Botan  2.8.0
Crypto and TLS for C++11
Public Member Functions | Static Public Member Functions | List of all members
Botan::FE_25519 Class Reference

#include <ed25519_fe.h>

Public Member Functions

 FE_25519 (int init=0)
 
 FE_25519 (std::initializer_list< int32_t > x)
 
 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)
 
 FE_25519 (const FE_25519 &other)=default
 
 FE_25519 (FE_25519 &&other)=default
 
void from_bytes (const uint8_t b[32])
 
bool is_negative () const
 
bool is_zero () const
 
FE_25519operator= (const FE_25519 &other)=default
 
FE_25519operator= (FE_25519 &&other)=default
 
int32_t operator[] (size_t i) const
 
int32_t & operator[] (size_t i)
 
void to_bytes (uint8_t b[32]) const
 
 ~FE_25519 ()
 

Static Public Member Functions

static FE_25519 add (const FE_25519 &a, const FE_25519 &b)
 
static FE_25519 invert (const FE_25519 &a)
 
static FE_25519 mul (const FE_25519 &a, const FE_25519 &b)
 
static FE_25519 negate (const FE_25519 &a)
 
static FE_25519 pow_22523 (const FE_25519 &a)
 
static FE_25519 sqr (const FE_25519 &a)
 
static FE_25519 sqr2 (const FE_25519 &a)
 
static FE_25519 sqr_iter (const FE_25519 &a, size_t iter)
 
static FE_25519 sub (const FE_25519 &a, const FE_25519 &b)
 

Detailed Description

An element of the field \Z/(2^255-19)

Definition at line 21 of file ed25519_fe.h.

Constructor & Destructor Documentation

◆ ~FE_25519()

Botan::FE_25519::~FE_25519 ( )
inline

Definition at line 24 of file ed25519_fe.h.

References Botan::secure_scrub_memory().

24 { secure_scrub_memory(m_fe, sizeof(m_fe)); }
void secure_scrub_memory(void *ptr, size_t n)
Definition: os_utils.cpp:43

◆ FE_25519() [1/5]

Botan::FE_25519::FE_25519 ( int  init = 0)
inline

Zero element

Definition at line 29 of file ed25519_fe.h.

References init.

Referenced by mul(), sqr2(), and sqr_iter().

30  {
31  if(init != 0 && init != 1)
32  { throw std::invalid_argument("Invalid FE_25519 initial value"); }
33  memset(m_fe, 0, 10 * sizeof(int32_t));
34  m_fe[0] = init;
35  }
int(* init)(CTX *)

◆ FE_25519() [2/5]

Botan::FE_25519::FE_25519 ( std::initializer_list< int32_t >  x)
inline

Definition at line 37 of file ed25519_fe.h.

38  {
39  if(x.size() != 10)
40  { throw std::invalid_argument("Invalid FE_25519 initializer list"); }
41  memcpy(m_fe, x.begin(), 10 * sizeof(int32_t));
42  }

◆ FE_25519() [3/5]

Botan::FE_25519::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 
)
inline

Definition at line 44 of file ed25519_fe.h.

46  {
47  m_fe[0] = static_cast<int32_t>(h0);
48  m_fe[1] = static_cast<int32_t>(h1);
49  m_fe[2] = static_cast<int32_t>(h2);
50  m_fe[3] = static_cast<int32_t>(h3);
51  m_fe[4] = static_cast<int32_t>(h4);
52  m_fe[5] = static_cast<int32_t>(h5);
53  m_fe[6] = static_cast<int32_t>(h6);
54  m_fe[7] = static_cast<int32_t>(h7);
55  m_fe[8] = static_cast<int32_t>(h8);
56  m_fe[9] = static_cast<int32_t>(h9);
57  }

◆ FE_25519() [4/5]

Botan::FE_25519::FE_25519 ( const FE_25519 other)
default

◆ FE_25519() [5/5]

Botan::FE_25519::FE_25519 ( FE_25519 &&  other)
default

Member Function Documentation

◆ add()

static FE_25519 Botan::FE_25519::add ( const FE_25519 a,
const FE_25519 b 
)
inlinestatic

Definition at line 95 of file ed25519_fe.h.

Referenced by Botan::fe_add().

96  {
97  FE_25519 z;
98  for(size_t i = 0; i != 10; ++i)
99  { z[i] = a[i] + b[i]; }
100  return z;
101  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ from_bytes()

void Botan::FE_25519::from_bytes ( const uint8_t  b[32])

Definition at line 605 of file ed25519_fe.cpp.

References Botan::load_3(), and Botan::load_4().

Referenced by Botan::fe_frombytes().

