bigint.h

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/*
* BigInt
* (C) 1999-2008,2012,2018 Jack Lloyd
*     2007 FlexSecure
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
 
#ifndef BOTAN_BIGINT_H_
#define BOTAN_BIGINT_H_
 
#include <botan/secmem.h>
#include <botan/types.h>
#include <iosfwd>
#include <span>
#include <string>
#include <string_view>
 
namespace Botan {
 
class RandomNumberGenerator;
 
/**
 * Arbitrary precision integer
 */
class BOTAN_PUBLIC_API(2, 0) BigInt final {
   public:
      /**
       * Base enumerator for encoding and decoding
       */
      enum Base : uint16_t /* NOLINT(*-use-enum-class) */ {
         Decimal BOTAN_DEPRECATED("All functions using this enum are deprecated") = 10,
         Hexadecimal BOTAN_DEPRECATED("All functions using this enum are deprecated") = 16,
         Binary BOTAN_DEPRECATED("All functions using this enum are deprecated") = 256
      };
 
      /**
       * Sign symbol definitions for positive and negative numbers
       */
      enum Sign : uint8_t /* NOLINT(*-use-enum-class) */ { Negative = 0, Positive = 1 };
 
      /**
       * Create empty (zero) BigInt
       */
      BigInt() = default;
 
      /**
       * Create a 0-value BigInt
       */
      static BigInt zero() { return BigInt(); }
 
      /**
       * Create a 1-value BigInt
       */
      static BigInt one() { return BigInt::from_u64(1); }
 
      /**
       * Create BigInt from an unsigned 64 bit integer
       * @param n initial value of this BigInt
       */
      static BigInt from_u64(uint64_t n);
 
      /**
       * Create BigInt from a word (limb)
       * @param n initial value of this BigInt
       */
      //BOTAN_DEPRECATED("Use BigInt::from_u64 instead")
      static BigInt from_word(word n);
 
      /**
       * Create BigInt from a signed 32 bit integer
       * @param n initial value of this BigInt
       */
      BOTAN_DEPRECATED("Use BigInt::from_u64 plus negation if required instead") static BigInt from_s32(int32_t n);
 
      /**
       * Create BigInt from an unsigned 64 bit integer
       * @param n initial value of this BigInt
       *
       * Prefer BigInt::from_u64
       */
      BigInt(uint64_t n);  // NOLINT(*-explicit-conversions) TODO(Botan4) make this explicit
 
      /**
       * Copy Constructor
       * @param other the BigInt to copy
       */
      BigInt(const BigInt& other) = default;
 
      /**
       * 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.
       *
       * @param str the string to parse for an integer value
       */
      //BOTAN_DEPRECATED("Use BigInt::from_string")
      explicit BigInt(std::string_view str) { *this = BigInt::from_string(str); }
 
      /**
       * 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.
       *
       * A prefix of "-" will result in a negative integer
       *
       * @param str the string to parse for an integer value
       */
      static BigInt from_string(std::string_view str);
 
      /**
       * Create BigInt from a sequence of digits
       *
       * The string is interpreted as a sequence of digits in base @p radix.
       *
       * Each character must be interpretable as such a digit; there is no support
       * for whitespace or prefixes (eg '0x' or '-').
       *
       * Currently radix must be 10 or 16.
       *
       * @param digits the sequence of digits
       * @param radix the base
       */
      static BigInt from_radix_digits(std::string_view digits, size_t radix);
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the byte array holding the value
       * @param length size of buf
       */
      BigInt(const uint8_t buf[], size_t length) { assign_from_bytes(std::span{buf, length}); }
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param bytes the byte vector holding the value
       */
      explicit BigInt(std::span<const uint8_t> bytes) { assign_from_bytes(bytes); }
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the byte array holding the value
       * @param length size of buf
       * @param base is the number base of the integer in buf
       */
      BOTAN_DEPRECATED("For hex/decimal use from_string") BigInt(const uint8_t buf[], size_t length, Base base);
 
      /**
       * 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.
       *
       * @param buf the byte array holding the value
       * @param length size of buf
       * @param max_bits if the resulting integer is more than max_bits,
       *        it will be shifted so it is at most max_bits in length.
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      static BigInt from_bytes_with_max_bits(const uint8_t buf[], size_t length, size_t max_bits);
 
