Botan  2.1.0
Crypto and TLS for C++11
Public Types | Public Member Functions | Static Public Member Functions | Friends | List of all members
Botan::PointGFp Class Reference

#include <point_gfp.h>

Public Types

enum  Compression_Type { UNCOMPRESSED = 0, COMPRESSED = 1, HYBRID = 2 }
 

Public Member Functions

BigInt get_affine_x () const
 
BigInt get_affine_y () const
 
const CurveGFpget_curve () const
 
bool is_zero () const
 
PointGFpnegate ()
 
bool on_the_curve () const
 
PointGFpoperator*= (const BigInt &scalar)
 
PointGFpoperator+= (const PointGFp &rhs)
 
PointGFpoperator-= (const PointGFp &rhs)
 
PointGFpoperator= (const PointGFp &)=default
 
PointGFpoperator= (PointGFp &&other)
 
bool operator== (const PointGFp &other) const
 
 PointGFp ()=default
 
 PointGFp (const CurveGFp &curve)
 
 PointGFp (const PointGFp &)=default
 
 PointGFp (PointGFp &&other)
 
 PointGFp (const CurveGFp &curve, const BigInt &x, const BigInt &y)
 
void randomize_repr (RandomNumberGenerator &rng)
 
void swap (PointGFp &other)
 

Static Public Member Functions

static PointGFp zero_of (const CurveGFp &curve)
 

Friends

class Blinded_Point_Multiply
 
BOTAN_DLL PointGFp multi_exponentiate (const PointGFp &p1, const BigInt &z1, const PointGFp &p2, const BigInt &z2)
 
BOTAN_DLL PointGFp operator* (const BigInt &scalar, const PointGFp &point)
 

Detailed Description

This class represents one point on a curve of GF(p)

Definition at line 41 of file point_gfp.h.

Member Enumeration Documentation

Enumerator
UNCOMPRESSED 
COMPRESSED 
HYBRID 

Definition at line 44 of file point_gfp.h.

Constructor & Destructor Documentation

Botan::PointGFp::PointGFp ( )
default

Construct an uninitialized PointGFp

Referenced by operator-=().

Botan::PointGFp::PointGFp ( const CurveGFp curve)
explicit

Construct the zero point

Parameters
curveThe base curve

Definition at line 18 of file point_gfp.cpp.

References Botan::CurveGFp::to_rep().

18  :
19  m_curve(curve),
20  m_coord_x(0),
21  m_coord_y(1),
22  m_coord_z(0)
23  {
24  m_curve.to_rep(m_coord_x, m_monty_ws);
25  m_curve.to_rep(m_coord_y, m_monty_ws);
26  m_curve.to_rep(m_coord_z, m_monty_ws);
27  }
void to_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:97
Botan::PointGFp::PointGFp ( const PointGFp )
default

Copy constructor

Botan::PointGFp::PointGFp ( PointGFp &&  other)
inline

Move Constructor

Definition at line 74 of file point_gfp.h.

75  {
76  this->swap(other);
77  }
void swap(PointGFp &other)
Definition: point_gfp.cpp:447
Botan::PointGFp::PointGFp ( const CurveGFp curve,
const BigInt x,
const BigInt y 
)

Construct a point from its affine coordinates

Parameters
curvethe base curve
xaffine x coordinate
yaffine y coordinate

Definition at line 29 of file point_gfp.cpp.

References Botan::CurveGFp::get_p(), and Botan::CurveGFp::to_rep().

29  :
30  m_curve(curve),
31  m_coord_x(x),
32  m_coord_y(y),
33  m_coord_z(1)
34  {
35  if(x <= 0 || x >= curve.get_p())
36  throw Invalid_Argument("Invalid PointGFp affine x");
37  if(y <= 0 || y >= curve.get_p())
38  throw Invalid_Argument("Invalid PointGFp affine y");
39 
40  m_curve.to_rep(m_coord_x, m_monty_ws);
41  m_curve.to_rep(m_coord_y, m_monty_ws);
42  m_curve.to_rep(m_coord_z, m_monty_ws);
43  }
void to_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:97

Member Function Documentation

BigInt Botan::PointGFp::get_affine_x ( ) const

get affine x coordinate

Returns
affine x coordinate

Definition at line 390 of file point_gfp.cpp.

