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/*
* Ed25519 field element
* (C) 2017 Ribose Inc
*
* Based on the public domain code from SUPERCOP ref10 by
* Peter Schwabe, Daniel J. Bernstein, Niels Duif, Tanja Lange, Bo-Yin Yang
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#ifndef BOTAN_ED25519_FE_H_
#define BOTAN_ED25519_FE_H_
#include <botan/mem_ops.h>
#include <botan/exceptn.h>
namespace Botan {
/**
* An element of the field \\Z/(2^255-19)
*/
class FE_25519
{
public:
~FE_25519() { secure_scrub_memory(m_fe, sizeof(m_fe)); }
/**
* Zero element
*/
FE_25519(int init = 0)
{
if(init != 0 && init != 1)
throw Invalid_Argument("Invalid FE_25519 initial value");
clear_mem(m_fe, 10);
m_fe[0] = init;
}
FE_25519(std::initializer_list<int32_t> x)
{
if(x.size() != 10)
throw Invalid_Argument("Invalid FE_25519 initializer list");
copy_mem(m_fe, x.begin(), 10);
}
FE_25519(int64_t h0, int64_t h1, int64_t h2, int64_t h3, int64_t h4,
int64_t h5, int64_t h6, int64_t h7, int64_t h8, int64_t h9)
{
m_fe[0] = static_cast<int32_t>(h0);
m_fe[1] = static_cast<int32_t>(h1);
m_fe[2] = static_cast<int32_t>(h2);
m_fe[3] = static_cast<int32_t>(h3);
m_fe[4] = static_cast<int32_t>(h4);
m_fe[5] = static_cast<int32_t>(h5);
m_fe[6] = static_cast<int32_t>(h6);
m_fe[7] = static_cast<int32_t>(h7);
m_fe[8] = static_cast<int32_t>(h8);
m_fe[9] = static_cast<int32_t>(h9);
}
FE_25519(const FE_25519& other) = default;
FE_25519& operator=(const FE_25519& other) = default;
FE_25519(FE_25519&& other) = default;
FE_25519& operator=(FE_25519&& other) = default;
void from_bytes(const uint8_t b[32]);
void to_bytes(uint8_t b[32]) const;
bool is_zero() const
{
uint8_t s[32];
to_bytes(s);
uint8_t sum = 0;
for(size_t i = 0; i != 32; ++i)
{ sum |= s[i]; }
// TODO avoid ternary here
return (sum == 0) ? 1 : 0;
}
/*
return 1 if f is in {1,3,5,...,q-2}
return 0 if f is in {0,2,4,...,q-1}
*/
bool is_negative() const
{
// TODO could avoid most of the to_bytes computation here
uint8_t s[32];
to_bytes(s);
return s[0] & 1;
}
static FE_25519 add(const FE_25519& a, const FE_25519& b)
{
FE_25519 z;
for(size_t i = 0; i != 10; ++i)
{ z[i] = a[i] + b[i]; }
return z;
}
static FE_25519 sub(const FE_25519& a, const FE_25519& b)
{
FE_25519 z;
for(size_t i = 0; i != 10; ++i)
{ z[i] = a[i] - b[i]; }
return z;
}
static FE_25519 negate(const FE_25519& a)
{
FE_25519 z;
for(size_t i = 0; i != 10; ++i)
{ z[i] = -a[i]; }
return z;
}
static FE_25519 mul(const FE_25519& a, const FE_25519& b);
static FE_25519 sqr_iter(const FE_25519& a, size_t iter);
static FE_25519 sqr(const FE_25519& a) { return sqr_iter(a, 1); }
static FE_25519 sqr2(const FE_25519& a);
static FE_25519 pow_22523(const FE_25519& a);
static FE_25519 invert(const FE_25519& a);
// TODO remove
int32_t operator[](size_t i) const { return m_fe[i]; }
int32_t& operator[](size_t i) { return m_fe[i]; }
private:
int32_t m_fe[10];
};
typedef FE_25519 fe;
/*
fe means field element.
Here the field is
An element t, entries t[0]...t[9], represents the integer
t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
Bounds on each t[i] vary depending on context.
*/
inline void fe_frombytes(fe& x, const uint8_t* b)
{
x.from_bytes(b);
}
inline void fe_tobytes(uint8_t* b, const fe& x)
{
x.to_bytes(b);
}
inline void fe_copy(fe& a, const fe& b)
{
a = b;
}
inline int fe_isnonzero(const fe& x)
{
return x.is_zero() ? 0 : 1;
}
inline int fe_isnegative(const fe& x)
{
return x.is_negative();
}
inline void fe_0(fe& x)
{
x = FE_25519();
}
inline void fe_1(fe& x)
{
x = FE_25519(1);
}
inline void fe_add(fe& x, const fe& a, const fe& b)
{
x = FE_25519::add(a, b);
}
inline void fe_sub(fe& x, const fe& a, const fe& b)
{
x = FE_25519::sub(a, b);
}
inline void fe_neg(fe& x, const fe& z)
{
x = FE_25519::negate(z);
}
inline void fe_mul(fe& x, const fe& a, const fe& b)
{
x = FE_25519::mul(a, b);
}
inline void fe_sq(fe& x, const fe& z)
{
x = FE_25519::sqr(z);
}
inline void fe_sq_iter(fe& x, const fe& z, size_t iter)
{
x = FE_25519::sqr_iter(z, iter);
}
inline void fe_sq2(fe& x, const fe& z)
{
x = FE_25519::sqr2(z);
}
inline void fe_invert(fe& x, const fe& z)
{
x = FE_25519::invert(z);
}
inline void fe_pow22523(fe& x, const fe& y)
{
x = FE_25519::pow_22523(y);
}
}
#endif