606  {
607  int64_t h0 = load_4(s);
608  int64_t h1 = load_3(s + 4) << 6;
609  int64_t h2 = load_3(s + 7) << 5;
610  int64_t h3 = load_3(s + 10) << 3;
611  int64_t h4 = load_3(s + 13) << 2;
612  int64_t h5 = load_4(s + 16);
613  int64_t h6 = load_3(s + 20) << 7;
614  int64_t h7 = load_3(s + 23) << 5;
615  int64_t h8 = load_3(s + 26) << 4;
616  int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
617 
618  carry<25,19>(h9, h0);
619  carry<25>(h1, h2);
620  carry<25>(h3, h4);
621  carry<25>(h5, h6);
622  carry<25>(h7, h8);
623 
624  carry<26>(h0, h1);
625  carry<26>(h2, h3);
626  carry<26>(h4, h5);
627  carry<26>(h6, h7);
628  carry<26>(h8, h9);
629 
630  m_fe[0] = static_cast<int32_t>(h0);
631  m_fe[1] = static_cast<int32_t>(h1);
632  m_fe[2] = static_cast<int32_t>(h2);
633  m_fe[3] = static_cast<int32_t>(h3);
634  m_fe[4] = static_cast<int32_t>(h4);
635  m_fe[5] = static_cast<int32_t>(h5);
636  m_fe[6] = static_cast<int32_t>(h6);
637  m_fe[7] = static_cast<int32_t>(h7);
638  m_fe[8] = static_cast<int32_t>(h8);
639  m_fe[9] = static_cast<int32_t>(h9);
640  }
uint64_t load_4(const uint8_t *in)
uint64_t load_3(const uint8_t in[3])

◆ invert()

FE_25519 Botan::FE_25519::invert ( const FE_25519 a)
static

Definition at line 17 of file ed25519_fe.cpp.

References Botan::fe_mul(), Botan::fe_sq(), and Botan::fe_sq_iter().

Referenced by Botan::fe_invert().

18  {
19  fe t0;
20  fe t1;
21  fe t2;
22  fe t3;
23 
24  fe_sq(t0, z);
25  fe_sq_iter(t1, t0, 2);
26  fe_mul(t1, z, t1);
27  fe_mul(t0, t0, t1);
28  fe_sq(t2, t0);
29  fe_mul(t1, t1, t2);
30  fe_sq_iter(t2, t1, 5);
31  fe_mul(t1, t2, t1);
32  fe_sq_iter(t2, t1, 10);
33  fe_mul(t2, t2, t1);
34  fe_sq_iter(t3, t2, 20);
35  fe_mul(t2, t3, t2);
36  fe_sq_iter(t2, t2, 10);
37  fe_mul(t1, t2, t1);
38  fe_sq_iter(t2, t1, 50);
39  fe_mul(t2, t2, t1);
40  fe_sq_iter(t3, t2, 100);
41  fe_mul(t2, t3, t2);
42  fe_sq_iter(t2, t2, 50);
43  fe_mul(t1, t2, t1);
44  fe_sq_iter(t1, t1, 5);
45 
46  fe_mul(t0, t1, t0);
47  return t0;
48  }
void fe_sq(fe &x, const fe &z)
Definition: ed25519_fe.h:201
void fe_sq_iter(fe &x, const fe &z, size_t iter)
Definition: ed25519_fe.h:206
FE_25519 fe
Definition: ed25519_fe.h:135
void fe_mul(fe &x, const fe &a, const fe &b)
Definition: ed25519_fe.h:196

◆ is_negative()

bool Botan::FE_25519::is_negative ( ) const
inline

Definition at line 87 of file ed25519_fe.h.

References to_bytes().

Referenced by Botan::fe_isnegative().

88  {
89  // TODO could avoid most of the to_bytes computation here
90  uint8_t s[32];
91  to_bytes(s);
92  return s[0] & 1;
93  }
void to_bytes(uint8_t b[32]) const
Definition: ed25519_fe.cpp:667

◆ is_zero()

bool Botan::FE_25519::is_zero ( ) const
inline

Definition at line 70 of file ed25519_fe.h.

References to_bytes().

Referenced by Botan::fe_isnonzero().

71  {
72  uint8_t s[32];
73  to_bytes(s);
74 
75  uint8_t sum = 0;
76  for(size_t i = 0; i != 32; ++i)
77  { sum |= s[i]; }
78 
79  // TODO avoid ternary here
80  return (sum == 0) ? 1 : 0;
81  }
void to_bytes(uint8_t b[32]) const
Definition: ed25519_fe.cpp:667

◆ mul()

FE_25519 Botan::FE_25519::mul ( const FE_25519 a,
const FE_25519 b 
)
static

Definition at line 115 of file ed25519_fe.cpp.

References FE_25519().

Referenced by Botan::fe_mul().

