint.h.

        {
        binary_decode(buf.data(), buf.size());
        }

binary_decode() [2/2]

void Botan::BigInt::binary_decode	(	const uint8_t	buf[],
		size_t	length
	)

Read integer value from a byte array with given size

Parameters

buf	byte array buffer containing the integer
length	size of buf

Definition at line 431 of file bigint.cpp.

   {
   clear();
 
   const size_t full_words = length / sizeof(word);
   const size_t extra_bytes = length % sizeof(word);
 
   secure_vector<word> reg((round_up(full_words + (extra_bytes > 0 ? 1 : 0), 8)));
 
   for(size_t i = 0; i != full_words; ++i)
      {
      reg[i] = load_be<word>(buf + length - sizeof(word)*(i+1), 0);
      }
 
   if(extra_bytes > 0)
      {
      for(size_t i = 0; i != extra_bytes; ++i)
         reg[full_words] = (reg[full_words] << 8) | buf[i];
      }
 
   m_data.swap(reg);
   }

References clear(), and Botan::round_up().

Referenced by BigInt(), decode(), from_bytes_with_max_bits(), Botan::generate_dsa_primes(), Botan::RFC6979_Nonce_Generator::nonce_for(), and randomize().

binary_encode() [1/2]

void Botan::BigInt::binary_encode

(

uint8_t

buf[]

)

const

Store BigInt-value in a given byte array

Parameters

buf	destination byte array for the integer value

Definition at line 398 of file bigint.cpp.

   {
   this->binary_encode(buf, bytes());
   }

References binary_encode(), and bytes().

Referenced by binary_encode(), encode(), Botan::DER_Encoder::encode(), encode_1363(), encode_fixed_length_int_pair(), encode_locked(), Botan::GOST_3410_PublicKey::public_key_bits(), and to_hex_string().

binary_encode() [2/2]

void Botan::BigInt::binary_encode	(	uint8_t	buf[],
		size_t	len
	)		const

Store BigInt-value in a given byte array. If len is less than the size of the value, then it will be truncated. If len is greater than the size of the value, it will be zero-padded. If len exactly equals this->bytes(), this function behaves identically to binary_encode.

Parameters

buf	destination byte array for the integer value
len	how many bytes to write

Definition at line 406 of file bigint.cpp.

   {
   const size_t full_words = len / sizeof(word);
   const size_t extra_bytes = len % sizeof(word);
 
   for(size_t i = 0; i != full_words; ++i)
      {
      const word w = word_at(i);
      store_be(w, output + (len - (i+1)*sizeof(word)));
      }
 
   if(extra_bytes > 0)
      {
      const word w = word_at(full_words);
 
      for(size_t i = 0; i != extra_bytes; ++i)
         {
         output[extra_bytes - i - 1] = get_byte_var(sizeof(word) - i - 1, w);
         }
      }
   }

References Botan::get_byte_var(), Botan::store_be(), and word_at().

bits()

size_t Botan::BigInt::bits

(

)

const

Get the bit length of the integer

Returns

bit length of the represented integer value

Definition at line 312 of file bigint.cpp.

   {
   const size_t words = sig_words();
 
   if(words == 0)
      return 0;
 
   const size_t full_words = (words - 1) * BOTAN_MP_WORD_BITS;
   const size_t top_bits = BOTAN_MP_WORD_BITS - top_bits_free();
 
   return full_words + top_bits;
   }

References BOTAN_MP_WORD_BITS, sig_words(), and top_bits_free().

Referenced by BigInt(), bytes(), Botan::ct_divide(), Botan::ct_divide_word(), Botan::ct_modulo(), Botan::BER_Decoder::decode(), Botan::BER_Decoder::decode_constrained_integer(), Botan::DL_Group::DL_Group(), Botan::EC_Point_Base_Point_Precompute::EC_Point_Base_Point_Precompute(), Botan::EC_Point_Var_Point_Precompute::EC_Point_Var_Point_Precompute(), Botan::DER_Encoder::encode(), Botan::gcd(), Botan::generate_dsa_primes(), Botan::generate_rsa_prime(), Botan::inverse_mod(), Botan::is_lucas_probable_prime(), Botan::is_perfect_square(), Botan::is_prime(), Botan::TPM_PrivateKey::key_length(), Botan::monty_multi_exp(), Botan::EC_Point_Base_Point_Precompute::mul(), Botan::EC_Point_Var_Point_Precompute::mul(), Botan::EC_Point_Multi_Point_Precompute::multi_exp(), Botan::operator*(), Botan::passes_miller_rabin_test(), Botan::DL_Group::power_g_p(), Botan::power_mod(), random_integer(), Botan::random_prime(), Botan::RSA_PrivateKey::RSA_PrivateKey(), Botan::srp6_client_agree(), Botan::srp6_group_identifier(), to_dec_string(), to_hex_string(), and to_u32bit().

byte_at()

uint8_t Botan::BigInt::byte_at

(

size_t

n

)

const

Parameters

n	the offset to get a byte from

Returns

byte at offset n

Definition at line 135 of file bigint.cpp.

   {
   return get_byte_var(sizeof(word) - (n % sizeof(word)) - 1,
                       word_at(n / sizeof(word)));
   }

References Botan::get_byte_var(), and word_at().

Referenced by Botan::BER_Decoder::decode(), Botan::BER_Decoder::decode_constrained_integer(), and to_u32bit().

bytes()

size_t Botan::BigInt::bytes

(

)

const

Give byte length of the integer

Returns

byte length of the represented integer value

Definition at line 297 of file bigint.cpp.

   {
   return round_up(bits(), 8) / 8;
   }

References bits(), and Botan::round_up().

Referenced by binary_encode(), Botan::ECIES_KA_Operation::derive_secret(), encode(), Botan::DER_Encoder::encode(), Botan::EC_Point::encode(), encode_1363(), encode_fixed_length_int_pair(), encode_locked(), Botan::EC_PrivateKey::private_key_bits(), Botan::GOST_3410_PublicKey::public_key_bits(), and to_hex_string().

clear()

void Botan::BigInt::clear ( )

inline

Zeroize the BigInt. The size of the underlying register is not modified.

Definition at line 379 of file bigint.h.

{ m_data.set_to_zero(); m_signedness = Positive; }

Referenced by Botan::EC_Point::add(), Botan::EC_Point::add_affine(), binary_decode(), Botan::BER_Decoder::decode(), mul(), operator*=(), and randomize().

clear_bit()

void Botan::BigInt::clear_bit

(

size_t

n

)

Clear bit at specified position

Parameters

n	bit position to clear

Definition at line 286 of file bigint.cpp.

   {
   const size_t which = n / BOTAN_MP_WORD_BITS;
 
   if(which < size())
      {
      const word mask = ~(static_cast<word>(1) << (n % BOTAN_MP_WORD_BITS));
      m_data.set_word_at(which, word_at(which) & mask);
      }
   }

References BOTAN_MP_WORD_BITS, size(), and word_at().

cmp()

int32_t Botan::BigInt::cmp	(	const BigInt &	n,
		bool	check_signs = true
	)		const

Compare this to another BigInt

Parameters

n	the BigInt value to compare with
check_signs	include sign in comparison?

Returns

if (this<n) return -1, if (this>n) return 1, if both values are identical return 0 [like Perl's <=> operator]

Definition at line 156 of file bigint.cpp.

   {
   if(check_signs)
      {
      if(other.is_positive() && this->is_negative())
         return -1;
 
      if(other.is_negative() && this->is_positive())
         return 1;
 
      if(other.is_negative() && this->is_negative())
         return (-bigint_cmp(this->data(), this->size(),
                             other.data(), other.size()));
      }
 
   return bigint_cmp(this->data(), this->size(),
                     other.data(), other.size());
   }

References Botan::bigint_cmp(), data(), is_negative(), is_positive(), and size().

Referenced by Botan::operator<=(), and Botan::operator>=().

cmp_word()

int32_t Botan::BigInt::cmp_word

(

word

n

)

const

Compare this to an integer

Parameters

n	the value to compare with

Returns

if (this<n) return -1, if (this>n) return 1, if both values are identical return 0 [like Perl's <=> operator]

Definition at line 141 of file bigint.cpp.

   {
   if(is_negative())
      return -1; // other is positive ...
 
   const size_t sw = this->sig_words();
   if(sw > 1)
      return 1; // must be larger since other is just one word ...
 
   return bigint_cmp(this->data(), sw, &other, 1);
   }

References Botan::bigint_cmp(), data(), is_negative(), and sig_words().

Referenced by Botan::operator!=(), Botan::operator<(), Botan::operator<=(), Botan::operator==(), Botan::operator>(), and Botan::operator>=().

cond_flip_sign()

void Botan::BigInt::cond_flip_sign

(

bool

predicate

)

If predicate is true flip the sign of *this

Definition at line 474 of file bigint.cpp.