      /**
       * @brief Create a random BigInt of the specified size
       *
       * @param rng random number generator
       * @param bits size in bits
       * @param set_high_bit if true, the highest bit is always set
       *
       * @see randomize
       */
      BigInt(RandomNumberGenerator& rng, size_t bits, bool set_high_bit = true);
 
      /**
       * Create BigInt of specified size, all zeros
       * @param n size of the internal register in words
       */
      BOTAN_DEPRECATED("Deprecated no replacement") static BigInt with_capacity(size_t n);
 
      /**
       * Move constructor
       */
      BigInt(BigInt&& other) noexcept { this->swap(other); }
 
      ~BigInt() { _const_time_unpoison(); }
 
      /**
       * Move assignment
       */
      BigInt& operator=(BigInt&& other) noexcept {
         if(this != &other) {
            this->swap(other);
         }
 
         return (*this);
      }
 
      /**
       * Copy assignment
       */
      BigInt& operator=(const BigInt&) = default;
 
      /**
       * Swap this value with another
       * @param other BigInt to swap values with
       */
      void swap(BigInt& other) noexcept {
         m_data.swap(other.m_data);
         std::swap(m_signedness, other.m_signedness);
      }
 
      friend void swap(BigInt& x, BigInt& y) noexcept { x.swap(y); }
 
      BOTAN_DEPRECATED("Deprecated no replacement") void swap_reg(secure_vector<word>& reg) {
         m_data.swap(reg);
         // sign left unchanged
      }
 
      /**
       * += operator
       * @param y the BigInt to add to this
       */
      BigInt& operator+=(const BigInt& y) { return add(y._data(), y.sig_words(), y.sign()); }
 
      /**
       * += operator
       * @param y the word to add to this
       */
      BigInt& operator+=(word y) { return add(&y, 1, Positive); }
 
      /**
       * -= operator
       * @param y the BigInt to subtract from this
       */
      BigInt& operator-=(const BigInt& y) { return sub(y._data(), y.sig_words(), y.sign()); }
 
      /**
       * -= operator
       * @param y the word to subtract from this
       */
      BigInt& operator-=(word y) { return sub(&y, 1, Positive); }
 
      /**
       * *= operator
       * @param y the BigInt to multiply with this
       */
      BigInt& operator*=(const BigInt& y);
 
      /**
       * *= operator
       * @param y the word to multiply with this
       */
      BigInt& operator*=(word y);
 
      /**
       * /= operator
       * @param y the BigInt to divide this by
       */
      BigInt& operator/=(const BigInt& y);
 
      /**
       * Modulo operator
       * @param y the modulus to reduce this by
       */
      BigInt& operator%=(const BigInt& y);
 
      /**
       * Modulo operator
       * @param y the modulus (word) to reduce this by
       */
      word operator%=(word y);
 
      /**
       * Left shift operator
       * @param shift the number of bits to shift this left by
       */
      BigInt& operator<<=(size_t shift);
 
      /**
       * Right shift operator
       * @param shift the number of bits to shift this right by
       */
      BigInt& operator>>=(size_t shift);
 
      /**
       * Increment operator
       */
      BigInt& operator++() { return (*this += 1); }
 
      /**
       * Decrement operator
       */
      BigInt& operator--() { return (*this -= 1); }
 
      /**
       * Postfix increment operator
       */
      BigInt operator++(int) {
         BigInt x = (*this);
         ++(*this);
         return x;
      }
 
      /**
       * Postfix decrement operator
       */
      BigInt operator--(int) {
         BigInt x = (*this);
         --(*this);
         return x;
      }
 
      /**
       * Unary negation operator
       * @return negative this
       */
      BigInt operator-() const;
 
      /**
       * ! operator
       * @return true iff this is zero, otherwise false
       */
      bool operator!() const { return (!is_nonzero()); }
 
      //BOTAN_DEPRECATED("Just use operator+/operator-")
      static BigInt add2(const BigInt& x, const word y[], size_t y_words, Sign y_sign);
 
