#include <pcurves_impl.h>

Public Types
using	Self = IntMod<Rep>

Public Member Functions
constexpr void	conditional_assign (CT::Choice cond, const Self &other)

constexpr void	ct_poison () const

constexpr void	ct_unpoison () const

constexpr	IntMod ()

	IntMod (const Self &other)=default

	IntMod (Self &&other)=default

constexpr Self	invert () const

constexpr CT::Choice	is_even () const

constexpr CT::Choice	is_nonzero () const

constexpr CT::Choice	is_one () const

constexpr CT::Choice	is_square () const

constexpr CT::Choice	is_zero () const

Self	mul2 () const
	Return (*this) multiplied by 2.

constexpr Self	mul3 () const
	Return (*this) multiplied by 3.

constexpr Self	mul4 () const
	Return (*this) multiplied by 4.

constexpr Self	mul8 () const
	Return (*this) multiplied by 8.

constexpr Self	negate () const

constexpr CT::Choice	operator!= (const Self &other) const

constexpr Self &	operator*= (const Self &other)

IntMod &	operator= (const Self &other)=default

IntMod &	operator= (Self &&other)=default

constexpr CT::Choice	operator== (const Self &other) const

constexpr Self	pow_vartime (const std::array< W, N > &exp) const

constexpr void	serialize_to (std::span< uint8_t, Self::BYTES > bytes) const

constexpr Self	sqrt () const

constexpr Self	square () const

template<size_t L>
std::array< W, L >	stash_value () const

constexpr std::array< W, Self::N >	to_words () const

Static Public Member Functions
static consteval Self	constant (int8_t x)

static constexpr std::optional< Self >	deserialize (std::span< const uint8_t > bytes)

static Self	from_bits_with_trunc (std::span< const uint8_t > bytes)

template<size_t L>
static Self	from_stash (const std::array< W, L > &stash)

template<size_t L>
static constexpr Self	from_wide_bytes (std::span< const uint8_t, L > bytes)

static constexpr std::optional< Self >	from_wide_bytes_varlen (std::span< const uint8_t > bytes)

static constexpr Self	from_word (W x)

template<size_t L>
static constexpr Self	from_words (std::array< W, L > w)

static constexpr Self	one ()

static Self	random (RandomNumberGenerator &rng)

static constexpr Self	zero ()

Static Public Attributes
static constexpr size_t	BITS = count_bits(P)

static constexpr size_t	BYTES = (BITS + 7) / 8

static constexpr auto	P_MOD_4 = P[0] % 4

Friends
constexpr Self	operator* (const Self &a, const Self &b)

constexpr Self	operator+ (const Self &a, const Self &b)

constexpr Self	operator- (const Self &a, const Self &b)

Detailed Description

template<typename Rep>
class Botan::IntMod< Rep >

Definition at line 68 of file pcurves_impl.h.

Member Typedef Documentation

◆ Self

template<typename Rep >

using Botan::IntMod< Rep >::Self = IntMod<Rep>

Definition at line 84 of file pcurves_impl.h.

Constructor & Destructor Documentation

◆ IntMod() [1/3]

template<typename Rep >

Botan::IntMod< Rep >::IntMod ( )

inlineconstexpr

Definition at line 87 of file pcurves_impl.h.

87: m_val({}) {}

◆ IntMod() [2/3]

template<typename Rep >

Botan::IntMod< Rep >::IntMod ( const Self & other )

default

◆ IntMod() [3/3]

template<typename Rep >

Botan::IntMod< Rep >::IntMod ( Self && other )

default

Member Function Documentation

◆ conditional_assign()

template<typename Rep >

void Botan::IntMod< Rep >::conditional_assign	(	CT::Choice	cond,
		const Self &	other )

inlineconstexpr

Definition at line 170 of file pcurves_impl.h.

                                                                          {
         CT::conditional_assign_mem(cond, m_val.data(), other.data(), N);
      }

References Botan::CT::conditional_assign_mem().

◆ constant()

template<typename Rep >

static consteval Self Botan::IntMod< Rep >::constant ( int8_t x )

inlinestaticconsteval

Definition at line 394 of file pcurves_impl.h.

                                               {
         std::array<W, 1> v;
         v[0] = (x >= 0) ? x : -x;
         auto s = Self::from_words(v);
         return (x >= 0) ? s : s.negate();
      }

References Botan::IntMod< Rep >::from_words().