   {
   // This code is assuming Negative == 0, Positive == 1
 
   const auto mask = CT::Mask<uint8_t>::expand(predicate);
 
   const uint8_t current_sign = static_cast<uint8_t>(sign());
 
   const uint8_t new_sign = mask.select(current_sign ^ 1, current_sign);
 
   set_sign(static_cast<Sign>(new_sign));
   }

References Botan::CT::Mask< T >::expand(), set_sign(), and sign().

Referenced by ct_cond_assign(), Botan::operator*(), and rev_sub().

conditionally_set_bit()

void Botan::BigInt::conditionally_set_bit ( size_t  n, bool  set_it  )

inline

Conditionally set bit at specified position. Note if set_it is false, nothing happens, and if the bit is already set, it remains set.

Parameters

n	bit position to set
set_it	if the bit should be set

Definition at line 456 of file bigint.h.

        {
        const size_t which = n / BOTAN_MP_WORD_BITS;
        const word mask = static_cast<word>(set_it) << (n % BOTAN_MP_WORD_BITS);
        m_data.set_word_at(which, word_at(which) | mask);
        }

References BOTAN_MP_WORD_BITS.

Referenced by Botan::ct_divide(), Botan::ct_divide_word(), and Botan::ct_modulo().

const_time_poison()

void Botan::BigInt::const_time_poison ( ) const

inline

Definition at line 749 of file bigint.h.

{}

Referenced by Botan::gcd().

const_time_unpoison()

void Botan::BigInt::const_time_unpoison ( ) const

inline

Definition at line 750 of file bigint.h.

{}

Referenced by Botan::gcd().

ct_cond_add()

void Botan::BigInt::ct_cond_add	(	bool	predicate,
		const BigInt &	value
	)

If predicate is true add value to *this

Definition at line 454 of file bigint.cpp.

   {
   if(this->is_negative() || value.is_negative())
      throw Invalid_Argument("BigInt::ct_cond_add requires both values to be positive");
   this->grow_to(1 + value.sig_words());
 
   bigint_cnd_add(static_cast<word>(predicate),
                  this->mutable_data(), this->size(),
                  value.data(), value.sig_words());
   }

References Botan::bigint_cnd_add(), data(), grow_to(), is_negative(), mutable_data(), sig_words(), and size().

Referenced by Botan::gcd(), Botan::inverse_mod(), and Botan::is_lucas_probable_prime().

ct_cond_assign()

void Botan::BigInt::ct_cond_assign	(	bool	predicate,
		const BigInt &	other
	)

If predicate is true assign other to *this Uses a masked operation to avoid side channels

Definition at line 487 of file bigint.cpp.

   {
   const size_t t_words = size();
   const size_t o_words = other.size();
 
   if(o_words < t_words)
      grow_to(o_words);
 
   const size_t r_words = std::max(t_words, o_words);
 
   const auto mask = CT::Mask<word>::expand(predicate);
 
   for(size_t i = 0; i != r_words; ++i)
      {
      const word o_word = other.word_at(i);
      const word t_word = this->word_at(i);
      this->set_word_at(i, mask.select(o_word, t_word));
      }
 
   const bool different_sign = sign() != other.sign();
   cond_flip_sign(predicate && different_sign);
   }

References cond_flip_sign(), Botan::CT::Mask< T >::expand(), grow_to(), set_word_at(), sign(), size(), and word_at().

Referenced by Botan::inverse_mod(), Botan::is_lucas_probable_prime(), and Botan::power_mod().

ct_cond_swap()

void Botan::BigInt::ct_cond_swap	(	bool	predicate,
		BigInt &	other
	)

If predicate is true swap *this and other Uses a masked operation to avoid side channels

Definition at line 465 of file bigint.cpp.

   {
   const size_t max_words = std::max(size(), other.size());
   grow_to(max_words);
   other.grow_to(max_words);
 
   bigint_cnd_swap(predicate, this->mutable_data(), other.mutable_data(), max_words);
   }

References Botan::bigint_cnd_swap(), grow_to(), mutable_data(), and size().

Referenced by Botan::ct_divide(), Botan::ct_modulo(), and Botan::gcd().

ct_reduce_below()

void Botan::BigInt::ct_reduce_below	(	const BigInt &	mod,
		secure_vector< word > &	ws,
		size_t	bound
	)

Return *this % mod

Assumes that *this is (if anything) only slightly larger than mod and performs repeated subtractions. It should not be used if *this is much larger than mod, instead use modulo operator.

Performs exactly bound subtractions, so if *this is >= bound*mod then the result will not be fully reduced. If bound is zero, nothing happens.

Definition at line 365 of file bigint.cpp.

   {
   if(mod.is_negative() || this->is_negative())
      throw Invalid_Argument("BigInt::ct_reduce_below both values must be positive");
 
   const size_t mod_words = mod.sig_words();
 
   grow_to(mod_words);
 
   const size_t sz = size();
 
   ws.resize(sz);
 
   clear_mem(ws.data(), sz);
 
   for(size_t i = 0; i != bound; ++i)
      {
      word borrow = bigint_sub3(ws.data(), data(), sz, mod.data(), mod_words);
 
      CT::Mask<word>::is_zero(borrow).select_n(mutable_data(), ws.data(), data(), sz);
      }
   }

References Botan::bigint_sub3(), Botan::clear_mem(), data(), grow_to(), is_negative(), Botan::CT::Mask< T >::is_zero(), mutable_data(), sig_words(), and size().

Referenced by Botan::Modular_Reducer::reduce().

data()

const word * Botan::BigInt::data ( ) const

inline

Return a const pointer to the register

Returns

a pointer to the start of the internal register

Definition at line 649 of file bigint.h.

{ return m_data.const_data(); }

Referenced by Botan::EC_Point::add(), add(), add2(), Botan::EC_Point::add_affine(), cmp(), cmp_word(), ct_cond_add(), Botan::ct_divide(), Botan::ct_modulo(), ct_reduce_below(), Botan::CurveGFp_Repr::curve_mul(), Botan::CurveGFp_Repr::curve_sqr(), encode_words(), is_equal(), is_less_than(), mod_add(), mod_sub(), Botan::Montgomery_Params::mul(), mul(), Botan::Montgomery_Params::mul_by(), Botan::operator*(), Botan::operator<<(), Botan::operator>>(), Botan::Montgomery_Params::redc(), Botan::redc_p521(), Botan::Modular_Reducer::reduce(), reduce_below(), rev_sub(), Botan::Montgomery_Params::sqr(), square(), and Botan::Montgomery_Params::square_this().

decode() [1/4]

template<typename Alloc >

static BigInt Botan::BigInt::decode ( const std::vector< uint8_t, Alloc > &  buf )

inlinestatic

Create a BigInt from an integer in a byte array

Parameters

buf	the binary value to load

Returns

BigInt representing the integer in the byte array

Definition at line 816 of file bigint.h.

        {
        return BigInt(buf);
        }

decode() [2/4]

template<typename Alloc >

static BigInt Botan::BigInt::decode ( const std::vector< uint8_t, Alloc > &  buf, Base  base  )

inlinestatic

Create a BigInt from an integer in a byte array

Parameters

buf	the binary value to load
base	number-base of the integer in buf

Returns

BigInt representing the integer in the byte array

Definition at line 838 of file bigint.h.

        {
        if(base == Binary)
           return BigInt(buf);
        return BigInt::decode(buf.data(), buf.size(), base);
        }

decode() [3/4]

static BigInt Botan::BigInt::decode ( const uint8_t  buf[], size_t  length  )

inlinestatic

Create a BigInt from an integer in a byte array

Parameters

buf	the binary value to load
length	size of buf

Returns

BigInt representing the integer in the byte array

Definition at line 805 of file bigint.h.

        {
        return BigInt(buf, length);
        }

Referenced by BigInt(), botan_srp6_client_agree(), botan_srp6_server_session_step1(), botan_srp6_server_session_step2(), Botan::TLS::Client_Key_Exchange::Client_Key_Exchange(), Botan::BER_Decoder::decode_octet_string_bigint(), Botan::CRL_Entry::encode_into(), Botan::TPM_PrivateKey::get_e(), Botan::TPM_PrivateKey::get_n(), Botan::OCSP::CertID::is_id_for(), Botan::OS2ECP(), and Botan::TLS::Callbacks::tls_ephemeral_key_agreement().

decode() [4/4]

BigInt Botan::BigInt::decode ( const uint8_t  buf[], size_t  length, Base  base  )

static

Create a BigInt from an integer in a byte array

Parameters

buf	the binary value to load
length	size of buf
base	number-base of the integer in buf

Returns

BigInt representing the integer in the byte array

Definition at line 144 of file big_code.cpp.