      //BOTAN_DEPRECATED("Just use operator+/operator-")
      BigInt& add(const word y[], size_t y_words, Sign sign);
 
      //BOTAN_DEPRECATED("Just use operator+/operator-")
      BigInt& sub(const word y[], size_t y_words, Sign sign) {
         return add(y, y_words, sign == Positive ? Negative : Positive);
      }
 
      /**
       * Multiply this with y
       * @param y the BigInt to multiply with this
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Just use operator*") BigInt& mul(const BigInt& y, secure_vector<word>& ws);
 
      /**
       * Square value of *this
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Deprecated no replacement") BigInt& square(secure_vector<word>& ws);
 
      /**
       * Set *this to y - *this
       * @param y the BigInt to subtract from as a sequence of words
       * @param y_words length of y in words
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      BigInt& rev_sub(const word y[], size_t y_words, secure_vector<word>& ws);
 
      /**
       * Set *this to (*this + y) % mod
       * This function assumes *this is >= 0 && < mod
       * @param y the BigInt to add - assumed y >= 0 and y < mod
       * @param mod the positive modulus
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      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
       * @param y the BigInt to subtract - assumed y >= 0 and y < mod
       * @param mod the positive modulus
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      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
       * y should be small, less than 16
       * @param y the small integer to multiply by
       * @param mod the positive modulus
       * @param ws a temp workspace
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      BigInt& mod_mul(uint8_t y, 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.
       */
      BOTAN_DEPRECATED("Deprecated no replacement") size_t 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.
       *
       * Performs exactly bound subtractions, so if *this is >= bound*mod then the
       * result will not be fully reduced. If bound is zero, nothing happens.
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      void ct_reduce_below(const BigInt& mod, secure_vector<word>& ws, size_t bound);
 
      /**
       * Zeroize the BigInt. The size of the underlying register is not
       * modified.
       */
      void clear() {
         m_data.set_to_zero();
         m_signedness = Positive;
      }
 
      /**
       * Compare this to another BigInt
       * @param n the BigInt value to compare with
       * @param check_signs include sign in comparison?
       * @result if (this<n) return -1, if (this>n) return 1, if both
       * values are identical return 0 [like Perl's <=> operator]
       */
      int32_t cmp(const BigInt& n, bool check_signs = true) const;
 
      /**
       * Compare this to another BigInt
       * @param n the BigInt value to compare with
       * @result true if this == n or false otherwise
       */
      bool is_equal(const BigInt& n) const;
 
      /**
       * Compare this to another BigInt
       * @param n the BigInt value to compare with
       * @result true if this < n or false otherwise
       */
      bool is_less_than(const BigInt& n) const;
 
      /**
       * Compare this to an integer
       * @param n the value to compare with
       * @result if (this<n) return -1, if (this>n) return 1, if both
       * values are identical return 0 [like Perl's <=> operator]
       */
      int32_t cmp_word(word n) const;
 
      /**
       * Test if the integer has an even value
       * @result true if the integer is even, false otherwise
       */
      bool is_even() const { return !get_bit(0); }
 
      /**
       * Test if the integer has an odd value
       * @result true if the integer is odd, false otherwise
       */
      bool is_odd() const { return get_bit(0); }
 
      /**
       * Test if the integer is not zero
       * @result true if the integer is non-zero, false otherwise
       */
      bool is_nonzero() const { return (!is_zero()); }
 
      /**
       * Test if the integer is zero
       * @result true if the integer is zero, false otherwise
       */
      bool is_zero() const { return (sig_words() == 0); }
 
      /**
       * Set bit at specified position
       * @param n bit position to set
       */
      void set_bit(size_t n) { conditionally_set_bit(n, true); }
 
      /**
       * Conditionally set bit at specified position. Note if set_it is
       * false, nothing happens, and if the bit is already set, it
       * remains set.
       *
       * @param n bit position to set
       * @param set_it if the bit should be set
       */
      void conditionally_set_bit(size_t n, bool set_it) {
         const size_t which = n / (sizeof(word) * 8);
         const word mask = static_cast<word>(set_it) << (n % (sizeof(word) * 8));
         m_data.set_word_at(which, word_at(which) | mask);
      }
 