◆ ct_poison()

template<typename Rep >

void Botan::IntMod< Rep >::ct_poison ( ) const

inlineconstexpr

Definition at line 401 of file pcurves_impl.h.

401{ CT::poison(m_val.data(), m_val.size()); }

Botan::CT::poison

constexpr void poison(const T *p, size_t n)

Definition ct_utils.h:46

References Botan::CT::poison().

◆ ct_unpoison()

template<typename Rep >

void Botan::IntMod< Rep >::ct_unpoison ( ) const

inlineconstexpr

Definition at line 403 of file pcurves_impl.h.

403{ CT::unpoison(m_val.data(), m_val.size()); }

Botan::CT::unpoison

constexpr void unpoison(const T *p, size_t n)

Definition ct_utils.h:57

References Botan::CT::unpoison().

◆ deserialize()

template<typename Rep >

static constexpr std::optional< Self > Botan::IntMod< Rep >::deserialize ( std::span< const uint8_t > bytes )

inlinestaticconstexpr

Definition at line 308 of file pcurves_impl.h.

                                                                                   {
         // We could allow either short inputs or longer zero padded
         // inputs here, however it seems best to avoid non-canonical
         // representations unless required
         if(bytes.size() != Self::BYTES) {
            return {};
         }
 
         const auto words = bytes_to_words<W, N, BYTES>(bytes.first<Self::BYTES>());
 
         if(!bigint_ct_is_lt(words.data(), N, P.data(), N).as_bool()) {
            return {};
         }
 
         return Self::from_words(words);
      }

References Botan::bigint_ct_is_lt(), Botan::IntMod< Rep >::BYTES, and Botan::IntMod< Rep >::from_words().

Referenced by Botan::IntMod< Rep >::random().

◆ from_bits_with_trunc()

template<typename Rep >

static Self Botan::IntMod< Rep >::from_bits_with_trunc ( std::span< const uint8_t > bytes )

inlinestatic

Definition at line 328 of file pcurves_impl.h.

                                                                     {
         const size_t bit_length = bytes.size() * 8;
 
         if(bit_length <= Self::BITS) {
            // No shifting required, but might still need to reduce by modulus
            std::array<uint8_t, 2 * BYTES> padded_bytes = {};
            copy_mem(std::span{padded_bytes}.last(bytes.size()), bytes);
            return Self(Rep::wide_to_rep(bytes_to_words<W, 2 * N, 2 * BYTES>(std::span{padded_bytes})));
         } else {
            const size_t shift = bit_length - Self::BITS;
 
            if(shift % 8 == 0) {
               // Easy case just copy different bytes
               const size_t new_length = bytes.size() - (shift / 8);
               return Self::from_bits_with_trunc(bytes.first(new_length));
            } else {
               // fixme
               throw Not_Implemented("Bit shifting for hash to scalar conversion not implemented");
            }
         }
      }

References Botan::IntMod< Rep >::BITS, Botan::copy_mem(), and Botan::IntMod< Rep >::from_bits_with_trunc().

Referenced by Botan::IntMod< Rep >::from_bits_with_trunc().

◆ from_stash()

template<typename Rep >

template<size_t L>

static Self Botan::IntMod< Rep >::from_stash ( const std::array< W, L > & stash )

inlinestatic

Definition at line 298 of file pcurves_impl.h.

                                                          {
         static_assert(L >= N);
         std::array<W, N> val = {};
         for(size_t i = 0; i != N; ++i) {
            val[i] = stash[i];
         }
         return Self(val);
      }

◆ from_wide_bytes()

template<typename Rep >

template<size_t L>

static constexpr Self Botan::IntMod< Rep >::from_wide_bytes ( std::span< const uint8_t, L > bytes )

inlinestaticconstexpr

Definition at line 352 of file pcurves_impl.h.

                                                                             {
         static_assert(8 * L <= 2 * Self::BITS);
         std::array<uint8_t, 2 * BYTES> padded_bytes = {};
         copy_mem(std::span{padded_bytes}.template last<L>(), bytes);
         return Self(Rep::wide_to_rep(bytes_to_words<W, 2 * N, 2 * BYTES>(std::span{padded_bytes})));
      }

References Botan::IntMod< Rep >::BITS, and Botan::copy_mem().