116  {
117  const int32_t f0 = f[0];
118  const int32_t f1 = f[1];
119  const int32_t f2 = f[2];
120  const int32_t f3 = f[3];
121  const int32_t f4 = f[4];
122  const int32_t f5 = f[5];
123  const int32_t f6 = f[6];
124  const int32_t f7 = f[7];
125  const int32_t f8 = f[8];
126  const int32_t f9 = f[9];
127 
128  const int32_t g0 = g[0];
129  const int32_t g1 = g[1];
130  const int32_t g2 = g[2];
131  const int32_t g3 = g[3];
132  const int32_t g4 = g[4];
133  const int32_t g5 = g[5];
134  const int32_t g6 = g[6];
135  const int32_t g7 = g[7];
136  const int32_t g8 = g[8];
137  const int32_t g9 = g[9];
138 
139  const int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
140  const int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
141  const int32_t g3_19 = 19 * g3;
142  const int32_t g4_19 = 19 * g4;
143  const int32_t g5_19 = 19 * g5;
144  const int32_t g6_19 = 19 * g6;
145  const int32_t g7_19 = 19 * g7;
146  const int32_t g8_19 = 19 * g8;
147  const int32_t g9_19 = 19 * g9;
148  const int32_t f1_2 = 2 * f1;
149  const int32_t f3_2 = 2 * f3;
150  const int32_t f5_2 = 2 * f5;
151  const int32_t f7_2 = 2 * f7;
152  const int32_t f9_2 = 2 * f9;
153 
154  const int64_t f0g0 = f0 * static_cast<int64_t>(g0);
155  const int64_t f0g1 = f0 * static_cast<int64_t>(g1);
156  const int64_t f0g2 = f0 * static_cast<int64_t>(g2);
157  const int64_t f0g3 = f0 * static_cast<int64_t>(g3);
158  const int64_t f0g4 = f0 * static_cast<int64_t>(g4);
159  const int64_t f0g5 = f0 * static_cast<int64_t>(g5);
160  const int64_t f0g6 = f0 * static_cast<int64_t>(g6);
161  const int64_t f0g7 = f0 * static_cast<int64_t>(g7);
162  const int64_t f0g8 = f0 * static_cast<int64_t>(g8);
163  const int64_t f0g9 = f0 * static_cast<int64_t>(g9);
164  const int64_t f1g0 = f1 * static_cast<int64_t>(g0);
165  const int64_t f1g1_2 = f1_2 * static_cast<int64_t>(g1);
166  const int64_t f1g2 = f1 * static_cast<int64_t>(g2);
167  const int64_t f1g3_2 = f1_2 * static_cast<int64_t>(g3);
168  const int64_t f1g4 = f1 * static_cast<int64_t>(g4);
169  const int64_t f1g5_2 = f1_2 * static_cast<int64_t>(g5);
170  const int64_t f1g6 = f1 * static_cast<int64_t>(g6);
171  const int64_t f1g7_2 = f1_2 * static_cast<int64_t>(g7);
172  const int64_t f1g8 = f1 * static_cast<int64_t>(g8);
173  const int64_t f1g9_38 = f1_2 * static_cast<int64_t>(g9_19);
174  const int64_t f2g0 = f2 * static_cast<int64_t>(g0);
175  const int64_t f2g1 = f2 * static_cast<int64_t>(g1);
176  const int64_t f2g2 = f2 * static_cast<int64_t>(g2);
177  const int64_t f2g3 = f2 * static_cast<int64_t>(g3);
178  const int64_t f2g4 = f2 * static_cast<int64_t>(g4);
179  const int64_t f2g5 = f2 * static_cast<int64_t>(g5);
180  const int64_t f2g6 = f2 * static_cast<int64_t>(g6);
181  const int64_t f2g7 = f2 * static_cast<int64_t>(g7);
182  const int64_t f2g8_19 = f2 * static_cast<int64_t>(g8_19);
183  const int64_t f2g9_19 = f2 * static_cast<int64_t>(g9_19);
184  const int64_t f3g0 = f3 * static_cast<int64_t>(g0);
185  const int64_t f3g1_2 = f3_2 * static_cast<int64_t>(g1);
186  const int64_t f3g2 = f3 * static_cast<int64_t>(g2);
187  const int64_t f3g3_2 = f3_2 * static_cast<int64_t>(g3);
188  const int64_t f3g4 = f3 * static_cast<int64_t>(g4);
189  const int64_t f3g5_2 = f3_2 * static_cast<int64_t>(g5);
190  const int64_t f3g6 = f3 * static_cast<int64_t>(g6);
191  const int64_t f3g7_38 = f3_2 * static_cast<int64_t>(g7_19);
192  const int64_t f3g8_19 = f3 * static_cast<int64_t>(g8_19);
193  const int64_t f3g9_38 = f3_2 * static_cast<int64_t>(g9_19);
194  const int64_t f4g0 = f4 * static_cast<int64_t>(g0);
195  const int64_t f4g1 = f4 * static_cast<int64_t>(g1);
196  const int64_t f4g2 = f4 * static_cast<int64_t>(g2);
197  const int64_t f4g3 = f4 * static_cast<int64_t>(g3);
198  const int64_t f4g4 = f4 * static_cast<int64_t>(g4);
199  const int64_t f4g5 = f4 * static_cast<int64_t>(g5);
200  const int64_t f4g6_19 = f4 * static_cast<int64_t>(g6_19);
201  const int64_t f4g7_19 = f4 * static_cast<int64_t>(g7_19);
202  const int64_t f4g8_19 = f4 * static_cast<int64_t>(g8_19);
203  const int64_t f4g9_19 = f4 * static_cast<int64_t>(g9_19);
204  const int64_t f5g0 = f5 * static_cast<int64_t>(g0);
205  const int64_t f5g1_2 = f5_2 * static_cast<int64_t>(g1);
206  const int64_t f5g2 = f5 * static_cast<int64_t>(g2);
207  const int64_t f5g3_2 = f5_2 * static_cast<int64_t>(g3);
208  const int64_t f5g4 = f5 * static_cast<int64_t>(g4);
209  const int64_t f5g5_38 = f5_2 * static_cast<int64_t>(g5_19);
210  const int64_t f5g6_19 = f5 * static_cast<int64_t>(g6_19);
211  const int64_t f5g7_38 = f5_2 * static_cast<int64_t>(g7_19);
212  const int64_t f5g8_19 = f5 * static_cast<int64_t>(g8_19);
213  const int64_t f5g9_38 = f5_2 * static_cast<int64_t>(g9_19);
214  const int64_t f6g0 = f6 * static_cast<int64_t>(g0);