      /**
       * Clear bit at specified position
       * @param n bit position to clear
       */
      void clear_bit(size_t n);
 
      /**
       * Clear all but the lowest n bits
       * @param n amount of bits to keep
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void mask_bits(size_t n) { m_data.mask_bits(n); }
 
      /**
       * Return bit value at specified position
       * @param n the bit offset to test
       * @result true, if the bit at position n is set, false otherwise
       */
      bool get_bit(size_t n) const { return ((word_at(n / (sizeof(word) * 8)) >> (n % (sizeof(word) * 8))) & 1) == 1; }
 
      /**
       * Return (a maximum of) 32 bits of the complete value
       * @param offset the offset to start extracting
       * @param length amount of bits to extract (starting at offset)
       * @result the integer extracted from the register starting at
       * offset with specified length
       */
      BOTAN_DEPRECATED("Deprecated no replacement") uint32_t get_substring(size_t offset, size_t length) const;
 
      /**
       * Convert this value into a uint32_t, if it is in the range
       * [0 ... 2**32-1], or otherwise throw an exception.
       * @result the value as a uint32_t if conversion is possible
       */
      BOTAN_DEPRECATED("Deprecated no replacement") uint32_t to_u32bit() 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.
       */
      std::string to_dec_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"
       */
      std::string to_hex_string() const;
 
      /**
       * @param n the offset to get a byte from
       * @result byte at offset n
       */
      uint8_t byte_at(size_t n) const;
 
      /**
       * Return the word at a specified position of the internal register
       * @param n position in the register
       * @return value at position n
       */
      word word_at(size_t n) const { return m_data.get_word_at(n); }
 
      BOTAN_DEPRECATED("Deprecated no replacement") void set_word_at(size_t i, word w) { m_data.set_word_at(i, w); }
 
      BOTAN_DEPRECATED("Deprecated no replacement") void set_words(const word w[], size_t len) {
         m_data.set_words(w, len);
      }
 
      /**
       * Tests if the sign of the integer is negative
       * @result true, iff the integer has a negative sign
       */
      bool is_negative() const { return (sign() == Negative); }
 
      /**
       * Tests if the sign of the integer is positive
       * @result true, iff the integer has a positive sign
       */
      bool is_positive() const { return (sign() == Positive); }
 
      /**
       * Return the sign of the integer
       * @result the sign of the integer
       */
      Sign sign() const { return (m_signedness); }
 
      /**
       * @result the opposite sign of the represented integer value
       */
      Sign reverse_sign() const {
         if(sign() == Positive) {
            return Negative;
         }
         return Positive;
      }
 
      /**
       * Flip the sign of this BigInt
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void flip_sign() { set_sign(reverse_sign()); }
 
      /**
       * Set sign of the integer
       * @param sign new Sign to set
       */
      void set_sign(Sign sign) {
         if(sign == Negative && is_zero()) {
            sign = Positive;
         }
 
         m_signedness = sign;
      }
 
      /**
       * @result absolute (positive) value of this
       */
      BigInt abs() const;
 
      /**
       * Give size of internal register
       * @result size of internal register in words
       */
      size_t size() const { return m_data.size(); }
 
      /**
       * Return how many words we need to hold this value
       * @result significant words of the represented integer value
       */
      size_t sig_words() const { return m_data.sig_words(); }
 
      /**
       * Give byte length of the integer
       * @result byte length of the represented integer value
       */
      size_t bytes() const;
 
      /**
       * Get the bit length of the integer
       * @result bit length of the represented integer value
       */
      size_t bits() const;
 
      /**
       * Get the number of high bits unset in the top (allocated) word
       * of this integer. Returns (sizeof(word) * 8) only iff *this is
       * zero. Ignores sign.
       */
      BOTAN_DEPRECATED("Deprecated no replacement") size_t top_bits_free() const;
 
      /**
       * Return a mutable pointer to the register
       * @result a pointer to the start of the internal register
       */
      BOTAN_DEPRECATED("Deprecated no replacement") word* mutable_data() { return m_data.mutable_data(); }
 