◆ from_wide_bytes_varlen()

template<typename Rep >

static constexpr std::optional< Self > Botan::IntMod< Rep >::from_wide_bytes_varlen ( std::span< const uint8_t > bytes )

inlinestaticconstexpr

Definition at line 360 of file pcurves_impl.h.

                                                                                              {
         if(8 * bytes.size() > 2 * Self::BITS) {
            return {};
         }
         std::array<uint8_t, 2 * BYTES> padded_bytes = {};
         copy_mem(std::span{padded_bytes}.last(bytes.size()), bytes);
         return Self(Rep::wide_to_rep(bytes_to_words<W, 2 * N, 2 * BYTES>(std::span{padded_bytes})));
      }

References Botan::IntMod< Rep >::BITS, and Botan::copy_mem().

◆ from_word()

template<typename Rep >

static constexpr Self Botan::IntMod< Rep >::from_word ( W x )

inlinestaticconstexpr

Definition at line 98 of file pcurves_impl.h.

                                           {
         std::array<W, 1> v{x};
         return Self::from_words(v);
      }

References Botan::IntMod< Rep >::from_words().

◆ from_words()

template<typename Rep >

template<size_t L>

static constexpr Self Botan::IntMod< Rep >::from_words ( std::array< W, L > w )

inlinestaticconstexpr

Definition at line 104 of file pcurves_impl.h.

                                                         {
         if constexpr(L == N) {
            return Self(Rep::to_rep(w));
         } else {
            static_assert(L < N);
            std::array<W, N> ew = {};
            copy_mem(std::span{ew}.template first<L>(), w);
            return Self(Rep::to_rep(ew));
         }
      }

References Botan::copy_mem().

Referenced by Botan::IntMod< Rep >::constant(), Botan::IntMod< Rep >::deserialize(), and Botan::IntMod< Rep >::from_word().

◆ invert()

template<typename Rep >

Self Botan::IntMod< Rep >::invert ( ) const

inlineconstexpr

Returns the modular inverse, or 0 if no modular inverse exists.

If the modulus is prime the only value that has no modular inverse is 0.

This uses Fermat's little theorem, and so assumes that p is prime

Definition at line 238 of file pcurves_impl.h.

238{ return pow_vartime(Self::P_MINUS_2); }

Botan::IntMod::pow_vartime

constexpr Self pow_vartime(const std::array< W, N > &exp) const

Definition pcurves_impl.h:190

References Botan::IntMod< Rep >::pow_vartime().

◆ is_even()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::is_even ( ) const

inlineconstexpr

Definition at line 121 of file pcurves_impl.h.

                                         {
         auto v = Rep::from_rep(m_val);
         return CT::Choice::from_int(0x01 ^ (v[0] & 0x01));
      }

References Botan::CT::Choice::from_int().

◆ is_nonzero()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::is_nonzero ( ) const

inlineconstexpr

Definition at line 117 of file pcurves_impl.h.

117{ return !is_zero(); }

Botan::IntMod::is_zero

constexpr CT::Choice is_zero() const

Definition pcurves_impl.h:115

References Botan::IntMod< Rep >::is_zero().

◆ is_one()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::is_one ( ) const

inlineconstexpr

Definition at line 119 of file pcurves_impl.h.

119{ return (*this == Self::one()); }

Botan::IntMod::one

static constexpr Self one()

Definition pcurves_impl.h:96

References Botan::IntMod< Rep >::one().

Referenced by Botan::IntMod< Rep >::is_square().

◆ is_square()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::is_square ( ) const

inlineconstexpr

Definition at line 254 of file pcurves_impl.h.

      {
         auto z = pow_vartime(Self::P_MINUS_1_OVER_2);
         const CT::Choice is_one = z.is_one();
         const CT::Choice is_zero = z.is_zero();
         return (is_one || is_zero);
      }

References Botan::IntMod< Rep >::is_one(), Botan::IntMod< Rep >::is_zero(), and Botan::IntMod< Rep >::pow_vartime().

◆ is_zero()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::is_zero ( ) const

inlineconstexpr

Definition at line 115 of file pcurves_impl.h.

115{ return CT::all_zeros(m_val.data(), m_val.size()).as_choice(); }

Botan::CT::all_zeros

constexpr CT::Mask< T > all_zeros(const T elem[], size_t len)

Definition ct_utils.h:473

References Botan::CT::all_zeros().