   {
   BigInt r;
   if(base == Binary)
      {
      r.binary_decode(buf, length);
      }
   else if(base == Hexadecimal)
      {
      secure_vector<uint8_t> binary;
 
      if(length % 2)
         {
         // Handle lack of leading 0
         const char buf0_with_leading_0[2] =
            { '0', static_cast<char>(buf[0]) };
 
         binary = hex_decode_locked(buf0_with_leading_0, 2);
 
         binary += hex_decode_locked(cast_uint8_ptr_to_char(&buf[1]),
                                     length - 1,
                                     false);
         }
      else
         binary = hex_decode_locked(cast_uint8_ptr_to_char(buf),
                                    length, false);
 
      r.binary_decode(binary.data(), binary.size());
      }
   else if(base == Decimal)
      {
      // This could be made faster using the same trick as to_dec_string
      for(size_t i = 0; i != length; ++i)
         {
         const char c = buf[i];
 
         if(c < '0' || c > '9')
            throw Invalid_Argument("BigInt::decode: invalid decimal char");
 
         const uint8_t x = c - '0';
         BOTAN_ASSERT_NOMSG(x < 10);
 
         r *= 10;
         r += x;
         }
      }
   else
      throw Invalid_Argument("Unknown BigInt decoding method");
   return r;
   }

References Binary, binary_decode(), BOTAN_ASSERT_NOMSG, Botan::cast_uint8_ptr_to_char(), Decimal, Botan::hex_decode_locked(), and Hexadecimal.

encode()

static std::vector< uint8_t > Botan::BigInt::encode ( const BigInt &  n )

inlinestatic

Encode the integer value from a BigInt to a std::vector of bytes

Parameters

n	the BigInt to use as integer source

Returns

secure_vector of bytes containing the bytes of the integer

Definition at line 780 of file bigint.h.

        {
        std::vector<uint8_t> output(n.bytes());
        n.binary_encode(output.data());
        return output;
        }

References binary_encode(), and bytes().

Referenced by botan_generate_srp6_verifier(), botan_srp6_client_agree(), botan_srp6_server_session_step1(), Botan::CRL_Entry::decode_from(), Botan::FPE_FE1::FPE_FE1(), and Botan::TLS::Server_Key_Exchange::Server_Key_Exchange().

encode_1363() [1/2]

secure_vector< uint8_t > Botan::BigInt::encode_1363 ( const BigInt &  n, size_t  bytes  )

static

Encode a BigInt to a byte array according to IEEE 1363

Parameters

n	the BigInt to encode
bytes	the length of the resulting secure_vector<uint8_t>

Returns

a secure_vector<uint8_t> containing the encoded BigInt

Definition at line 107 of file big_code.cpp.

   {
   if(n.bytes() > bytes)
      throw Encoding_Error("encode_1363: n is too large to encode properly");
 
   secure_vector<uint8_t> output(bytes);
   n.binary_encode(output.data(), output.size());
   return output;
   }

References binary_encode(), and bytes().

Referenced by Botan::EC_Group::DER_encode(), Botan::EC_Point::encode(), Botan::RFC6979_Nonce_Generator::nonce_for(), Botan::EC_PrivateKey::private_key_bits(), Botan::DL_PublicKey::public_key_as_bytes(), Botan::RFC6979_Nonce_Generator::RFC6979_Nonce_Generator(), Botan::Montgomery_Int::serialize(), Botan::sm2_compute_za(), Botan::srp6_client_agree(), and Botan::SRP6_Server_Session::step2().

encode_1363() [2/2]

void Botan::BigInt::encode_1363 ( uint8_t  out[], size_t  bytes, const BigInt &  n  )

static

Definition at line 118 of file big_code.cpp.

   {
   if(n.bytes() > bytes)
      throw Encoding_Error("encode_1363: n is too large to encode properly");
 
   n.binary_encode(output, bytes);
   }

References binary_encode(), and bytes().

encode_fixed_length_int_pair()

secure_vector< uint8_t > Botan::BigInt::encode_fixed_length_int_pair ( const BigInt &  n1, const BigInt &  n2, size_t  bytes  )

static

Encode two BigInt to a byte array according to IEEE 1363

Parameters

n1	the first BigInt to encode
n2	the second BigInt to encode
bytes	the length of the encoding of each single BigInt

Returns

a secure_vector<uint8_t> containing the concatenation of the two encoded BigInt

Definition at line 129 of file big_code.cpp.

   {
   if(n1.is_negative() || n2.is_negative())
      throw Encoding_Error("encode_fixed_length_int_pair: values must be positive");
   if(n1.bytes() > bytes || n2.bytes() > bytes)
      throw Encoding_Error("encode_fixed_length_int_pair: values too large to encode properly");
   secure_vector<uint8_t> output(2 * bytes);
   n1.binary_encode(output.data()        , bytes);
   n2.binary_encode(output.data() + bytes, bytes);
   return output;
   }

References binary_encode(), bytes(), and is_negative().

encode_locked()

static secure_vector< uint8_t > Botan::BigInt::encode_locked ( const BigInt &  n )

inlinestatic

Encode the integer value from a BigInt to a secure_vector of bytes

Parameters

n	the BigInt to use as integer source

Returns

secure_vector of bytes containing the bytes of the integer

Definition at line 792 of file bigint.h.

        {
        secure_vector<uint8_t> output(n.bytes());
        n.binary_encode(output.data());
        return output;
        }

References binary_encode(), and bytes().

Referenced by Botan::DL_PrivateKey::raw_private_key_bits(), and Botan::EC_PrivateKey::raw_private_key_bits().

encode_words()

void Botan::BigInt::encode_words	(	word	out[],
		size_t	size
	)		const

Place the value into out, zero-padding up to size words Throw if *this cannot be represented in size words

Definition at line 202 of file bigint.cpp.

   {
   const size_t words = sig_words();
 
   if(words > size)
      throw Encoding_Error("BigInt::encode_words value too large to encode");
 
   clear_mem(out, size);
   copy_mem(out, data(), words);
   }

References Botan::clear_mem(), Botan::copy_mem(), data(), sig_words(), and size().

flip_sign()

void Botan::BigInt::flip_sign ( )

inline

Flip the sign of this BigInt

Definition at line 583 of file bigint.h.

        {
        set_sign(reverse_sign());
        }

Referenced by Botan::ct_divide_word(), Botan::BER_Decoder::decode(), Botan::is_lucas_probable_prime(), and operator-().

from_bytes_with_max_bits()

BigInt Botan::BigInt::from_bytes_with_max_bits ( const uint8_t  buf[], size_t  length, size_t  max_bits  )

static

Create a BigInt from an integer in a byte array

Note this function is primarily used for implementing signature schemes and is not useful in typical applications.

Parameters

buf	the byte array holding the value
length	size of buf
max_bits	if the resulting integer is more than max_bits, it will be shifted so it is at most max_bits in length.

Definition at line 110 of file bigint.cpp.

   {
   const size_t input_bits = 8 * length;
 
   BigInt bn;
   bn.binary_decode(input, length);
 
   if(input_bits > max_bits)
      {
      const size_t bits_to_shift = input_bits - max_bits;
 
      bn >>= bits_to_shift;
      }
 
   return bn;
   }

References binary_decode().

from_s32()

BigInt Botan::BigInt::from_s32 ( int32_t  n )

static

Create BigInt from a signed 32 bit integer

Parameters

n	initial value of this BigInt

Definition at line 51 of file bigint.cpp.

   {
   if(n >= 0)
      return BigInt::from_u64(static_cast<uint64_t>(n));
   else
      return -BigInt::from_u64(static_cast<uint64_t>(-n));
   }

References from_u64().

Referenced by botan_mp_set_from_int(), and Botan::sqrt_modulo_prime().

from_u64()

BigInt Botan::BigInt::from_u64 ( uint64_t  n )

static

Create BigInt from an unsigned 64 bit integer

Parameters

n	initial value of this BigInt

Definition at line 28 of file bigint.cpp.

   {
   BigInt bn;
 
#if BOTAN_MP_WORD_BITS == 64
   bn.set_word_at(0, n);
#else
   bn.set_word_at(1, static_cast<word>(n >> 32));
   bn.set_word_at(0, static_cast<word>(n));
#endif
 
   return bn;
   }

References set_word_at().

Referenced by Botan::DER_Encoder::encode(), from_s32(), and Botan::RSA_PrivateKey::RSA_PrivateKey().

from_word()

BigInt Botan::BigInt::from_word ( word  n )

static

Create BigInt from a word (limb)

Parameters

n	initial value of this BigInt

Definition at line 43 of file bigint.cpp.