References Botan::CurveGFp::from_rep(), Botan::CurveGFp::get_p(), Botan::inverse_mod(), and is_zero().

Referenced by Botan::EC2OSP(), operator==(), and Botan::GOST_3410_PublicKey::public_key_bits().

391  {
392  if(is_zero())
393  throw Illegal_Transformation("Cannot convert zero point to affine");
394 
395  BigInt z2 = curve_sqr(m_coord_z);
396  m_curve.from_rep(z2, m_monty_ws);
397  z2 = inverse_mod(z2, m_curve.get_p());
398 
399  return curve_mult(z2, m_coord_x);
400  }
void from_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:102
BigInt inverse_mod(const BigInt &n, const BigInt &mod)
Definition: numthry.cpp:276
const BigInt & get_p() const
Definition: curve_gfp.h:91
bool is_zero() const
Definition: point_gfp.h:177
BigInt Botan::PointGFp::get_affine_y ( ) const

get affine y coordinate

Returns
affine y coordinate

Definition at line 402 of file point_gfp.cpp.

References Botan::CurveGFp::get_p(), Botan::inverse_mod(), is_zero(), and Botan::CurveGFp::to_rep().

Referenced by Botan::EC2OSP(), operator==(), and Botan::GOST_3410_PublicKey::public_key_bits().

403  {
404  if(is_zero())
405  throw Illegal_Transformation("Cannot convert zero point to affine");
406 
407  BigInt z3 = curve_mult(m_coord_z, curve_sqr(m_coord_z));
408  z3 = inverse_mod(z3, m_curve.get_p());
409  m_curve.to_rep(z3, m_monty_ws);
410 
411  return curve_mult(z3, m_coord_y);
412  }
void to_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:97
BigInt inverse_mod(const BigInt &n, const BigInt &mod)
Definition: numthry.cpp:276
const BigInt & get_p() const
Definition: curve_gfp.h:91
bool is_zero() const
Definition: point_gfp.h:177
const CurveGFp& Botan::PointGFp::get_curve ( ) const
inline

Return base curve of this point

Returns
the curve over GF(p) of this point

Definition at line 159 of file point_gfp.h.

References m_curve.

Referenced by Botan::Blinded_Point_Multiply::Blinded_Point_Multiply(), Botan::EC2OSP(), Botan::multi_exponentiate(), Botan::operator*(), and operator==().

159 { return m_curve; }
bool Botan::PointGFp::is_zero ( ) const
inline

Is this the point at infinity?

Returns
true, if this point is at infinity, false otherwise.

Definition at line 177 of file point_gfp.h.

Referenced by Botan::EC_PublicKey::check_key(), Botan::ECIES_KA_Operation::derive_secret(), Botan::EC2OSP(), get_affine_x(), get_affine_y(), on_the_curve(), operator-=(), and operator==().

178  { return (m_coord_x.is_zero() && m_coord_z.is_zero()); }
bool is_zero() const
Definition: bigint.h:250
PointGFp& Botan::PointGFp::negate ( )
inline

Negate this point

Returns
*this

Definition at line 148 of file point_gfp.h.

References Botan::CT::is_zero(), and m_curve.

Referenced by Botan::operator-().

149  {
150  if(!is_zero())
151  m_coord_y = m_curve.get_p() - m_coord_y;
152  return *this;
153  }
const BigInt & get_p() const
Definition: curve_gfp.h:91
bool is_zero() const
Definition: point_gfp.h:177
bool Botan::PointGFp::on_the_curve ( ) const

Checks whether the point is to be found on the underlying curve; used to prevent fault attacks.

Returns
if the point is on the curve

Definition at line 414 of file point_gfp.cpp.

References Botan::CurveGFp::from_rep(), Botan::CurveGFp::get_a_rep(), Botan::CurveGFp::get_b_rep(), and is_zero().

Referenced by Botan::EC_PublicKey::check_key(), Botan::EC_PrivateKey::EC_PrivateKey(), Botan::GOST_3410_PublicKey::GOST_3410_PublicKey(), Botan::OS2ECP(), and Botan::EC_Group::verify_group().