215  const int64_t f6g1 = f6 * static_cast<int64_t>(g1);
216  const int64_t f6g2 = f6 * static_cast<int64_t>(g2);
217  const int64_t f6g3 = f6 * static_cast<int64_t>(g3);
218  const int64_t f6g4_19 = f6 * static_cast<int64_t>(g4_19);
219  const int64_t f6g5_19 = f6 * static_cast<int64_t>(g5_19);
220  const int64_t f6g6_19 = f6 * static_cast<int64_t>(g6_19);
221  const int64_t f6g7_19 = f6 * static_cast<int64_t>(g7_19);
222  const int64_t f6g8_19 = f6 * static_cast<int64_t>(g8_19);
223  const int64_t f6g9_19 = f6 * static_cast<int64_t>(g9_19);
224  const int64_t f7g0 = f7 * static_cast<int64_t>(g0);
225  const int64_t f7g1_2 = f7_2 * static_cast<int64_t>(g1);
226  const int64_t f7g2 = f7 * static_cast<int64_t>(g2);
227  const int64_t f7g3_38 = f7_2 * static_cast<int64_t>(g3_19);
228  const int64_t f7g4_19 = f7 * static_cast<int64_t>(g4_19);
229  const int64_t f7g5_38 = f7_2 * static_cast<int64_t>(g5_19);
230  const int64_t f7g6_19 = f7 * static_cast<int64_t>(g6_19);
231  const int64_t f7g7_38 = f7_2 * static_cast<int64_t>(g7_19);
232  const int64_t f7g8_19 = f7 * static_cast<int64_t>(g8_19);
233  const int64_t f7g9_38 = f7_2 * static_cast<int64_t>(g9_19);
234  const int64_t f8g0 = f8 * static_cast<int64_t>(g0);
235  const int64_t f8g1 = f8 * static_cast<int64_t>(g1);
236  const int64_t f8g2_19 = f8 * static_cast<int64_t>(g2_19);
237  const int64_t f8g3_19 = f8 * static_cast<int64_t>(g3_19);
238  const int64_t f8g4_19 = f8 * static_cast<int64_t>(g4_19);
239  const int64_t f8g5_19 = f8 * static_cast<int64_t>(g5_19);
240  const int64_t f8g6_19 = f8 * static_cast<int64_t>(g6_19);
241  const int64_t f8g7_19 = f8 * static_cast<int64_t>(g7_19);
242  const int64_t f8g8_19 = f8 * static_cast<int64_t>(g8_19);
243  const int64_t f8g9_19 = f8 * static_cast<int64_t>(g9_19);
244  const int64_t f9g0 = f9 * static_cast<int64_t>(g0);
245  const int64_t f9g1_38 = f9_2 * static_cast<int64_t>(g1_19);
246  const int64_t f9g2_19 = f9 * static_cast<int64_t>(g2_19);
247  const int64_t f9g3_38 = f9_2 * static_cast<int64_t>(g3_19);
248  const int64_t f9g4_19 = f9 * static_cast<int64_t>(g4_19);
249  const int64_t f9g5_38 = f9_2 * static_cast<int64_t>(g5_19);
250  const int64_t f9g6_19 = f9 * static_cast<int64_t>(g6_19);
251  const int64_t f9g7_38 = f9_2 * static_cast<int64_t>(g7_19);
252  const int64_t f9g8_19 = f9 * static_cast<int64_t>(g8_19);
253  const int64_t f9g9_38 = f9_2 * static_cast<int64_t>(g9_19);
254 
255  int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
256  int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
257  int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
258  int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
259  int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
260  int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
261  int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
262  int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
263  int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
264  int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
265 
266  /*
267  |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
268  i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
269  |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
270  i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
271  */
272  carry<26>(h0, h1);
273  carry<26>(h4, h5);
274 
275  /* |h0| <= 2^25 */
276  /* |h4| <= 2^25 */
277  /* |h1| <= 1.71*2^59 */
278  /* |h5| <= 1.71*2^59 */
279 
280  carry<25>(h1, h2);
281  carry<25>(h5, h6);
282 
283  /* |h1| <= 2^24; from now on fits into int32 */
284  /* |h5| <= 2^24; from now on fits into int32 */
285  /* |h2| <= 1.41*2^60 */
286  /* |h6| <= 1.41*2^60 */
287 
288  carry<26>(h2, h3);
289  carry<26>(h6, h7);
290  /* |h2| <= 2^25; from now on fits into int32 unchanged */
291  /* |h6| <= 2^25; from now on fits into int32 unchanged */
292  /* |h3| <= 1.71*2^59 */
293  /* |h7| <= 1.71*2^59 */
294 
295  carry<25>(h3, h4);
296  carry<25>(h7, h8);
297  /* |h3| <= 2^24; from now on fits into int32 unchanged */
298  /* |h7| <= 2^24; from now on fits into int32 unchanged */
299  /* |h4| <= 1.72*2^34 */
300  /* |h8| <= 1.41*2^60 */
301 
302  carry<26>(h4, h5);
303  carry<26>(h8, h9);
304  /* |h4| <= 2^25; from now on fits into int32 unchanged */
305  /* |h8| <= 2^25; from now on fits into int32 unchanged */
306  /* |h5| <= 1.01*2^24 */
307  /* |h9| <= 1.71*2^59 */
308 
309  carry<25, 19>(h9, h0);
310 
311  /* |h9| <= 2^24; from now on fits into int32 unchanged */
312  /* |h0| <= 1.1*2^39 */
313 
314  carry<26>(h0, h1);
315  /* |h0| <= 2^25; from now on fits into int32 unchanged */
316  /* |h1| <= 1.01*2^24 */
317 
318  return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9);
319  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ negate()

