Botan: src/math/ec_gfp/point_gfp.h Source File

Botan 1.10.17

point_gfp.h
Go to the documentation of this file.
1 /*
2 * Point arithmetic on elliptic curves over GF(p)
3 *
4 * (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
5 * 2008-2011 Jack Lloyd
6 *
7 * Distributed under the terms of the Botan license
8 */
9
10 #ifndef BOTAN_POINT_GFP_H__
11 #define BOTAN_POINT_GFP_H__
12
13 #include <botan/curve_gfp.h>
14 #include <vector>
15
16 namespace Botan {
17
18 /**
19 * Exception thrown if you try to convert a zero point to an affine
20 * coordinate
21 */
22 struct BOTAN_DLL Illegal_Transformation : public Exception
23 {
24 Illegal_Transformation(const std::string& err =
25 "Requested transformation is not possible") :
26 Exception(err) {}
27 };
28
29 /**
30 * Exception thrown if some form of illegal point is decoded
31 */
32 struct BOTAN_DLL Illegal_Point : public Exception
33 {
34 Illegal_Point(const std::string& err = "Malformed ECP point detected") :
35 Exception(err) {}
36 };
37
38 /**
39 * This class represents one point on a curve of GF(p)
40 */
41 class BOTAN_DLL PointGFp
42 {
43 public:
44 enum Compression_Type {
45 UNCOMPRESSED = 0,
46 COMPRESSED = 1,
47 HYBRID = 2
48 };
49
50 /**
51 * Construct an uninitialized PointGFp
52 */
53 PointGFp() {}
54
55 /**
56 * Construct the zero point
57 * @param curve The base curve
58 */
59 PointGFp(const CurveGFp& curve);
60
61 /**
62 * Construct a point from its affine coordinates
63 * @param curve the base curve
64 * @param x affine x coordinate
65 * @param y affine y coordinate
66 */
67 PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y);
68
69 //PointGFp(const PointGFp& other) = default;
70 //PointGFp& operator=(const PointGFp& other) = default;
71
72 /**
73 * += Operator
74 * @param rhs the PointGFp to add to the local value
75 * @result resulting PointGFp
76 */
77 PointGFp& operator+=(const PointGFp& rhs);
78
79 /**
80 * -= Operator
81 * @param rhs the PointGFp to subtract from the local value
82 * @result resulting PointGFp
83 */
84 PointGFp& operator-=(const PointGFp& rhs);
85
86 /**
87 * *= Operator
88 * @param scalar the PointGFp to multiply with *this
89 * @result resulting PointGFp
90 */
91 PointGFp& operator*=(const BigInt& scalar);
92
93 /**
94 * Multiplication Operator
95 * @param scalar the scalar value
96 * @param point the point value
97 * @return scalar*point on the curve
98 */
99 friend BOTAN_DLL PointGFp operator*(const BigInt& scalar, const PointGFp& point);
100
101 /**
102 * Multiexponentiation
103 * @param p1 a point
104 * @param z1 a scalar
105 * @param p2 a point
106 * @param z2 a scalar
107 * @result (p1 * z1 + p2 * z2)
108 */
109 friend BOTAN_DLL PointGFp multi_exponentiate(
110 const PointGFp& p1, const BigInt& z1,
111 const PointGFp& p2, const BigInt& z2);
112
113 /**
114 * Negate this point
115 * @return *this
116 */
117 PointGFp& negate()
118 {
119 if(!is_zero())
120 coord_y = curve.get_p() - coord_y;
121 return *this;
122 }
123
124 /**
125 * Return base curve of this point
126 * @result the curve over GF(p) of this point
127 */
128 const CurveGFp& get_curve() const { return curve; }
129
130 /**
131 * get affine x coordinate
132 * @result affine x coordinate
133 */
134 BigInt get_affine_x() const;
135
136 /**
137 * get affine y coordinate
138 * @result affine y coordinate
139 */
140 BigInt get_affine_y() const;
141
142 /**
143 * Is this the point at infinity?
144 * @result true, if this point is at infinity, false otherwise.
145 */
146 bool is_zero() const
147 { return (coord_x.is_zero() && coord_z.is_zero()); }
148
149 /**
150 * Checks whether the point is to be found on the underlying
151 * curve; used to prevent fault attacks.
152 * @return if the point is on the curve
153 */
154 bool on_the_curve() const;
155
156 /**
157 * swaps the states of *this and other, does not throw!