415  {
416  /*
417  Is the point still on the curve?? (If everything is correct, the
418  point is always on its curve; then the function will return true.
419  If somehow the state is corrupted, which suggests a fault attack
420  (or internal computational error), then return false.
421  */
422  if(is_zero())
423  return true;
424 
425  const BigInt y2 = m_curve.from_rep(curve_sqr(m_coord_y), m_monty_ws);
426  const BigInt x3 = curve_mult(m_coord_x, curve_sqr(m_coord_x));
427  const BigInt ax = curve_mult(m_coord_x, m_curve.get_a_rep());
428  const BigInt z2 = curve_sqr(m_coord_z);
429 
430  if(m_coord_z == z2) // Is z equal to 1 (in Montgomery form)?
431  {
432  if(y2 != m_curve.from_rep(x3 + ax + m_curve.get_b_rep(), m_monty_ws))
433  return false;
434  }
435 
436  const BigInt z3 = curve_mult(m_coord_z, z2);
437  const BigInt ax_z4 = curve_mult(ax, curve_sqr(z2));
438  const BigInt b_z6 = curve_mult(m_curve.get_b_rep(), curve_sqr(z3));
439 
440  if(y2 != m_curve.from_rep(x3 + ax_z4 + b_z6, m_monty_ws))
441  return false;
442 
443  return true;
444  }
const BigInt & get_a_rep() const
Definition: curve_gfp.h:93
void from_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:102
const BigInt & get_b_rep() const
Definition: curve_gfp.h:95
bool is_zero() const
Definition: point_gfp.h:177
PointGFp & Botan::PointGFp::operator*= ( const BigInt scalar)

*= Operator

Parameters
scalarthe PointGFp to multiply with *this
Returns
resulting PointGFp

Definition at line 242 of file point_gfp.cpp.

243  {
244  *this = scalar * *this;
245  return *this;
246  }
PointGFp & Botan::PointGFp::operator+= ( const PointGFp rhs)

+= Operator

Parameters
rhsthe PointGFp to add to the local value
Returns
resulting PointGFp

Definition at line 223 of file point_gfp.cpp.

224  {
225  std::vector<BigInt> ws(9);
226  add(rhs, ws);
227  return *this;
228  }
PointGFp & Botan::PointGFp::operator-= ( const PointGFp rhs)

-= Operator

Parameters
rhsthe PointGFp to subtract from the local value
Returns
resulting PointGFp

Definition at line 230 of file point_gfp.cpp.

References is_zero(), and PointGFp().

231  {
232  PointGFp minus_rhs = PointGFp(rhs).negate();
233 
234  if(is_zero())
235  *this = minus_rhs;
236  else
237  *this += minus_rhs;
238 
239  return *this;
240  }
PointGFp()=default
bool is_zero() const
Definition: point_gfp.h:177
PointGFp& Botan::PointGFp::operator= ( const PointGFp )
default

Standard Assignment

PointGFp& Botan::PointGFp::operator= ( PointGFp &&  other)
inline

Move Assignment

Definition at line 87 of file point_gfp.h.

88  {
89  if(this != &other)
90  this->swap(other);
91  return (*this);
92  }
void swap(PointGFp &other)
Definition: point_gfp.cpp:447
bool Botan::PointGFp::operator== ( const PointGFp other) const

Equality operator

Definition at line 456 of file point_gfp.cpp.

References get_affine_x(), get_affine_y(), get_curve(), and is_zero().

457  {
458  if(get_curve() != other.get_curve())
459  return false;
460 
461  // If this is zero, only equal if other is also zero
462  if(is_zero())
463  return other.is_zero();
464 
465  return (get_affine_x() == other.get_affine_x() &&
466  get_affine_y() == other.get_affine_y());
467  }
BigInt get_affine_y() const
Definition: point_gfp.cpp:402
const CurveGFp & get_curve() const
Definition: point_gfp.h:159
BigInt get_affine_x() const
Definition: point_gfp.cpp:390
bool is_zero() const
Definition: point_gfp.h:177
void Botan::PointGFp::randomize_repr ( RandomNumberGenerator rng)

Randomize the point representation The actual value (get_affine_x, get_affine_y) does not change

Definition at line 45 of file point_gfp.cpp.

References Botan::BigInt::is_zero(), Botan::BigInt::randomize(), and Botan::CurveGFp::to_rep().

Referenced by Botan::Blinded_Point_Multiply::blinded_multiply().