Referenced by Botan::IntMod< Rep >::is_nonzero(), and Botan::IntMod< Rep >::is_square().

◆ mul2()

template<typename Rep >

Self Botan::IntMod< Rep >::mul2 ( ) const

inline

Return (*this) multiplied by 2.

Definition at line 138 of file pcurves_impl.h.

                        {
         std::array<W, N> t = value();
         W carry = shift_left<1>(t);
 
         std::array<W, N> r;
         bigint_monty_maybe_sub<N>(r.data(), carry, t.data(), P.data());
         return Self(r);
      }

References Botan::bigint_monty_maybe_sub(), Botan::carry(), and Botan::shift_left().

Referenced by Botan::IntMod< Rep >::mul3(), Botan::IntMod< Rep >::mul4(), and Botan::IntMod< Rep >::mul8().

◆ mul3()

template<typename Rep >

Self Botan::IntMod< Rep >::mul3 ( ) const

inlineconstexpr

Return (*this) multiplied by 3.

Definition at line 148 of file pcurves_impl.h.

148{ return mul2() + (*this); }

Botan::IntMod::mul2

Self mul2() const

Return (*this) multiplied by 2.

Definition pcurves_impl.h:138

References Botan::IntMod< Rep >::mul2().

◆ mul4()

template<typename Rep >

Self Botan::IntMod< Rep >::mul4 ( ) const

inlineconstexpr

Return (*this) multiplied by 4.

Definition at line 151 of file pcurves_impl.h.

151{ return mul2().mul2(); }

References Botan::IntMod< Rep >::mul2().

◆ mul8()

template<typename Rep >

Self Botan::IntMod< Rep >::mul8 ( ) const

inlineconstexpr

Return (*this) multiplied by 8.

Definition at line 154 of file pcurves_impl.h.

154{ return mul2().mul2().mul2(); }

References Botan::IntMod< Rep >::mul2().

◆ negate()

template<typename Rep >

Self Botan::IntMod< Rep >::negate ( ) const

inlineconstexpr

Definition at line 181 of file pcurves_impl.h.

                                    {
         auto x_is_zero = CT::all_zeros(this->data(), N);
 
         std::array<W, N> r;
         bigint_sub3(r.data(), P.data(), N, this->data(), N);
         x_is_zero.if_set_zero_out(r.data(), N);
         return Self(r);
      }

References Botan::CT::all_zeros(), and Botan::bigint_sub3().

◆ one()

template<typename Rep >

static constexpr Self Botan::IntMod< Rep >::one ( )

inlinestaticconstexpr

Definition at line 96 of file pcurves_impl.h.

96{ return Self(Rep::one()); }

Referenced by Botan::IntMod< Rep >::is_one(), and Botan::IntMod< Rep >::pow_vartime().

◆ operator!=()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::operator!= ( const Self & other ) const

inlineconstexpr

Definition at line 267 of file pcurves_impl.h.

                                                             {
         return CT::is_not_equal(this->data(), other.data(), N).as_choice();
      }

References Botan::CT::is_not_equal().

◆ operator*=()

template<typename Rep >

Self & Botan::IntMod< Rep >::operator*= ( const Self & other )

inlineconstexpr

Definition at line 162 of file pcurves_impl.h.

                                                    {
         std::array<W, 2 * N> z;
         comba_mul<N>(z.data(), data(), other.data());
         m_val = Rep::redc(z);
         return (*this);
      }

References Botan::comba_mul().

◆ operator=() [1/2]

template<typename Rep >

IntMod & Botan::IntMod< Rep >::operator= ( const Self & other )

default

◆ operator=() [2/2]

template<typename Rep >

IntMod & Botan::IntMod< Rep >::operator= ( Self && other )

default

◆ operator==()

template<typename Rep >

CT::Choice Botan::IntMod< Rep >::operator== ( const Self & other ) const

inlineconstexpr

Definition at line 263 of file pcurves_impl.h.

                                                             {
         return CT::is_equal(this->data(), other.data(), N).as_choice();
      }

References Botan::CT::is_equal().

◆ pow_vartime()

template<typename Rep >

Self Botan::IntMod< Rep >::pow_vartime ( const std::array< W, N > & exp ) const

inlineconstexpr

Definition at line 190 of file pcurves_impl.h.