static FE_25519 Botan::FE_25519::negate ( const FE_25519 a)
inlinestatic

Definition at line 111 of file ed25519_fe.h.

Referenced by Botan::fe_neg().

112  {
113  FE_25519 z;
114  for(size_t i = 0; i != 10; ++i)
115  { z[i] = -a[i]; }
116  return z;
117  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ operator=() [1/2]

FE_25519& Botan::FE_25519::operator= ( const FE_25519 other)
default

◆ operator=() [2/2]

FE_25519& Botan::FE_25519::operator= ( FE_25519 &&  other)
default

◆ operator[]() [1/2]

int32_t Botan::FE_25519::operator[] ( size_t  i) const
inline

Definition at line 127 of file ed25519_fe.h.

127 { return m_fe[i]; }

◆ operator[]() [2/2]

int32_t& Botan::FE_25519::operator[] ( size_t  i)
inline

Definition at line 128 of file ed25519_fe.h.

128 { return m_fe[i]; }

◆ pow_22523()

FE_25519 Botan::FE_25519::pow_22523 ( const FE_25519 a)
static

Definition at line 50 of file ed25519_fe.cpp.

References Botan::fe_mul(), Botan::fe_sq(), and Botan::fe_sq_iter().

Referenced by Botan::fe_pow22523().

51  {
52  fe t0;
53  fe t1;
54  fe t2;
55 
56  fe_sq(t0, z);
57  fe_sq_iter(t1, t0, 2);
58  fe_mul(t1, z, t1);
59  fe_mul(t0, t0, t1);
60  fe_sq(t0, t0);
61  fe_mul(t0, t1, t0);
62  fe_sq_iter(t1, t0, 5);
63  fe_mul(t0, t1, t0);
64  fe_sq_iter(t1, t0, 10);
65  fe_mul(t1, t1, t0);
66  fe_sq_iter(t2, t1, 20);
67  fe_mul(t1, t2, t1);
68  fe_sq_iter(t1, t1, 10);
69  fe_mul(t0, t1, t0);
70  fe_sq_iter(t1, t0, 50);
71  fe_mul(t1, t1, t0);
72  fe_sq_iter(t2, t1, 100);
73  fe_mul(t1, t2, t1);
74  fe_sq_iter(t1, t1, 50);
75  fe_mul(t0, t1, t0);
76  fe_sq_iter(t0, t0, 2);
77 
78  fe_mul(t0, t0, z);
79  return t0;
80  }
void fe_sq(fe &x, const fe &z)
Definition: ed25519_fe.h:201
void fe_sq_iter(fe &x, const fe &z, size_t iter)
Definition: ed25519_fe.h:206
FE_25519 fe
Definition: ed25519_fe.h:135
void fe_mul(fe &x, const fe &a, const fe &b)
Definition: ed25519_fe.h:196

◆ sqr()

static FE_25519 Botan::FE_25519::sqr ( const FE_25519 a)
inlinestatic

Definition at line 121 of file ed25519_fe.h.

References sqr_iter().

Referenced by Botan::fe_sq().

121 { return sqr_iter(a, 1); }
static FE_25519 sqr_iter(const FE_25519 &a, size_t iter)
Definition: ed25519_fe.cpp:337

◆ sqr2()

FE_25519 Botan::FE_25519::sqr2 ( const FE_25519 a)
static

Definition at line 479 of file ed25519_fe.cpp.

References FE_25519().

Referenced by Botan::fe_sq2().