46  {
47  if(BOTAN_POINTGFP_RANDOMIZE_BLINDING_BITS > 1)
48  {
49  BigInt mask;
50  while(mask.is_zero())
51  mask.randomize(rng, BOTAN_POINTGFP_RANDOMIZE_BLINDING_BITS, false);
52 
53  m_curve.to_rep(mask, m_monty_ws);
54  const BigInt mask2 = curve_mult(mask, mask);
55  const BigInt mask3 = curve_mult(mask2, mask);
56 
57  m_coord_x = curve_mult(m_coord_x, mask2);
58  m_coord_y = curve_mult(m_coord_y, mask3);
59  m_coord_z = curve_mult(m_coord_z, mask);
60  }
61  }
void to_rep(BigInt &x, secure_vector< word > &ws) const
Definition: curve_gfp.h:97
void Botan::PointGFp::swap ( PointGFp other)

swaps the states of *this and other, does not throw!

Parameters
otherthe object to swap values with

Definition at line 447 of file point_gfp.cpp.

References Botan::BigInt::swap(), and Botan::CurveGFp::swap().

448  {
449  m_curve.swap(other.m_curve);
450  m_coord_x.swap(other.m_coord_x);
451  m_coord_y.swap(other.m_coord_y);
452  m_coord_z.swap(other.m_coord_z);
453  m_monty_ws.swap(other.m_monty_ws);
454  }
void swap(BigInt &other)
Definition: bigint.h:122
void swap(CurveGFp &other)
Definition: curve_gfp.h:140
static PointGFp Botan::PointGFp::zero_of ( const CurveGFp curve)
inlinestatic

Definition at line 61 of file point_gfp.h.

Referenced by Botan::Blinded_Point_Multiply::Blinded_Point_Multiply().

62  {
63  return PointGFp(curve);
64  }
PointGFp()=default

Friends And Related Function Documentation

friend class Blinded_Point_Multiply
friend

Definition at line 204 of file point_gfp.h.

BOTAN_DLL PointGFp multi_exponentiate ( const PointGFp p1,
const BigInt z1,
const PointGFp p2,
const BigInt z2 
)
friend

Multiexponentiation

Parameters
p1a point
z1a scalar
p2a point
z2a scalar
Returns
(p1 * z1 + p2 * z2)

Definition at line 248 of file point_gfp.cpp.

250  {
251  const PointGFp p3 = p1 + p2;
252 
253  PointGFp H(p1.get_curve()); // create as zero
254  size_t bits_left = std::max(z1.bits(), z2.bits());
255 
256  std::vector<BigInt> ws(9);
257 
258  while(bits_left)
259  {
260  H.mult2(ws);
261 
262  const bool z1_b = z1.get_bit(bits_left - 1);
263  const bool z2_b = z2.get_bit(bits_left - 1);
264 
265  if(z1_b == true && z2_b == true)
266  H.add(p3, ws);
267  else if(z1_b)
268  H.add(p1, ws);
269  else if(z2_b)
270  H.add(p2, ws);
271 
272  --bits_left;
273  }
274 
275  if(z1.is_negative() != z2.is_negative())
276  H.negate();
277 
278  return H;
279  }
PointGFp()=default
T max(T a, T b)
Definition: ct_utils.h:173
BOTAN_DLL PointGFp operator* ( const BigInt scalar,
const PointGFp point 
)
friend

Multiplication Operator

Parameters
scalarthe scalar value
pointthe point value
Returns
scalar*point on the curve

Definition at line 281 of file point_gfp.cpp.

282  {
283  //BOTAN_ASSERT(point.on_the_curve(), "Input is on the curve");
284 
285  const CurveGFp& curve = point.get_curve();
286 
287  const size_t scalar_bits = scalar.bits();
288 
289  std::vector<BigInt> ws(9);
290 
291  PointGFp R[2] = { PointGFp(curve), point };
292 
293  for(size_t i = scalar_bits; i > 0; i--)
294  {
295  const size_t b = scalar.get_bit(i - 1);
296  R[b ^ 1].add(R[b], ws);
297  R[b].mult2(ws);
298  }
299 
300  if(scalar.is_negative())
301  R[0].negate();
302 
303  //BOTAN_ASSERT(R[0].on_the_curve(), "Output is on the curve");
304 
305  return R[0];
306  }
PointGFp()=default
PointGFp & negate()
Definition: point_gfp.h:148

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