   {
   BigInt bn;
   bn.set_word_at(0, n);
   return bn;
   }

References set_word_at().

Referenced by Botan::DL_Group::DL_Group(), Botan::is_bailie_psw_probable_prime(), Botan::is_lucas_probable_prime(), Botan::is_miller_rabin_probable_prime(), Botan::operator%(), Botan::random_prime(), Botan::sqrt_modulo_prime(), and Botan::DL_Group::verify_group().

get_bit()

bool Botan::BigInt::get_bit ( size_t  n ) const

inline

Return bit value at specified position

Parameters

n	the bit offset to test

Returns

true, if the bit at position n is set, false otherwise

Definition at line 483 of file bigint.h.

        {
        return ((word_at(n / BOTAN_MP_WORD_BITS) >> (n % BOTAN_MP_WORD_BITS)) & 1);
        }

References BOTAN_MP_WORD_BITS.

Referenced by Botan::ct_divide(), Botan::ct_divide_word(), Botan::ct_modulo(), Botan::inverse_mod(), Botan::is_lucas_probable_prime(), Botan::operator*(), and Botan::power_mod().

get_substring()

uint32_t Botan::BigInt::get_substring	(	size_t	offset,
		size_t	length
	)		const

Return (a maximum of) 32 bits of the complete value

Parameters

offset	the offset to start extracting
length	amount of bits to extract (starting at offset)

Returns

the integer extracted from the register starting at offset with specified length

Definition at line 239 of file bigint.cpp.

   {
   if(length == 0 || length > 32)
      throw Invalid_Argument("BigInt::get_substring invalid substring length");
 
   const uint32_t mask = 0xFFFFFFFF >> (32 - length);
 
   const size_t word_offset = offset / BOTAN_MP_WORD_BITS;
   const size_t wshift = (offset % BOTAN_MP_WORD_BITS);
 
   /*
   * The substring is contained within one or at most two words. The
   * offset and length are not secret, so we can perform conditional
   * operations on those values.
   */
   const word w0 = word_at(word_offset);
 
   if(wshift == 0 || (offset + length) / BOTAN_MP_WORD_BITS == word_offset)
      {
      return static_cast<uint32_t>(w0 >> wshift) & mask;
      }
   else
      {
      const word w1 = word_at(word_offset + 1);
      return static_cast<uint32_t>((w0 >> wshift) | (w1 << (BOTAN_MP_WORD_BITS - wshift))) & mask;
      }
   }

References BOTAN_MP_WORD_BITS, and word_at().

Referenced by Botan::monty_multi_exp(), Botan::EC_Point_Base_Point_Precompute::mul(), Botan::EC_Point_Var_Point_Precompute::mul(), and Botan::EC_Point_Multi_Point_Precompute::multi_exp().

get_word_vector() [1/2]

secure_vector< word > & Botan::BigInt::get_word_vector ( )

inline

Don't use this function in application code

Definition at line 654 of file bigint.h.

{ return m_data.mutable_vector(); }

Referenced by Botan::EC_Point_Var_Point_Precompute::EC_Point_Var_Point_Precompute().

get_word_vector() [2/2]

const secure_vector< word > & Botan::BigInt::get_word_vector ( ) const

inline

Don't use this function in application code

Definition at line 659 of file bigint.h.

{ return m_data.const_vector(); }

grow_to()

void Botan::BigInt::grow_to ( size_t  n ) const

inline

Increase internal register buffer to at least n words

Parameters

n	new size of register

Definition at line 665 of file bigint.h.

{ m_data.grow_to(n); }

Referenced by add(), ct_cond_add(), ct_cond_assign(), ct_cond_swap(), ct_reduce_below(), Botan::Montgomery_Int::fix_size(), mod_add(), mod_sub(), mul(), Botan::Montgomery_Params::mul_by(), Botan::Montgomery_Params::redc(), Botan::redc_p192(), Botan::redc_p224(), Botan::redc_p256(), Botan::redc_p384(), Botan::redc_p521(), reduce_below(), Botan::Montgomery_Params::square_this(), Botan::vartime_divide(), and with_capacity().

is_equal()

bool Botan::BigInt::is_equal

(

const BigInt &

n

)

const

Compare this to another BigInt

Parameters

n	the BigInt value to compare with

Returns

true if this == n or false otherwise

Definition at line 175 of file bigint.cpp.

   {
   if(this->sign() != other.sign())
      return false;
 
   return bigint_ct_is_eq(this->data(), this->sig_words(),
                          other.data(), other.sig_words()).is_set();
   }

References Botan::bigint_ct_is_eq(), data(), sig_words(), and sign().

Referenced by Botan::operator!=().

is_even()

bool Botan::BigInt::is_even ( ) const

inline

Test if the integer has an even value

Returns

true if the integer is even, false otherwise

Definition at line 416 of file bigint.h.

{ return (get_bit(0) == 0); }

Referenced by Botan::gcd(), Botan::generate_rsa_prime(), Botan::inverse_mod(), Botan::is_bailie_psw_probable_prime(), Botan::is_lucas_probable_prime(), Botan::is_miller_rabin_probable_prime(), Botan::is_prime(), Botan::jacobi(), Botan::Montgomery_Params::Montgomery_Params(), Botan::passes_miller_rabin_test(), and Botan::random_prime().

is_less_than()

bool Botan::BigInt::is_less_than

(

const BigInt &

n

)

const

Compare this to another BigInt

Parameters

n	the BigInt value to compare with

Returns

true if this < n or false otherwise

Definition at line 184 of file bigint.cpp.

   {
   if(this->is_negative() && other.is_positive())
      return true;
 
   if(this->is_positive() && other.is_negative())
      return false;
 
   if(other.is_negative() && this->is_negative())
      {
      return bigint_ct_is_lt(other.data(), other.sig_words(),
                             this->data(), this->sig_words()).is_set();
      }
 
   return bigint_ct_is_lt(this->data(), this->sig_words(),
                          other.data(), other.sig_words()).is_set();
   }

References Botan::bigint_ct_is_lt(), data(), is_negative(), is_positive(), and sig_words().

Referenced by Botan::operator<().

is_negative()

bool Botan::BigInt::is_negative ( ) const

inline

Tests if the sign of the integer is negative

Returns

true, iff the integer has a negative sign

Definition at line 556 of file bigint.h.

{ return (sign() == Negative); }

Referenced by cmp(), cmp_word(), ct_cond_add(), Botan::ct_divide_word(), Botan::ct_modulo(), ct_reduce_below(), Botan::BER_Decoder::decode(), encode_fixed_length_int_pair(), Botan::inverse_mod(), is_less_than(), Botan::is_lucas_probable_prime(), mod_add(), mod_mul(), mod_sub(), Botan::monty_multi_exp(), Botan::EC_Point_Base_Point_Precompute::mul(), Botan::EC_Point_Var_Point_Precompute::mul(), Botan::EC_Point_Multi_Point_Precompute::multi_exp(), Botan::operator%(), Botan::operator*(), Botan::operator>>(), operator>>=(), Botan::power_mod(), random_integer(), Botan::random_prime(), Botan::Modular_Reducer::reduce(), reduce_below(), to_dec_string(), to_hex_string(), to_u32bit(), and Botan::vartime_divide().

is_nonzero()

bool Botan::BigInt::is_nonzero ( ) const

inline

Test if the integer is not zero

Returns

true if the integer is non-zero, false otherwise

Definition at line 428 of file bigint.h.

{ return (!is_zero()); }

Referenced by Botan::ct_modulo(), Botan::inverse_mod(), and Botan::Modular_Reducer::reduce().

is_odd()

bool Botan::BigInt::is_odd ( ) const

inline

Test if the integer has an odd value

Returns

true if the integer is odd, false otherwise

Definition at line 422 of file bigint.h.

{ return (get_bit(0) == 1); }

Referenced by Botan::gcd(), Botan::inverse_mod(), Botan::is_lucas_probable_prime(), Botan::power_mod(), and Botan::sqrt_modulo_prime().

is_positive()

bool Botan::BigInt::is_positive ( ) const

inline

Tests if the sign of the integer is positive

Returns

true, iff the integer has a positive sign

Definition at line 562 of file bigint.h.

{ return (sign() == Positive); }

Referenced by cmp(), is_less_than(), Botan::operator%(), Botan::redc_p192(), Botan::redc_p224(), Botan::redc_p256(), Botan::redc_p384(), and Botan::redc_p521().

is_zero()

bool Botan::BigInt::is_zero ( ) const

inline

Test if the integer is zero

Returns

true if the integer is zero, false otherwise

Definition at line 434 of file bigint.h.