480  {
481  const int32_t f0 = f[0];
482  const int32_t f1 = f[1];
483  const int32_t f2 = f[2];
484  const int32_t f3 = f[3];
485  const int32_t f4 = f[4];
486  const int32_t f5 = f[5];
487  const int32_t f6 = f[6];
488  const int32_t f7 = f[7];
489  const int32_t f8 = f[8];
490  const int32_t f9 = f[9];
491  const int32_t f0_2 = 2 * f0;
492  const int32_t f1_2 = 2 * f1;
493  const int32_t f2_2 = 2 * f2;
494  const int32_t f3_2 = 2 * f3;
495  const int32_t f4_2 = 2 * f4;
496  const int32_t f5_2 = 2 * f5;
497  const int32_t f6_2 = 2 * f6;
498  const int32_t f7_2 = 2 * f7;
499  const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
500  const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
501  const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
502  const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
503  const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
504  const int64_t f0f0 = f0 * static_cast<int64_t>(f0);
505  const int64_t f0f1_2 = f0_2 * static_cast<int64_t>(f1);
506  const int64_t f0f2_2 = f0_2 * static_cast<int64_t>(f2);
507  const int64_t f0f3_2 = f0_2 * static_cast<int64_t>(f3);
508  const int64_t f0f4_2 = f0_2 * static_cast<int64_t>(f4);
509  const int64_t f0f5_2 = f0_2 * static_cast<int64_t>(f5);
510  const int64_t f0f6_2 = f0_2 * static_cast<int64_t>(f6);
511  const int64_t f0f7_2 = f0_2 * static_cast<int64_t>(f7);
512  const int64_t f0f8_2 = f0_2 * static_cast<int64_t>(f8);
513  const int64_t f0f9_2 = f0_2 * static_cast<int64_t>(f9);
514  const int64_t f1f1_2 = f1_2 * static_cast<int64_t>(f1);
515  const int64_t f1f2_2 = f1_2 * static_cast<int64_t>(f2);
516  const int64_t f1f3_4 = f1_2 * static_cast<int64_t>(f3_2);
517  const int64_t f1f4_2 = f1_2 * static_cast<int64_t>(f4);
518  const int64_t f1f5_4 = f1_2 * static_cast<int64_t>(f5_2);
519  const int64_t f1f6_2 = f1_2 * static_cast<int64_t>(f6);
520  const int64_t f1f7_4 = f1_2 * static_cast<int64_t>(f7_2);
521  const int64_t f1f8_2 = f1_2 * static_cast<int64_t>(f8);
522  const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38);
523  const int64_t f2f2 = f2 * static_cast<int64_t>(f2);
524  const int64_t f2f3_2 = f2_2 * static_cast<int64_t>(f3);
525  const int64_t f2f4_2 = f2_2 * static_cast<int64_t>(f4);
526  const int64_t f2f5_2 = f2_2 * static_cast<int64_t>(f5);
527  const int64_t f2f6_2 = f2_2 * static_cast<int64_t>(f6);
528  const int64_t f2f7_2 = f2_2 * static_cast<int64_t>(f7);
529  const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19);
530  const int64_t f2f9_38 = f2 * static_cast<int64_t>(f9_38);
531  const int64_t f3f3_2 = f3_2 * static_cast<int64_t>(f3);
532  const int64_t f3f4_2 = f3_2 * static_cast<int64_t>(f4);
533  const int64_t f3f5_4 = f3_2 * static_cast<int64_t>(f5_2);
534  const int64_t f3f6_2 = f3_2 * static_cast<int64_t>(f6);
535  const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38);
536  const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19);
537  const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38);
538  const int64_t f4f4 = f4 * static_cast<int64_t>(f4);
539  const int64_t f4f5_2 = f4_2 * static_cast<int64_t>(f5);
540  const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19);
541  const int64_t f4f7_38 = f4 * static_cast<int64_t>(f7_38);
542  const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19);
543  const int64_t f4f9_38 = f4 * static_cast<int64_t>(f9_38);
544  const int64_t f5f5_38 = f5 * static_cast<int64_t>(f5_38);
545  const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19);
546  const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38);
547  const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19);
548  const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38);
549  const int64_t f6f6_19 = f6 * static_cast<int64_t>(f6_19);
550  const int64_t f6f7_38 = f6 * static_cast<int64_t>(f7_38);
551  const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19);
552  const int64_t f6f9_38 = f6 * static_cast<int64_t>(f9_38);
553  const int64_t f7f7_38 = f7 * static_cast<int64_t>(f7_38);
554  const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19);
555  const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38);
556  const int64_t f8f8_19 = f8 * static_cast<int64_t>(f8_19);
557  const int64_t f8f9_38 = f8 * static_cast<int64_t>(f9_38);
558  const int64_t f9f9_38 = f9 * static_cast<int64_t>(f9_38);
559 
560  int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
561  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
562  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
563  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
564  int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
565  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
566  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
567  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
568  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
569  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
570 
571  h0 += h0;
572  h1 += h1;
573  h2 += h2;
574  h3 += h3;
575  h4 += h4;
576  h5 += h5;
577  h6 += h6;
578  h7 += h7;
579  h8 += h8;
580  h9 += h9;
581 
582  carry<26>(h0, h1);
583  carry<26>(h4, h5);
584 
585  carry<25>(h1, h2);
586  carry<25>(h5, h6);
587 
588  carry<26>(h2, h3);
589  carry<26>(h6, h7);
590 
591  carry<25>(h3, h4);
592  carry<25>(h7, h8);
593  carry<26>(h4, h5);
594  carry<26>(h8, h9);
595  carry<25,19>(h9, h0);
596  carry<26>(h0, h1);
597 
598  return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9);
599  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ sqr_iter()

FE_25519 Botan::FE_25519::sqr_iter ( const FE_25519 a,
size_t  iter 
)
static

Definition at line 337 of file ed25519_fe.cpp.