      /**
       * Return a const pointer to the register
       * @result a pointer to the start of the internal register
       */
      BOTAN_DEPRECATED("Deprecated no replacement") const word* data() const { return m_data.const_data(); }
 
      /**
       * Don't use this function in application code
       */
      BOTAN_DEPRECATED("Deprecated no replacement") secure_vector<word>& get_word_vector() {
         return m_data.mutable_vector();
      }
 
      /**
       * Don't use this function in application code
       */
      BOTAN_DEPRECATED("Deprecated no replacement") const secure_vector<word>& get_word_vector() const {
         return m_data.const_vector();
      }
 
      /**
       * Increase internal register buffer to at least n words
       * @param n new size of register
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void grow_to(size_t n) const { m_data.grow_to(n); }
 
      BOTAN_DEPRECATED("Deprecated no replacement") void resize(size_t s) { m_data.resize(s); }
 
      /**
       * Fill BigInt with a random number with size of bitsize
       *
       * If \p set_high_bit is true, the highest bit will be set, which causes
       * the entropy to be \a bits-1. Otherwise the highest bit is randomly chosen
       * by the rng, causing the entropy to be \a bits.
       *
       * @param rng the random number generator to use
       * @param bitsize number of bits the created random value should have
       * @param set_high_bit if true, the highest bit is always set
       */
      void randomize(RandomNumberGenerator& rng, size_t bitsize, bool set_high_bit = true);
 
      /**
       * Serialize the absolute value of this BigInt as a big endian
       * encoding.
       *
       * If out is smaller than the total bytes of the BigInt then
       * an exception is thrown.
       *
       * If out is larger than the total bytes of the BigInt then the
       * necessary number of zeros are prefixed to produce the desired
       * output length
       *
       * Zero-padding the binary encoding is useful to ensure that other
       * applications correctly parse the encoded value as "positive integer",
       * as a leading 1-bit may be interpreted as a sign bit. It also is
       * necessary when using a fixed size encoding for the integers.
       *
       * @param out destination byte span for the integer value
       */
      void serialize_to(std::span<uint8_t> out) const;
 
      /**
       * Serialize the value of this BigInt as a big endian encoding,
       * always returning the specified number of bytes.
       *
       * Throws if the BigInt is too large to encode in the length
       * specified.
       */
      template <typename T = std::vector<uint8_t>>
      T serialize(size_t len) const {
         // TODO this supports std::vector and secure_vector
         // it would be nice if this also could work with std::array as in
         //   bn.serialize_to<std::array<uint8_t, 32>>(32);
         T out(len);
         this->serialize_to(out);
         return out;
      }
 
      /**
       * Serialize the value of this BigInt as a big endian encoding.
       */
      template <typename T = std::vector<uint8_t>>
      T serialize() const {
         return serialize<T>(this->bytes());
      }
 
      /**
       * Store BigInt-value in a given byte array
       * @param buf destination byte array for the integer value
       */
      BOTAN_DEPRECATED("Use BigInt::serialize_to") void binary_encode(uint8_t buf[]) const {
         this->serialize_to(std::span{buf, this->bytes()});
      }
 
      /**
       * 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.
       *
       * Zero-padding the binary encoding is useful to ensure that other
       * applications correctly parse the encoded value as "positive integer",
       * as a leading 1-bit may be interpreted as a sign bit.
       *
       * @param buf destination byte array for the integer value
       * @param len how many bytes to write
       */
      BOTAN_DEPRECATED("Use BigInt::serialize_to") void binary_encode(uint8_t buf[], size_t len) const;
 
      /**
       * Read integer value from a byte array with given size
       * @param buf byte array buffer containing the integer
       * @param length size of buf
       */
      BOTAN_DEPRECATED("Use BigInt::from_bytes") void binary_decode(const uint8_t buf[], size_t length) {
         this->assign_from_bytes(std::span{buf, length});
      }
 
      /**
       * Read integer value from a byte vector
       * @param buf the vector to load from
       */
      BOTAN_DEPRECATED("Use BigInt::from_bytes") void binary_decode(std::span<const uint8_t> buf) {
         this->assign_from_bytes(buf);
      }
 