                                                                  {
         constexpr size_t WindowBits = (Self::BITS <= 256) ? 4 : 5;
         constexpr size_t WindowElements = (1 << WindowBits) - 1;
 
         constexpr size_t Windows = (Self::BITS + WindowBits - 1) / WindowBits;
 
         std::array<Self, WindowElements> tbl;
 
         tbl[0] = (*this);
 
         for(size_t i = 1; i != WindowElements; ++i) {
            if(i % 2 == 1) {
               tbl[i] = tbl[i / 2].square();
            } else {
               tbl[i] = tbl[i - 1] * tbl[0];
            }
         }
 
         auto r = Self::one();
 
         const size_t w0 = read_window_bits<WindowBits>(std::span{exp}, (Windows - 1) * WindowBits);
 
         if(w0 > 0) {
            r = tbl[w0 - 1];
         }
 
         for(size_t i = 1; i != Windows; ++i) {
            for(size_t j = 0; j != WindowBits; ++j) {
               r = r.square();
            }
 
            const size_t w = read_window_bits<WindowBits>(std::span{exp}, (Windows - i - 1) * WindowBits);
 
            if(w > 0) {
               r *= tbl[w - 1];
            }
         }
 
         return r;
      }

References Botan::IntMod< Rep >::BITS, and Botan::IntMod< Rep >::one().

Referenced by Botan::IntMod< Rep >::invert(), Botan::IntMod< Rep >::is_square(), and Botan::IntMod< Rep >::sqrt().

◆ random()

template<typename Rep >

static Self Botan::IntMod< Rep >::random ( RandomNumberGenerator & rng )

inlinestatic

Definition at line 369 of file pcurves_impl.h.

                                                     {
         constexpr size_t MAX_ATTEMPTS = 1000;
 
         std::array<uint8_t, Self::BYTES> buf;
 
         for(size_t i = 0; i != MAX_ATTEMPTS; ++i) {
            rng.randomize(buf);
 
            // Zero off high bits that if set would certainly cause us
            // to be out of range
            if constexpr(Self::BITS % 8 != 0) {
               constexpr uint8_t mask = 0xFF >> (8 - (Self::BITS % 8));
               buf[0] &= mask;
            }
 
            if(auto s = Self::deserialize(buf)) {
               if(s.value().is_nonzero().as_bool()) {
                  return s.value();
               }
            }
         }
 
         throw Internal_Error("Failed to generate random Scalar within bounded number of attempts");
      }

References Botan::IntMod< Rep >::BITS, Botan::IntMod< Rep >::deserialize(), and Botan::RandomNumberGenerator::randomize().

◆ serialize_to()

template<typename Rep >

void Botan::IntMod< Rep >::serialize_to ( std::span< uint8_t, Self::BYTES > bytes ) const

inlineconstexpr

Definition at line 273 of file pcurves_impl.h.

                                                                           {
         auto v = Rep::from_rep(m_val);
         std::reverse(v.begin(), v.end());
 
         if constexpr(Self::BYTES == N * WordInfo<W>::bytes) {
            store_be(bytes, v);
         } else {
            // Remove leading zero bytes
            const auto padded_bytes = store_be(v);
            constexpr size_t extra = N * WordInfo<W>::bytes - Self::BYTES;
            copy_mem(bytes, std::span{padded_bytes}.template subspan<extra, Self::BYTES>());
         }
      }

References Botan::IntMod< Rep >::BYTES, Botan::copy_mem(), and Botan::store_be().

◆ sqrt()

template<typename Rep >

Self Botan::IntMod< Rep >::sqrt ( ) const

inlineconstexpr

Return the modular square root, or zero if no root exists

Current impl assumes p == 3 (mod 4)

Definition at line 245 of file pcurves_impl.h.

      {
         auto z = pow_vartime(Self::P_PLUS_1_OVER_4);
         const CT::Choice correct = (z.square() == *this);
         z.conditional_assign(!correct, Self::zero());
         return z;
      }

References Botan::IntMod< Rep >::pow_vartime(), and Botan::IntMod< Rep >::zero().

◆ square()

template<typename Rep >

Self Botan::IntMod< Rep >::square ( ) const

inlineconstexpr

Definition at line 174 of file pcurves_impl.h.