        {
        return (sig_words() == 0);
        }

Referenced by Botan::EC_Point::add(), Botan::EC_Point::add_affine(), Botan::gcd(), Botan::inverse_mod(), Botan::Montgomery_Int::is_zero(), Botan::jacobi(), Botan::EC_Point::mult2(), Botan::EC_Point::mult2i(), Botan::operator%(), operator>>=(), Botan::power_mod(), Botan::random_prime(), Botan::RSA_PrivateKey::RSA_PrivateKey(), to_dec_string(), Botan::vartime_divide(), and Botan::DL_Group::verify_public_element().

mask_bits()

void Botan::BigInt::mask_bits ( size_t  n )

inline

Clear all but the lowest n bits

Parameters

n	amount of bits to keep

Definition at line 473 of file bigint.h.

        {
        m_data.mask_bits(n);
        }

Referenced by Botan::inverse_mod(), Botan::redc_p192(), Botan::redc_p224(), Botan::redc_p256(), Botan::redc_p384(), Botan::redc_p521(), and Botan::Modular_Reducer::reduce().

mod_add()

BigInt & Botan::BigInt::mod_add	(	const BigInt &	y,
		const BigInt &	mod,
		secure_vector< word > &	ws
	)

Set *this to (*this + y) % mod This function assumes *this is >= 0 && < mod

Parameters

y	the BigInt to add - assumed y >= 0 and y < mod
mod	the positive modulus
ws	a temp workspace

Definition at line 50 of file big_ops2.cpp.

   {
   if(this->is_negative() || s.is_negative() || mod.is_negative())
      throw Invalid_Argument("BigInt::mod_add expects all arguments are positive");
 
   BOTAN_DEBUG_ASSERT(*this < mod);
   BOTAN_DEBUG_ASSERT(s < mod);
 
   /*
   t + s or t + s - p == t - (p - s)
 
   So first compute ws = p - s
 
   Then compute t + s and t - ws
 
   If t - ws does not borrow, then that is the correct valued
   */
 
   const size_t mod_sw = mod.sig_words();
   BOTAN_ARG_CHECK(mod_sw > 0, "BigInt::mod_add modulus must be positive");
 
   this->grow_to(mod_sw);
   s.grow_to(mod_sw);
 
   // First mod_sw for p - s, 2*mod_sw for bigint_addsub workspace
   if(ws.size() < 3*mod_sw)
      ws.resize(3*mod_sw);
 
   word borrow = bigint_sub3(&ws[0], mod.data(), mod_sw, s.data(), mod_sw);
   BOTAN_DEBUG_ASSERT(borrow == 0);
   BOTAN_UNUSED(borrow);
 
   // Compute t - ws
   borrow = bigint_sub3(&ws[mod_sw], this->data(), mod_sw, &ws[0], mod_sw);
 
   // Compute t + s
   bigint_add3_nc(&ws[mod_sw*2], this->data(), mod_sw, s.data(), mod_sw);
 
   CT::conditional_copy_mem(borrow, &ws[0], &ws[mod_sw*2], &ws[mod_sw], mod_sw);
   set_words(&ws[0], mod_sw);
 
   return (*this);
   }

References Botan::bigint_add3_nc(), Botan::bigint_sub3(), BOTAN_ARG_CHECK, BOTAN_DEBUG_ASSERT, BOTAN_UNUSED, Botan::CT::conditional_copy_mem(), data(), grow_to(), is_negative(), set_words(), and sig_words().

Referenced by Botan::Montgomery_Int::add(), Botan::EC_Point::mult2(), and Botan::Montgomery_Int::operator+().

mod_mul()

BigInt & Botan::BigInt::mod_mul	(	uint8_t	y,
		const BigInt &	mod,
		secure_vector< word > &	ws
	)

Set *this to (*this * y) % mod This function assumes *this is >= 0 && < mod y should be small, less than 16

Parameters

y	the small integer to multiply by
mod	the positive modulus
ws	a temp workspace

Definition at line 121 of file big_ops2.cpp.

   {
   BOTAN_ARG_CHECK(this->is_negative() == false, "*this must be positive");
   BOTAN_ARG_CHECK(y < 16, "y too large");
 
   BOTAN_DEBUG_ASSERT(*this < mod);
 
   *this *= static_cast<word>(y);
   this->reduce_below(mod, ws);
   return (*this);
   }

References BOTAN_ARG_CHECK, BOTAN_DEBUG_ASSERT, is_negative(), reduce_below(), and y.

Referenced by Botan::Montgomery_Int::mul_by_2(), Botan::Montgomery_Int::mul_by_3(), Botan::Montgomery_Int::mul_by_4(), Botan::Montgomery_Int::mul_by_8(), and Botan::EC_Point::mult2().

mod_sub()

BigInt & Botan::BigInt::mod_sub	(	const BigInt &	y,
		const BigInt &	mod,
		secure_vector< word > &	ws
	)

Set *this to (*this - y) % mod This function assumes *this is >= 0 && < mod

Parameters

y	the BigInt to subtract - assumed y >= 0 and y < mod
mod	the positive modulus
ws	a temp workspace

Definition at line 94 of file big_ops2.cpp.

   {
   if(this->is_negative() || s.is_negative() || mod.is_negative())
      throw Invalid_Argument("BigInt::mod_sub expects all arguments are positive");
 
   // We are assuming in this function that *this and s are no more than mod_sw words long
   BOTAN_DEBUG_ASSERT(*this < mod);
   BOTAN_DEBUG_ASSERT(s < mod);
 
   const size_t mod_sw = mod.sig_words();
 
   this->grow_to(mod_sw);
   s.grow_to(mod_sw);
 
   if(ws.size() < mod_sw)
      ws.resize(mod_sw);
 
   if(mod_sw == 4)
      bigint_mod_sub_n<4>(mutable_data(), s.data(), mod.data(), ws.data());
   else if(mod_sw == 6)
      bigint_mod_sub_n<6>(mutable_data(), s.data(), mod.data(), ws.data());
   else
      bigint_mod_sub(mutable_data(), s.data(), mod.data(), mod_sw, ws.data());
 
   return (*this);
   }

References Botan::bigint_mod_sub(), BOTAN_DEBUG_ASSERT, data(), grow_to(), is_negative(), mutable_data(), and sig_words().

Referenced by Botan::EC_Point::add(), Botan::EC_Point::add_affine(), Botan::EC_Point::mult2(), Botan::Montgomery_Int::operator-(), and Botan::Montgomery_Int::sub().

mul()

BigInt & Botan::BigInt::mul	(	const BigInt &	y,
		secure_vector< word > &	ws
	)

Multiply this with y

Parameters

y	the BigInt to multiply with this
ws	a temp workspace

Definition at line 160 of file big_ops2.cpp.

   {
   const size_t x_sw = sig_words();
   const size_t y_sw = y.sig_words();
   set_sign((sign() == y.sign()) ? Positive : Negative);
 
   if(x_sw == 0 || y_sw == 0)
      {
      clear();
      set_sign(Positive);
      }
   else if(x_sw == 1 && y_sw)
      {
      grow_to(y_sw + 1);
      bigint_linmul3(mutable_data(), y.data(), y_sw, word_at(0));
      }
   else if(y_sw == 1 && x_sw)
      {
      word carry = bigint_linmul2(mutable_data(), x_sw, y.word_at(0));
      set_word_at(x_sw, carry);
      }
   else
      {
      const size_t new_size = x_sw + y_sw + 1;
      ws.resize(new_size);
      secure_vector<word> z_reg(new_size);
 
      bigint_mul(z_reg.data(), z_reg.size(),
                 data(), size(), x_sw,
                 y.data(), y.size(), y_sw,
                 ws.data(), ws.size());
 
      this->swap_reg(z_reg);
      }
 
   return (*this);
   }

References Botan::bigint_linmul2(), Botan::bigint_linmul3(), Botan::bigint_mul(), Botan::carry(), clear(), data(), grow_to(), mutable_data(), Negative, Positive, set_sign(), set_word_at(), sig_words(), sign(), size(), swap_reg(), word_at(), and y.

Referenced by operator*=(), and Botan::Modular_Reducer::reduce().

mutable_data()

word * Botan::BigInt::mutable_data ( )

inline

Return a mutable pointer to the register

Returns

a pointer to the start of the internal register

Definition at line 643 of file bigint.h.

{ return m_data.mutable_data(); }

Referenced by add(), add2(), ct_cond_add(), ct_cond_swap(), Botan::ct_divide(), Botan::ct_modulo(), ct_reduce_below(), mod_sub(), Botan::Montgomery_Params::mul(), mul(), Botan::Montgomery_Params::mul_by(), Botan::operator*(), operator*=(), Botan::Montgomery_Params::redc(), Botan::redc_p192(), Botan::redc_p224(), Botan::redc_p256(), Botan::redc_p384(), Botan::redc_p521(), Botan::Montgomery_Params::sqr(), Botan::Montgomery_Params::square_this(), and Botan::vartime_divide().

one()

static BigInt Botan::BigInt::one ( )

inlinestatic

Create a 1-value BigInt

Definition at line 50 of file bigint.h.