      /**
       * Place the value into out, zero-padding up to size words
       * Throw if *this cannot be represented in size words
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void encode_words(word out[], size_t size) const;
 
      /**
       * If predicate is true assign other to *this
       * Uses a masked operation to avoid side channels
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void ct_cond_assign(bool predicate, const BigInt& other);
 
      /**
       * If predicate is true swap *this and other
       * Uses a masked operation to avoid side channels
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void ct_cond_swap(bool predicate, BigInt& other);
 
      /**
       * If predicate is true add value to *this
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void ct_cond_add(bool predicate, const BigInt& value);
 
      /**
       * Shift @p shift bits to the left, runtime is independent of
       * the value of @p shift.
       */
      BOTAN_DEPRECATED("Deprecated no replacement") void ct_shift_left(size_t shift);
 
      /**
       * If predicate is true flip the sign of *this
       */
      void cond_flip_sign(bool predicate);
 
      BOTAN_DEPRECATED("replaced by internal API") void const_time_poison() const { _const_time_poison(); }
 
      BOTAN_DEPRECATED("replaced by internal API") void const_time_unpoison() const { _const_time_unpoison(); }
 
      /**
       * @param rng a random number generator
       * @param min the minimum value (must be non-negative)
       * @param max the maximum value (must be non-negative and > min)
       * @return random integer in [min,max)
       */
      static BigInt random_integer(RandomNumberGenerator& rng, const BigInt& min, const BigInt& max);
 
      /**
       * Create a power of two
       * @param n the power of two to create
       * @return bigint representing 2^n
       */
      static BigInt power_of_2(size_t n) {
         BigInt b;
         b.set_bit(n);
         return b;
      }
 
      /**
       * Encode the integer value from a BigInt to a std::vector of bytes
       * @param n the BigInt to use as integer source
       * @result secure_vector of bytes containing the bytes of the integer
       */
      BOTAN_DEPRECATED("Use BigInt::serialize") static std::vector<uint8_t> encode(const BigInt& n) {
         return n.serialize<std::vector<uint8_t>>(n.bytes());
      }
 
      /**
       * Encode the integer value from a BigInt to a secure_vector of bytes
       * @param n the BigInt to use as integer source
       * @result secure_vector of bytes containing the bytes of the integer
       */
      BOTAN_DEPRECATED("Use BigInt::serialize") static secure_vector<uint8_t> encode_locked(const BigInt& n) {
         return n.serialize<secure_vector<uint8_t>>(n.bytes());
      }
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param bytes the binary value to load
       * @result BigInt representing the integer in the byte array
       */
      static BigInt from_bytes(std::span<const uint8_t> bytes);
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the binary value to load
       * @param length size of buf
       * @result BigInt representing the integer in the byte array
       */
      BOTAN_DEPRECATED("Use BigInt::from_bytes") static BigInt decode(const uint8_t buf[], size_t length) {
         return BigInt::from_bytes(std::span{buf, length});
      }
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the binary value to load
       * @result BigInt representing the integer in the byte array
       */
      BOTAN_DEPRECATED("Use BigInt::from_bytes") static BigInt decode(std::span<const uint8_t> buf) {
         return BigInt::from_bytes(buf);
      }
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the binary value to load
       * @param length size of buf
       * @param base number-base of the integer in buf
       * @result BigInt representing the integer in the byte array
       */
      BOTAN_DEPRECATED("For decimal/hex use from_string")
      static BigInt decode(const uint8_t buf[], size_t length, Base base);
 
      /**
       * Create a BigInt from an integer in a byte array
       * @param buf the binary value to load
       * @param base number-base of the integer in buf
       * @result BigInt representing the integer in the byte array
       */
      BOTAN_DEPRECATED("For decimal/hex use from_string") static BigInt decode(std::span<const uint8_t> buf, Base base);
 
      /**
       * Encode a BigInt to a byte array according to IEEE 1363
       * @param n the BigInt to encode
       * @param bytes the length of the resulting secure_vector<uint8_t>
       * @result a secure_vector<uint8_t> containing the encoded BigInt
       */
      BOTAN_DEPRECATED("Use BigInt::serialize")
      static secure_vector<uint8_t> encode_1363(const BigInt& n, size_t bytes) {
         return n.serialize<secure_vector<uint8_t>>(bytes);
      }
 