References FE_25519().

Referenced by Botan::fe_sq_iter(), and sqr().

338  {
339  int32_t f0 = f[0];
340  int32_t f1 = f[1];
341  int32_t f2 = f[2];
342  int32_t f3 = f[3];
343  int32_t f4 = f[4];
344  int32_t f5 = f[5];
345  int32_t f6 = f[6];
346  int32_t f7 = f[7];
347  int32_t f8 = f[8];
348  int32_t f9 = f[9];
349 
350  for(size_t i = 0; i != iter; ++i)
351  {
352  const int32_t f0_2 = 2 * f0;
353  const int32_t f1_2 = 2 * f1;
354  const int32_t f2_2 = 2 * f2;
355  const int32_t f3_2 = 2 * f3;
356  const int32_t f4_2 = 2 * f4;
357  const int32_t f5_2 = 2 * f5;
358  const int32_t f6_2 = 2 * f6;
359  const int32_t f7_2 = 2 * f7;
360  const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
361  const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
362  const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
363  const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
364  const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
365 
366  const int64_t f0f0 = f0 * static_cast<int64_t>(f0);
367  const int64_t f0f1_2 = f0_2 * static_cast<int64_t>(f1);
368  const int64_t f0f2_2 = f0_2 * static_cast<int64_t>(f2);
369  const int64_t f0f3_2 = f0_2 * static_cast<int64_t>(f3);
370  const int64_t f0f4_2 = f0_2 * static_cast<int64_t>(f4);
371  const int64_t f0f5_2 = f0_2 * static_cast<int64_t>(f5);
372  const int64_t f0f6_2 = f0_2 * static_cast<int64_t>(f6);
373  const int64_t f0f7_2 = f0_2 * static_cast<int64_t>(f7);
374  const int64_t f0f8_2 = f0_2 * static_cast<int64_t>(f8);
375  const int64_t f0f9_2 = f0_2 * static_cast<int64_t>(f9);
376  const int64_t f1f1_2 = f1_2 * static_cast<int64_t>(f1);
377  const int64_t f1f2_2 = f1_2 * static_cast<int64_t>(f2);
378  const int64_t f1f3_4 = f1_2 * static_cast<int64_t>(f3_2);
379  const int64_t f1f4_2 = f1_2 * static_cast<int64_t>(f4);
380  const int64_t f1f5_4 = f1_2 * static_cast<int64_t>(f5_2);
381  const int64_t f1f6_2 = f1_2 * static_cast<int64_t>(f6);
382  const int64_t f1f7_4 = f1_2 * static_cast<int64_t>(f7_2);
383  const int64_t f1f8_2 = f1_2 * static_cast<int64_t>(f8);
384  const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38);
385  const int64_t f2f2 = f2 * static_cast<int64_t>(f2);
386  const int64_t f2f3_2 = f2_2 * static_cast<int64_t>(f3);
387  const int64_t f2f4_2 = f2_2 * static_cast<int64_t>(f4);
388  const int64_t f2f5_2 = f2_2 * static_cast<int64_t>(f5);
389  const int64_t f2f6_2 = f2_2 * static_cast<int64_t>(f6);
390  const int64_t f2f7_2 = f2_2 * static_cast<int64_t>(f7);
391  const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19);
392  const int64_t f2f9_38 = f2 * static_cast<int64_t>(f9_38);
393  const int64_t f3f3_2 = f3_2 * static_cast<int64_t>(f3);
394  const int64_t f3f4_2 = f3_2 * static_cast<int64_t>(f4);
395  const int64_t f3f5_4 = f3_2 * static_cast<int64_t>(f5_2);
396  const int64_t f3f6_2 = f3_2 * static_cast<int64_t>(f6);
397  const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38);
398  const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19);
399  const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38);
400  const int64_t f4f4 = f4 * static_cast<int64_t>(f4);
401  const int64_t f4f5_2 = f4_2 * static_cast<int64_t>(f5);
402  const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19);
403  const int64_t f4f7_38 = f4 * static_cast<int64_t>(f7_38);
404  const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19);
405  const int64_t f4f9_38 = f4 * static_cast<int64_t>(f9_38);
406  const int64_t f5f5_38 = f5 * static_cast<int64_t>(f5_38);
407  const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19);
408  const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38);
409  const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19);
410  const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38);
411  const int64_t f6f6_19 = f6 * static_cast<int64_t>(f6_19);
412  const int64_t f6f7_38 = f6 * static_cast<int64_t>(f7_38);
413  const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19);
414  const int64_t f6f9_38 = f6 * static_cast<int64_t>(f9_38);
415  const int64_t f7f7_38 = f7 * static_cast<int64_t>(f7_38);
416  const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19);
417  const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38);
418  const int64_t f8f8_19 = f8 * static_cast<int64_t>(f8_19);
419  const int64_t f8f9_38 = f8 * static_cast<int64_t>(f9_38);
420  const int64_t f9f9_38 = f9 * static_cast<int64_t>(f9_38);
421 
422  int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
423  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
424  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
425  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
426  int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
427  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
428  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
429  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
430  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
431  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
432 
433  carry<26>(h0, h1);
434  carry<26>(h4, h5);
435  carry<25>(h1, h2);
436  carry<25>(h5, h6);
437  carry<26>(h2, h3);
438  carry<26>(h6, h7);
439 
440  carry<25>(h3, h4);
441  carry<25>(h7, h8);
442 
443  carry<26>(h4, h5);
444  carry<26>(h8, h9);
445  carry<25,19>(h9, h0);
446  carry<26>(h0, h1);
447 
448  f0 = static_cast<int32_t>(h0);
449  f1 = static_cast<int32_t>(h1);
450  f2 = static_cast<int32_t>(h2);
451  f3 = static_cast<int32_t>(h3);
452  f4 = static_cast<int32_t>(h4);
453  f5 = static_cast<int32_t>(h5);
454  f6 = static_cast<int32_t>(h6);
455  f7 = static_cast<int32_t>(h7);
456  f8 = static_cast<int32_t>(h8);
457  f9 = static_cast<int32_t>(h9);
458  }
459 
460  return FE_25519(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9);
461  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ sub()