{ return BigInt::from_word(1); }

Referenced by Botan::gcd(), Botan::is_lucas_probable_prime(), Botan::is_perfect_square(), Botan::power_mod(), and Botan::EC_Group::random_scalar().

operator!()

bool Botan::BigInt::operator! ( ) const

inline

! operator

Returns

true iff this is zero, otherwise false

Definition at line 294 of file bigint.h.

{ return (!is_nonzero()); }

operator%=() [1/2]

BigInt & Botan::BigInt::operator%=

(

const BigInt &

y

)

Modulo operator

Parameters

y	the modulus to reduce this by

Definition at line 244 of file big_ops2.cpp.

   {
   return (*this = (*this) % mod);
   }

operator%=() [2/2]

word Botan::BigInt::operator%=

(

word

y

)

Modulo operator

Parameters

y	the modulus (word) to reduce this by

Definition at line 252 of file big_ops2.cpp.

   {
   if(mod == 0)
      throw Invalid_Argument("BigInt::operator%= divide by zero");
 
   word remainder = 0;
 
   if(is_power_of_2(mod))
       {
       remainder = (word_at(0) & (mod - 1));
       }
   else
      {
      const size_t sw = sig_words();
      for(size_t i = sw; i > 0; --i)
         remainder = bigint_modop(remainder, word_at(i-1), mod);
      }
 
   if(remainder && sign() == BigInt::Negative)
      remainder = mod - remainder;
 
   m_data.set_to_zero();
   m_data.set_word_at(0, remainder);
   set_sign(BigInt::Positive);
   return remainder;
   }

References Botan::bigint_modop(), Botan::is_power_of_2(), Negative, Positive, set_sign(), sig_words(), sign(), and word_at().

operator*=() [1/2]

BigInt & Botan::BigInt::operator*=

(

const BigInt &

y

)

*= operator

Parameters

y	the BigInt to multiply with this

Definition at line 154 of file big_ops2.cpp.

   {
   secure_vector<word> ws;
   return this->mul(y, ws);
   }

References mul().

operator*=() [2/2]

BigInt & Botan::BigInt::operator*=

(

word

y

)

*= operator

Parameters

y	the word to multiply with this

Definition at line 215 of file big_ops2.cpp.

   {
   if(y == 0)
      {
      clear();
      set_sign(Positive);
      }
 
   const word carry = bigint_linmul2(mutable_data(), size(), y);
   set_word_at(size(), carry);
 
   return (*this);
   }

References Botan::bigint_linmul2(), Botan::carry(), clear(), mutable_data(), Positive, set_sign(), set_word_at(), size(), and y.

operator++() [1/2]

BigInt & Botan::BigInt::operator++ ( )

inline

Increment operator

Definition at line 267 of file bigint.h.

{ return (*this += 1); }

operator++() [2/2]

BigInt Botan::BigInt::operator++ ( int  )

inline

Postfix increment operator

Definition at line 277 of file bigint.h.

{ BigInt x = (*this); ++(*this); return x; }

operator+=() [1/2]

BigInt & Botan::BigInt::operator+= ( const BigInt &  y )

inline

+= operator

Parameters

y	the BigInt to add to this

Definition at line 190 of file bigint.h.

        {
        return add(y.data(), y.sig_words(), y.sign());
        }

References y.

operator+=() [2/2]

BigInt & Botan::BigInt::operator+= ( word  y )

inline

+= operator

Parameters

y	the word to add to this

Definition at line 199 of file bigint.h.

        {
        return add(&y, 1, Positive);
        }

References y.

operator-()

BigInt Botan::BigInt::operator-

(

)

const

Unary negation operator

Returns

negative this

Definition at line 328 of file bigint.cpp.

   {
   BigInt x = (*this);
   x.flip_sign();
   return x;
   }

References flip_sign().

operator--() [1/2]

BigInt & Botan::BigInt::operator-- ( )

inline

Decrement operator

Definition at line 272 of file bigint.h.

{ return (*this -= 1); }

operator--() [2/2]

BigInt Botan::BigInt::operator-- ( int  )

inline

Postfix decrement operator

Definition at line 282 of file bigint.h.

{ BigInt x = (*this); --(*this); return x; }

operator-=() [1/2]

BigInt & Botan::BigInt::operator-= ( const BigInt &  y )

inline

-= operator

Parameters

y	the BigInt to subtract from this

Definition at line 208 of file bigint.h.

        {
        return sub(y.data(), y.sig_words(), y.sign());
        }

References y.

operator-=() [2/2]

BigInt & Botan::BigInt::operator-= ( word  y )

inline

-= operator

Parameters

y	the word to subtract from this

Definition at line 217 of file bigint.h.

        {
        return sub(&y, 1, Positive);
        }

References y.

operator/=()

BigInt & Botan::BigInt::operator/=

(

const BigInt &

y

)

/= operator

Parameters

y	the BigInt to divide this by

Definition at line 232 of file big_ops2.cpp.

   {
   if(y.sig_words() == 1 && is_power_of_2(y.word_at(0)))
      (*this) >>= (y.bits() - 1);
   else
      (*this) = (*this) / y;
   return (*this);
   }

References Botan::is_power_of_2(), and y.

operator<<=()

BigInt & Botan::BigInt::operator<<=

(

size_t

shift

)

Left shift operator

Parameters

shift

the number of bits to shift this left by

Definition at line 282 of file big_ops2.cpp.

   {
   const size_t shift_words = shift / BOTAN_MP_WORD_BITS;
   const size_t shift_bits  = shift % BOTAN_MP_WORD_BITS;
   const size_t size = sig_words();
 
   const size_t bits_free = top_bits_free();
 
   const size_t new_size = size + shift_words + (bits_free < shift_bits);
 
   m_data.grow_to(new_size);
 
   bigint_shl1(m_data.mutable_data(), new_size, size, shift_words, shift_bits);
 
   return (*this);
   }

References Botan::bigint_shl1(), BOTAN_MP_WORD_BITS, sig_words(), size(), and top_bits_free().

operator=() [1/2]

BigInt & Botan::BigInt::operator= ( BigInt &&  other )

inline

Move assignment

Definition at line 157 of file bigint.h.

        {
        if(this != &other)
           this->swap(other);
 
        return (*this);
        }

operator=() [2/2]

BigInt & Botan::BigInt::operator= ( const BigInt &  )

default

Copy assignment

operator>>=()

BigInt & Botan::BigInt::operator>>=

(

size_t

shift

)

Right shift operator

Parameters

shift

the number of bits to shift this right by

Definition at line 302 of file big_ops2.cpp.

   {
   const size_t shift_words = shift / BOTAN_MP_WORD_BITS;
   const size_t shift_bits  = shift % BOTAN_MP_WORD_BITS;
 
   bigint_shr1(m_data.mutable_data(), m_data.size(), shift_words, shift_bits);
 
   if(is_negative() && is_zero())
      set_sign(Positive);
 
   return (*this);
   }

References Botan::bigint_shr1(), BOTAN_MP_WORD_BITS, is_negative(), is_zero(), Positive, and set_sign().

power_of_2()

static BigInt Botan::BigInt::power_of_2 ( size_t  n )

inlinestatic

Create a power of two

Parameters

n	the power of two to create

Returns

bigint representing 2^n

Definition at line 768 of file bigint.h.

        {
        BigInt b;
        b.set_bit(n);
        return b;
        }

References b.

Referenced by Botan::inverse_mod(), Botan::is_perfect_square(), Botan::Montgomery_Params::Montgomery_Params(), and Botan::sqrt_modulo_prime().

random_integer()

BigInt Botan::BigInt::random_integer ( RandomNumberGenerator &  rng, const BigInt &  min, const BigInt &  max  )

static

Parameters

rng	a random number generator
min	the minimum value (must be non-negative)
max	the maximum value (must be non-negative and > min)

Returns

random integer in [min,max)

Definition at line 45 of file big_rand.cpp.

   {
   if(min.is_negative() || max.is_negative() || max <= min)
      throw Invalid_Argument("BigInt::random_integer invalid range");
 
   BigInt r;
 
   const size_t bits = max.bits();
 
   do
      {
      r.randomize(rng, bits, false);
      }
   while(r < min || r >= max);
 
   return r;
   }

References bits(), is_negative(), and randomize().