      BOTAN_DEPRECATED("Use BigInt::serialize_to") static void encode_1363(std::span<uint8_t> out, const BigInt& n) {
         n.serialize_to(out);
      }
 
      BOTAN_DEPRECATED("Use BigInt::serialize_to")
      static void encode_1363(uint8_t out[], size_t bytes, const BigInt& n) {
         n.serialize_to(std::span{out, bytes});
      }
 
      /**
       * Encode two BigInt to a byte array according to IEEE 1363
       * @param n1 the first BigInt to encode
       * @param n2 the second BigInt to encode
       * @param bytes the length of the encoding of each single BigInt
       * @result a secure_vector<uint8_t> containing the concatenation of the two encoded BigInt
       */
      BOTAN_DEPRECATED("Deprecated no replacement")
      static secure_vector<uint8_t> encode_fixed_length_int_pair(const BigInt& n1, const BigInt& n2, size_t bytes);
 
      /**
       * Return a span over the register
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer.
       *
       * @result span over the internal register
       */
      std::span<const word> _as_span() const { return m_data.const_span(); }
 
      /**
       * Return a const pointer to the register
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer.
       *
       * @result a pointer to the start of the internal register
       */
      const word* _data() const { return m_data.const_data(); }
 
      /**
       * Read integer value from a byte vector (big endian)
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer. In applications use
       * BigInt::from_bytes
       *
       * @param bytes the span of bytes to load
       */
      void _assign_from_bytes(std::span<const uint8_t> bytes) { assign_from_bytes(bytes); }
 
      /**
       * Create a BigInt from a word vector
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer.
       */
      static BigInt _from_words(secure_vector<word>& words) {
         BigInt bn;
         bn.m_data.swap(words);
         return bn;
      }
 
      /**
       * Mark this BigInt as holding secret data
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer.
       */
      void _const_time_poison() const;
 
      /**
       * Mark this BigInt as no longer holding secret data
       *
       * @warning this is an implementation detail which is not for
       * public use and not covered by SemVer.
       */
      void _const_time_unpoison() const;
 
   private:
      /**
       * Read integer value from a byte vector (big endian)
       * @param bytes the span of bytes to load
       */
      void assign_from_bytes(std::span<const uint8_t> bytes);
 
      class Data {
         public:
            word* mutable_data() {
               invalidate_sig_words();
               return m_reg.data();
            }
 
            const word* const_data() const { return m_reg.data(); }
 
            std::span<const word> const_span() const { return std::span{m_reg}; }
 
            secure_vector<word>& mutable_vector() {
               invalidate_sig_words();
               return m_reg;
            }
 
            const secure_vector<word>& const_vector() const { return m_reg; }
 
            word get_word_at(size_t n) const {
               if(n < m_reg.size()) {
                  return m_reg[n];
               }
               return 0;
            }
 
            void set_word_at(size_t i, word w) {
               invalidate_sig_words();
               if(i >= m_reg.size()) {
                  if(w == 0) {
                     return;
                  }
                  grow_to(i + 1);
               }
               m_reg[i] = w;
            }
 
            void set_words(const word w[], size_t len) {
               invalidate_sig_words();
               m_reg.assign(w, w + len);
            }
 
            void set_to_zero();
 
            void mask_bits(size_t n);
 
            void grow_to(size_t n) const {
               if(n > size()) {
                  if(n <= m_reg.capacity()) {
                     m_reg.resize(n);
                  } else {
                     m_reg.resize(n + (8 - (n % 8)));
                  }
               }
            }
 
            size_t size() const { return m_reg.size(); }
 
            void shrink_to_fit(size_t min_size = 0) {
               const size_t words = std::max(min_size, sig_words());
               m_reg.resize(words);
            }
 
            void resize(size_t s) { m_reg.resize(s); }
 
            void swap(Data& other) noexcept {
               m_reg.swap(other.m_reg);
               std::swap(m_sig_words, other.m_sig_words);
            }
 
            void swap(secure_vector<word>& reg) noexcept {
               m_reg.swap(reg);
               invalidate_sig_words();
            }
 
            void invalidate_sig_words() const noexcept { m_sig_words = sig_words_npos; }
 
            size_t sig_words() const {
               if(m_sig_words == sig_words_npos) {
                  m_sig_words = calc_sig_words();
               }
               return m_sig_words;
            }
 
         private:
            static const size_t sig_words_npos = static_cast<size_t>(-1);
 
            size_t calc_sig_words() const;
 
            mutable secure_vector<word> m_reg;
            mutable size_t m_sig_words = sig_words_npos;
      };
 