static FE_25519 Botan::FE_25519::sub ( const FE_25519 a,
const FE_25519 b 
)
inlinestatic

Definition at line 103 of file ed25519_fe.h.

Referenced by Botan::fe_sub().

104  {
105  FE_25519 z;
106  for(size_t i = 0; i != 10; ++i)
107  { z[i] = a[i] - b[i]; }
108  return z;
109  }
FE_25519(int init=0)
Definition: ed25519_fe.h:29

◆ to_bytes()

void Botan::FE_25519::to_bytes ( uint8_t  b[32]) const

Definition at line 667 of file ed25519_fe.cpp.

Referenced by Botan::fe_tobytes(), is_negative(), and is_zero().

668  {
669  const int64_t X25 = (1 << 25);
670 
671  int32_t h0 = m_fe[0];
672  int32_t h1 = m_fe[1];
673  int32_t h2 = m_fe[2];
674  int32_t h3 = m_fe[3];
675  int32_t h4 = m_fe[4];
676  int32_t h5 = m_fe[5];
677  int32_t h6 = m_fe[6];
678  int32_t h7 = m_fe[7];
679  int32_t h8 = m_fe[8];
680  int32_t h9 = m_fe[9];
681  int32_t q;
682 
683  q = (19 * h9 + ((static_cast<int32_t>(1) << 24))) >> 25;
684  q = (h0 + q) >> 26;
685  q = (h1 + q) >> 25;
686  q = (h2 + q) >> 26;
687  q = (h3 + q) >> 25;
688  q = (h4 + q) >> 26;
689  q = (h5 + q) >> 25;
690  q = (h6 + q) >> 26;
691  q = (h7 + q) >> 25;
692  q = (h8 + q) >> 26;
693  q = (h9 + q) >> 25;
694 
695  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
696  h0 += 19 * q;
697  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
698 
699  carry0<26>(h0, h1);
700  carry0<25>(h1, h2);
701  carry0<26>(h2, h3);
702  carry0<25>(h3, h4);
703  carry0<26>(h4, h5);
704  carry0<25>(h5, h6);
705  carry0<26>(h6, h7);
706  carry0<25>(h7, h8);
707  carry0<26>(h8, h9);
708 
709  int32_t carry9 = h9 >> 25;
710  h9 -= carry9 * X25;
711  /* h10 = carry9 */
712 
713  /*
714  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
715  Have h0+...+2^230 h9 between 0 and 2^255-1;
716  evidently 2^255 h10-2^255 q = 0.
717  Goal: Output h0+...+2^230 h9.
718  */
719 
720  s[0] = h0 >> 0;
721  s[1] = h0 >> 8;
722  s[2] = h0 >> 16;
723  s[3] = (h0 >> 24) | (h1 << 2);
724  s[4] = h1 >> 6;
725  s[5] = h1 >> 14;
726  s[6] = (h1 >> 22) | (h2 << 3);
727  s[7] = h2 >> 5;
728  s[8] = h2 >> 13;
729  s[9] = (h2 >> 21) | (h3 << 5);
730  s[10] = h3 >> 3;
731  s[11] = h3 >> 11;
732  s[12] = (h3 >> 19) | (h4 << 6);
733  s[13] = h4 >> 2;
734  s[14] = h4 >> 10;
735  s[15] = h4 >> 18;
736  s[16] = h5 >> 0;
737  s[17] = h5 >> 8;
738  s[18] = h5 >> 16;
739  s[19] = (h5 >> 24) | (h6 << 1);
740  s[20] = h6 >> 7;
741  s[21] = h6 >> 15;
742  s[22] = (h6 >> 23) | (h7 << 3);
743  s[23] = h7 >> 5;
744  s[24] = h7 >> 13;
745  s[25] = (h7 >> 21) | (h8 << 4);
746  s[26] = h8 >> 4;
747  s[27] = h8 >> 12;
748  s[28] = (h8 >> 20) | (h9 << 6);
749  s[29] = h9 >> 2;
750  s[30] = h9 >> 10;
751  s[31] = h9 >> 18;
752  }

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