Referenced by botan_mp_rand_range(), Botan::is_miller_rabin_probable_prime(), Botan::EC_Group::random_scalar(), and Botan::EC_Point::randomize_repr().

randomize()

void Botan::BigInt::randomize	(	RandomNumberGenerator &	rng,
		size_t	bitsize,
		bool	set_high_bit = true
	)

Fill BigInt with a random number with size of bitsize

If set_high_bit is true, the highest bit will be set, which causes the entropy to be bits-1. Otherwise the highest bit is randomly chosen by the rng, causing the entropy to be bits.

Parameters

rng	the random number generator to use
bitsize	number of bits the created random value should have
set_high_bit	if true, the highest bit is always set

Definition at line 17 of file big_rand.cpp.

   {
   set_sign(Positive);
 
   if(bitsize == 0)
      {
      clear();
      }
   else
      {
      secure_vector<uint8_t> array = rng.random_vec(round_up(bitsize, 8) / 8);
 
      // Always cut unwanted bits
      if(bitsize % 8)
         array[0] &= 0xFF >> (8 - (bitsize % 8));
 
      // Set the highest bit if wanted
      if (set_high_bit)
         array[0] |= 0x80 >> ((bitsize % 8) ? (8 - bitsize % 8) : 0);
 
      binary_decode(array);
      }
   }

References binary_decode(), clear(), Positive, Botan::RandomNumberGenerator::random_vec(), Botan::round_up(), and set_sign().

Referenced by BigInt(), Botan::EC_Point_Var_Point_Precompute::EC_Point_Var_Point_Precompute(), and random_integer().

reduce_below()

size_t Botan::BigInt::reduce_below	(	const BigInt &	mod,
		secure_vector< word > &	ws
	)

Return *this % mod

Assumes that *this is (if anything) only slightly larger than mod and performs repeated subtractions. It should not be used if *this is much larger than mod, instead use modulo operator.

Definition at line 335 of file bigint.cpp.

   {
   if(p.is_negative() || this->is_negative())
      throw Invalid_Argument("BigInt::reduce_below both values must be positive");
 
   const size_t p_words = p.sig_words();
 
   if(size() < p_words + 1)
      grow_to(p_words + 1);
 
   if(ws.size() < p_words + 1)
      ws.resize(p_words + 1);
 
   clear_mem(ws.data(), ws.size());
 
   size_t reductions = 0;
 
   for(;;)
      {
      word borrow = bigint_sub3(ws.data(), data(), p_words + 1, p.data(), p_words);
      if(borrow)
         break;
 
      ++reductions;
      swap_reg(ws);
      }
 
   return reductions;
   }

References Botan::bigint_sub3(), Botan::clear_mem(), data(), grow_to(), is_negative(), sig_words(), size(), and swap_reg().

Referenced by mod_mul(), and Botan::vartime_divide().

resize()

void Botan::BigInt::resize ( size_t  s )

inline

Definition at line 667 of file bigint.h.

{ m_data.resize(s); }

Referenced by Botan::EC_Point::force_all_affine().

rev_sub()

BigInt & Botan::BigInt::rev_sub	(	const word	y[],
		size_t	y_words,
		secure_vector< word > &	ws
	)

Set *this to y - *this

Parameters

y	the BigInt to subtract from as a sequence of words
y_words	length of y in words
ws	a temp workspace

Definition at line 133 of file big_ops2.cpp.

   {
   if(this->sign() != BigInt::Positive)
      throw Invalid_State("BigInt::sub_rev requires this is positive");
 
   const size_t x_sw = this->sig_words();
 
   ws.resize(std::max(x_sw, y_sw));
   clear_mem(ws.data(), ws.size());
 
   const int32_t relative_size = bigint_sub_abs(ws.data(), data(), x_sw, y, y_sw);
 
   this->cond_flip_sign(relative_size > 0);
   this->swap_reg(ws);
 
   return (*this);
   }

References Botan::bigint_sub_abs(), Botan::clear_mem(), cond_flip_sign(), data(), Positive, sig_words(), sign(), swap_reg(), and y.

Referenced by Botan::Modular_Reducer::reduce().

reverse_sign()

Sign Botan::BigInt::reverse_sign ( ) const

inline

Returns

the opposite sign of the represented integer value

Definition at line 573 of file bigint.h.

        {
        if(sign() == Positive)
           return Negative;
        return Positive;
        }

set_bit()

void Botan::BigInt::set_bit ( size_t  n )

inline

Set bit at specified position

Parameters

n	bit position to set

Definition at line 443 of file bigint.h.

        {
        conditionally_set_bit(n, true);
        }

Referenced by Botan::EC_Point_Var_Point_Precompute::EC_Point_Var_Point_Precompute(), Botan::generate_dsa_primes(), Botan::generate_rsa_prime(), Botan::Modular_Reducer::Modular_Reducer(), and Botan::random_prime().

set_sign()

void Botan::BigInt::set_sign ( Sign  sign )

inline

Set sign of the integer

Parameters

sign	new Sign to set

Definition at line 592 of file bigint.h.

        {
        if(sign == Negative && is_zero())
           sign = Positive;
 
        m_signedness = sign;
        }

Referenced by abs(), add(), add2(), BigInt(), cond_flip_sign(), Botan::gcd(), Botan::inverse_mod(), mul(), operator%=(), Botan::operator*(), operator*=(), operator>>=(), randomize(), Botan::Modular_Reducer::reduce(), square(), to_dec_string(), and Botan::vartime_divide().

set_word_at()

void Botan::BigInt::set_word_at ( size_t  i, word  w  )

inline

Definition at line 542 of file bigint.h.

        {
        m_data.set_word_at(i, w);
        }

Referenced by ct_cond_assign(), from_u64(), from_word(), mul(), and operator*=().

set_words()

void Botan::BigInt::set_words ( const word  w[], size_t  len  )

inline

Definition at line 547 of file bigint.h.

        {
        m_data.set_words(w, len);
        }

Referenced by Botan::EC_Point::add(), Botan::EC_Point::add_affine(), mod_add(), and Botan::Montgomery_Int::Montgomery_Int().

sig_words()

size_t Botan::BigInt::sig_words ( ) const

inline

Return how many words we need to hold this value

Returns

significant words of the represented integer value

Definition at line 615 of file bigint.h.

        {
        return m_data.sig_words();
        }

Referenced by add(), add2(), bits(), cmp_word(), ct_cond_add(), Botan::ct_divide(), Botan::ct_divide_word(), ct_reduce_below(), Botan::CurveGFp_Repr::curve_mul(), Botan::CurveGFp_Repr::curve_sqr(), encode_words(), Botan::Montgomery_Int::fix_size(), is_equal(), is_less_than(), mod_add(), mod_sub(), Botan::Modular_Reducer::Modular_Reducer(), Botan::Montgomery_Params::Montgomery_Params(), Botan::Montgomery_Params::mul(), mul(), Botan::Montgomery_Params::mul_by(), Botan::operator%(), operator%=(), Botan::operator*(), Botan::operator<<(), operator<<=(), Botan::operator>>(), Botan::Modular_Reducer::reduce(), reduce_below(), rev_sub(), Botan::Montgomery_Params::sqr(), square(), Botan::Montgomery_Params::square_this(), top_bits_free(), and Botan::vartime_divide().

sign()

Sign Botan::BigInt::sign ( ) const

inline

Return the sign of the integer

Returns

the sign of the integer

Definition at line 568 of file bigint.h.

{ return (m_signedness); }

Referenced by add(), add2(), cond_flip_sign(), ct_cond_assign(), is_equal(), mul(), Botan::operator%(), operator%=(), Botan::operator*(), Botan::operator<<(), Botan::operator>>(), and rev_sub().

size()

size_t Botan::BigInt::size ( ) const

inline

Give size of internal register

Returns

size of internal register in words

Definition at line 609 of file bigint.h.

{ return m_data.size(); }

Referenced by Botan::EC_Point::add(), add(), Botan::EC_Point::add_affine(), clear_bit(), cmp(), ct_cond_add(), ct_cond_assign(), ct_cond_swap(), Botan::ct_divide(), Botan::ct_modulo(), ct_reduce_below(), Botan::CurveGFp_Repr::curve_mul(), Botan::CurveGFp_Repr::curve_sqr(), encode_words(), Botan::low_zero_bits(), Botan::Montgomery_Params::mul(), mul(), Botan::Montgomery_Params::mul_by(), Botan::operator*(), operator*=(), operator<<=(), Botan::redc_p192(), Botan::redc_p224(), Botan::redc_p256(), Botan::redc_p384(), Botan::redc_p521(), Botan::Modular_Reducer::reduce(), reduce_below(), Botan::Montgomery_Params::sqr(), square(), Botan::Montgomery_Params::square_this(), and with_capacity().

square()

BigInt & Botan::BigInt::square

(

secure_vector< word > &

ws

)

Square value of *this

Parameters

ws	a temp workspace

Definition at line 198 of file big_ops2.cpp.