      Data m_data;
      Sign m_signedness = Positive;
};
 
/*
* Arithmetic Operators
*/
inline BigInt operator+(const BigInt& x, const BigInt& y) {
   return BigInt::add2(x, y._data(), y.sig_words(), y.sign());
}
 
inline BigInt operator+(const BigInt& x, word y) {
   return BigInt::add2(x, &y, 1, BigInt::Positive);
}
 
inline BigInt operator+(word x, const BigInt& y) {
   return y + x;
}
 
inline BigInt operator-(const BigInt& x, const BigInt& y) {
   return BigInt::add2(x, y._data(), y.sig_words(), y.reverse_sign());
}
 
inline BigInt operator-(const BigInt& x, word y) {
   return BigInt::add2(x, &y, 1, BigInt::Negative);
}
 
BOTAN_PUBLIC_API(2, 0) BigInt operator*(const BigInt& x, const BigInt& y);
BOTAN_PUBLIC_API(2, 8) BigInt operator*(const BigInt& x, word y);
 
inline BigInt operator*(word x, const BigInt& y) {
   return y * x;
}
 
BOTAN_PUBLIC_API(2, 0) BigInt operator/(const BigInt& x, const BigInt& d);
BOTAN_PUBLIC_API(2, 0) BigInt operator/(const BigInt& x, word m);
BOTAN_PUBLIC_API(2, 0) BigInt operator%(const BigInt& x, const BigInt& m);
BOTAN_PUBLIC_API(2, 0) word operator%(const BigInt& x, word m);
BOTAN_PUBLIC_API(2, 0) BigInt operator<<(const BigInt& x, size_t n);
BOTAN_PUBLIC_API(2, 0) BigInt operator>>(const BigInt& x, size_t n);
 
/*
 * Comparison Operators
 */
inline bool operator==(const BigInt& a, const BigInt& b) {
   return a.is_equal(b);
}
 
inline bool operator!=(const BigInt& a, const BigInt& b) {
   return !a.is_equal(b);
}
 
inline bool operator<=(const BigInt& a, const BigInt& b) {
   return (a.cmp(b) <= 0);
}
 
inline bool operator>=(const BigInt& a, const BigInt& b) {
   return (a.cmp(b) >= 0);
}
 
inline bool operator<(const BigInt& a, const BigInt& b) {
   return a.is_less_than(b);
}
 
inline bool operator>(const BigInt& a, const BigInt& b) {
   return b.is_less_than(a);
}
 
inline bool operator==(const BigInt& a, word b) {
   return (a.cmp_word(b) == 0);
}
 
inline bool operator!=(const BigInt& a, word b) {
   return (a.cmp_word(b) != 0);
}
 
inline bool operator<=(const BigInt& a, word b) {
   return (a.cmp_word(b) <= 0);
}
 
inline bool operator>=(const BigInt& a, word b) {
   return (a.cmp_word(b) >= 0);
}
 
inline bool operator<(const BigInt& a, word b) {
   return (a.cmp_word(b) < 0);
}
 
inline bool operator>(const BigInt& a, word b) {
   return (a.cmp_word(b) > 0);
}
 
/*
 * I/O Operators
 */
BOTAN_DEPRECATED("Use BigInt::to_{hex,dec}_string")
BOTAN_PUBLIC_API(2, 0) std::ostream& operator<<(std::ostream& stream, const BigInt& n);
 
BOTAN_DEPRECATED("Use BigInt::from_string")
BOTAN_PUBLIC_API(2, 0) std::istream& operator>>(std::istream& stream, BigInt& n);
 
}  // namespace Botan
 
#endif