                                    {
         std::array<W, 2 * N> z;
         comba_sqr<N>(z.data(), this->data());
         return Self(Rep::redc(z));
      }

References Botan::comba_sqr().

◆ stash_value()

template<typename Rep >

template<size_t L>

std::array< W, L > Botan::IntMod< Rep >::stash_value ( ) const

inline

Definition at line 288 of file pcurves_impl.h.

                                         {
         static_assert(L >= N);
         std::array<W, L> stash = {};
         for(size_t i = 0; i != N; ++i) {
            stash[i] = m_val[i];
         }
         return stash;
      }

◆ to_words()

template<typename Rep >

std::array< W, Self::N > Botan::IntMod< Rep >::to_words ( ) const

inlineconstexpr

Definition at line 271 of file pcurves_impl.h.

271{ return Rep::from_rep(m_val); }

◆ zero()

template<typename Rep >

static constexpr Self Botan::IntMod< Rep >::zero ( )

inlinestaticconstexpr

Definition at line 94 of file pcurves_impl.h.

94{ return Self(std::array<W, N>{0}); }

Referenced by Botan::IntMod< Rep >::sqrt().

Friends And Related Symbol Documentation

◆ operator*

template<typename Rep >

Self operator*	(	const Self &	a,
		const Self &	b )

friend

Definition at line 156 of file pcurves_impl.h.

                                                                    {
         std::array<W, 2 * N> z;
         comba_mul<N>(z.data(), a.data(), b.data());
         return Self(Rep::redc(z));
      }

◆ operator+

template<typename Rep >

Self operator+	(	const Self &	a,
		const Self &	b )

friend

Definition at line 126 of file pcurves_impl.h.

                                                                    {
         std::array<W, N> t;
         W carry = bigint_add<W, N>(t, a.value(), b.value());
 
         std::array<W, N> r;
         bigint_monty_maybe_sub<N>(r.data(), carry, t.data(), P.data());
         return Self(r);
      }

◆ operator-

template<typename Rep >

Self operator-	(	const Self &	a,
		const Self &	b )

friend

Definition at line 135 of file pcurves_impl.h.

135{ return a + b.negate(); }

Member Data Documentation

◆ BITS

template<typename Rep >

size_t Botan::IntMod< Rep >::BITS = count_bits(P)

staticconstexpr

Definition at line 79 of file pcurves_impl.h.

Referenced by Botan::IntMod< Rep >::from_bits_with_trunc(), Botan::IntMod< Rep >::from_wide_bytes(), Botan::IntMod< Rep >::from_wide_bytes_varlen(), Botan::IntMod< Rep >::pow_vartime(), and Botan::IntMod< Rep >::random().

◆ BYTES

template<typename Rep >

size_t Botan::IntMod< Rep >::BYTES = (BITS + 7) / 8

staticconstexpr

Definition at line 80 of file pcurves_impl.h.

Referenced by Botan::IntMod< Rep >::deserialize(), and Botan::IntMod< Rep >::serialize_to().

◆ P_MOD_4

template<typename Rep >

auto Botan::IntMod< Rep >::P_MOD_4 = P[0] % 4

staticconstexpr

Definition at line 82 of file pcurves_impl.h.

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

src/lib/math/pcurves/pcurves_impl.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Self

Constructor & Destructor Documentation

◆ IntMod() [1/3]

◆ IntMod() [2/3]

◆ IntMod() [3/3]

Member Function Documentation

◆ conditional_assign()

◆ constant()

◆ ct_poison()

◆ ct_unpoison()

◆ deserialize()

◆ from_bits_with_trunc()

◆ from_stash()

◆ from_wide_bytes()

◆ from_wide_bytes_varlen()

◆ from_word()

◆ from_words()

◆ invert()

◆ is_even()

◆ is_nonzero()

◆ is_one()

◆ is_square()

◆ is_zero()

◆ mul2()

◆ mul3()

◆ mul4()

◆ mul8()

◆ negate()

◆ one()

◆ operator!=()

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ pow_vartime()

◆ random()

◆ serialize_to()

◆ sqrt()

◆ square()

◆ stash_value()

◆ to_words()

◆ zero()

Friends And Related Symbol Documentation

◆ operator*

◆ operator+

◆ operator-

Member Data Documentation

◆ BITS

◆ BYTES

◆ P_MOD_4