   {
   const size_t sw = sig_words();
 
   secure_vector<word> z(2*sw);
   ws.resize(z.size());
 
   bigint_sqr(z.data(), z.size(),
              data(), size(), sw,
              ws.data(), ws.size());
 
   swap_reg(z);
   set_sign(BigInt::Positive);
 
   return (*this);
   }

References Botan::bigint_sqr(), data(), Positive, set_sign(), sig_words(), size(), and swap_reg().

Referenced by Botan::square().

sub()

BigInt & Botan::BigInt::sub ( const word  y[], size_t  y_words, Sign  sign  )

inline

Definition at line 300 of file bigint.h.

        {
        return add(y, y_words, sign == Positive ? Negative : Positive);
        }

References y.

swap()

void Botan::BigInt::swap ( BigInt &  other )

inline

Swap this value with another

Parameters

other

BigInt to swap values with

Definition at line 174 of file bigint.h.

        {
        m_data.swap(other.m_data);
        std::swap(m_signedness, other.m_signedness);
        }

Referenced by Botan::EC_Point::add_affine(), Botan::EC_Point::mult2(), Botan::EC_Point::swap(), and std::swap< Botan::BigInt >().

swap_reg()

void Botan::BigInt::swap_reg ( secure_vector< word > &  reg )

inline

Definition at line 180 of file bigint.h.

        {
        m_data.swap(reg);
        // sign left unchanged
        }

Referenced by mul(), reduce_below(), rev_sub(), and square().

to_dec_string()

std::string Botan::BigInt::to_dec_string

(

)

const

Convert this value to a decimal string. Warning: decimal conversions are relatively slow

If the integer is zero then "0" is returned. If the integer is negative then "-" is prefixed.

Definition at line 14 of file big_code.cpp.

   {
   // Use the largest power of 10 that fits in a word
#if (BOTAN_MP_WORD_BITS == 64)
   const word conversion_radix = 10000000000000000000U;
   const word radix_digits = 19;
#else
   const word conversion_radix = 1000000000U;
   const word radix_digits = 9;
#endif
 
   // (over-)estimate of the number of digits needed; log2(10) ~ 3.3219
   const size_t digit_estimate = static_cast<size_t>(1 + (this->bits() / 3.32));
 
   // (over-)estimate of db such that conversion_radix^db > *this
   const size_t digit_blocks = (digit_estimate + radix_digits - 1) / radix_digits;
 
   BigInt value = *this;
   value.set_sign(Positive);
 
   // Extract groups of digits into words
   std::vector<word> digit_groups(digit_blocks);
 
   for(size_t i = 0; i != digit_blocks; ++i)
      {
      word remainder = 0;
      ct_divide_word(value, conversion_radix, value, remainder);
      digit_groups[i] = remainder;
      }
 
   BOTAN_ASSERT_NOMSG(value.is_zero());
 
   // Extract digits from the groups
   std::vector<uint8_t> digits(digit_blocks * radix_digits);
 
   for(size_t i = 0; i != digit_blocks; ++i)
      {
      word remainder = digit_groups[i];
      for(size_t j = 0; j != radix_digits; ++j)
         {
         // Compiler should convert div/mod by 10 into mul by magic constant
         const word digit = remainder % 10;
         remainder /= 10;
         digits[radix_digits*i + j] = static_cast<uint8_t>(digit);
         }
      }
 
   // remove leading zeros
   while(!digits.empty() && digits.back() == 0)
      {
      digits.pop_back();
      }
 
   BOTAN_ASSERT_NOMSG(digit_estimate >= digits.size());
 
   // Reverse the digits to big-endian and format to text
   std::string s;
   s.reserve(1 + digits.size());
 
   if(is_negative())
      s += "-";
 
   // Reverse and convert to textual digits
   for(auto i = digits.rbegin(); i != digits.rend(); ++i)
      {
      s.push_back(*i + '0'); // assumes ASCII
      }
 
   if(s.empty())
      s += "0";
 
   return s;
   }

References bits(), BOTAN_ASSERT_NOMSG, Botan::ct_divide_word(), is_negative(), is_zero(), Positive, and set_sign().

Referenced by Botan::operator<<().

to_hex_string()

std::string Botan::BigInt::to_hex_string

(

)

const

Convert this value to a hexadecimal string.

If the integer is negative then "-" is prefixed. Then a prefix of "0x" is added. Follows is a sequence of hexadecimal characters in uppercase.

The number of hexadecimal characters is always an even number, with a zero prefix being included if necessary. For example encoding the integer "5" results in "0x05"

Definition at line 88 of file big_code.cpp.

   {
   const size_t this_bytes = this->bytes();
   std::vector<uint8_t> bits(std::max<size_t>(1, this_bytes));
 
   if(this_bytes > 0)
      this->binary_encode(bits.data());
 
   std::string hrep;
   if(is_negative())
      hrep += "-";
   hrep += "0x";
   hrep += hex_encode(bits);
   return hrep;
   }

References binary_encode(), bits(), bytes(), Botan::hex_encode(), and is_negative().

Referenced by Botan::operator<<().

to_u32bit()

uint32_t Botan::BigInt::to_u32bit

(

)

const

Convert this value into a uint32_t, if it is in the range [0 ... 2**32-1], or otherwise throw an exception.

Returns

the value as a uint32_t if conversion is possible

Definition at line 270 of file bigint.cpp.

   {
   if(is_negative())
      throw Encoding_Error("BigInt::to_u32bit: Number is negative");
   if(bits() > 32)
      throw Encoding_Error("BigInt::to_u32bit: Number is too big to convert");
 
   uint32_t out = 0;
   for(size_t i = 0; i != 4; ++i)
      out = (out << 8) | byte_at(3-i);
   return out;
   }

References bits(), byte_at(), and is_negative().

top_bits_free()

size_t Botan::BigInt::top_bits_free

(

)

const

Get the number of high bits unset in the top (allocated) word of this integer. Returns BOTAN_MP_WORD_BITS only iff *this is zero. Ignores sign.

Definition at line 302 of file bigint.cpp.

   {
   const size_t words = sig_words();
 
   const word top_word = word_at(words - 1);
   const size_t bits_used = high_bit(top_word);
   CT::unpoison(bits_used);
   return BOTAN_MP_WORD_BITS - bits_used;
   }

References BOTAN_MP_WORD_BITS, Botan::high_bit(), sig_words(), Botan::CT::unpoison(), and word_at().

Referenced by bits(), and operator<<=().

with_capacity()

BigInt Botan::BigInt::with_capacity ( size_t  n )

static

Create BigInt of specified size, all zeros

Parameters

n	size of the internal register in words

Definition at line 60 of file bigint.cpp.

   {
   BigInt bn;
   bn.grow_to(size);
   return bn;
   }

References grow_to(), and size().

Referenced by add2(), Botan::ct_divide(), Botan::ct_divide_word(), Botan::ct_modulo(), Botan::Montgomery_Params::mul(), Botan::operator*(), Botan::operator<<(), Botan::operator>>(), and Botan::Montgomery_Params::sqr().

word_at()

word Botan::BigInt::word_at ( size_t  n ) const

inline

Return the word at a specified position of the internal register

Parameters

n	position in the register

Returns

value at position n

Definition at line 537 of file bigint.h.

        {
        return m_data.get_word_at(n);
        }

Referenced by binary_encode(), byte_at(), clear_bit(), ct_cond_assign(), Botan::EC_Group::EC_group_identity_from_order(), get_substring(), Botan::is_prime(), Botan::low_zero_bits(), Botan::Montgomery_Params::Montgomery_Params(), mul(), Botan::operator%(), operator%=(), Botan::operator*(), Botan::redc_p521(), top_bits_free(), and Botan::vartime_divide().

zero()

static BigInt Botan::BigInt::zero ( )

inlinestatic

Create a 0-value BigInt

Definition at line 45 of file bigint.h.

{ return BigInt(); }

Referenced by Botan::EC_Group::blinded_base_point_multiply_x(), Botan::DL_Group::DL_Group(), Botan::inverse_mod(), Botan::is_perfect_square(), Botan::operator>>(), Botan::power_mod(), Botan::random_safe_prime(), and Botan::vartime_divide().

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The documentation for this class was generated from the following files:

• src/lib/math/bigint/bigint.h
• src/lib/math/bigint/big_code.cpp
• src/lib/math/bigint/big_ops2.cpp
• src/lib/math/bigint/big_ops3.cpp
• src/lib/math/bigint/big_rand.cpp
• src/lib/math/bigint/bigint.cpp