158 * @param other the object to swap values with
159 */
160 void swap(PointGFp& other);
161
162 /**
163 * Equality operator
164 */
165 bool operator==(const PointGFp& other) const;
166 private:
167
168 /**
169 * Montgomery multiplication/reduction
170 * @param x first multiplicand
171 * @param y second multiplicand
172 * @param workspace temp space
173 */
174 BigInt monty_mult(const BigInt& x, const BigInt& y) const
175 {
176 BigInt result;
177 monty_mult(result, x, y);
178 return result;
179 }
180
181 /**
182 * Montgomery multiplication/reduction
183 * @warning z cannot alias x or y
184 * @param z output
185 * @param x first multiplicand
186 * @param y second multiplicand
187 */
188 void monty_mult(BigInt& z, const BigInt& x, const BigInt& y) const;
189
190 /**
191 * Montgomery squaring/reduction
192 * @param x multiplicand
193 */
194 BigInt monty_sqr(const BigInt& x) const
195 {
196 BigInt result;
197 monty_sqr(result, x);
198 return result;
199 }
200
201 /**
202 * Montgomery squaring/reduction
203 * @warning z cannot alias x
204 * @param z output
205 * @param x multiplicand
206 */
207 void monty_sqr(BigInt& z, const BigInt& x) const;
208
209 /**
210 * Point addition
211 * @param workspace temp space, at least 11 elements
212 */
213 void add(const PointGFp& other, std::vector<BigInt>& workspace);
214
215 /**
216 * Point doubling
217 * @param workspace temp space, at least 9 elements
218 */
219 void mult2(std::vector<BigInt>& workspace);
220
221 CurveGFp curve;
222 BigInt coord_x, coord_y, coord_z;
223 mutable SecureVector<word> ws; // workspace for Montgomery
224 };
225
226 // relational operators
227 inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs)
228 {
229 return !(rhs == lhs);
230 }
231
232 // arithmetic operators
233 inline PointGFp operator-(const PointGFp& lhs)
234 {
235 return PointGFp(lhs).negate();
236 }
237
238 inline PointGFp operator+(const PointGFp& lhs, const PointGFp& rhs)
239 {
240 PointGFp tmp(lhs);
241 return tmp += rhs;
242 }
243
244 inline PointGFp operator-(const PointGFp& lhs, const PointGFp& rhs)
245 {
246 PointGFp tmp(lhs);
247 return tmp -= rhs;
248 }
249
250 inline PointGFp operator*(const PointGFp& point, const BigInt& scalar)
251 {
252 return scalar * point;
253 }
254
255 // encoding and decoding
256 SecureVector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format);
257
258 PointGFp BOTAN_DLL OS2ECP(const byte data[], size_t data_len,
259 const CurveGFp& curve);
260
261 inline PointGFp OS2ECP(const MemoryRegion<byte>& data, const CurveGFp& curve)
262 { return OS2ECP(&data[0], data.size(), curve); }
263
264 }
265
266 namespace std {
267
268 template<>
269 inline void swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y)
270 { x.swap(y); }
271
272 }
273
274 #endif
Botan::operator!=
bool operator!=(const OctetString &s1, const OctetString &s2)
Definition: symkey.cpp:106
Botan::BigInt
Definition: bigint.h:22
Botan::PointGFp
Definition: point_gfp.h:41
Botan::OS2ECP
PointGFp OS2ECP(const byte data[], size_t data_len, const CurveGFp &curve)
Definition: point_gfp.cpp:562
Botan::Illegal_Point::Illegal_Point
Illegal_Point(const std::string &err="Malformed ECP point detected")
Definition: point_gfp.h:34
Botan::operator==
bool operator==(const OctetString &s1, const OctetString &s2)
Definition: symkey.cpp:98
std
Definition: secmem.h:435
Botan::PointGFp::Compression_Type
Compression_Type
Definition: point_gfp.h:44
Botan::byte
unsigned char byte
Definition: types.h:22
Botan::EC2OSP
SecureVector< byte > EC2OSP(const PointGFp &point, byte format)
Definition: point_gfp.cpp:490
Botan::Illegal_Transformation::Illegal_Transformation
Illegal_Transformation(const std::string &err="Requested transformation is not possible")
Definition: point_gfp.h:24
Botan::operator+
OctetString operator+(const OctetString &k1, const OctetString &k2)
Definition: symkey.cpp:114
Botan::PointGFp::PointGFp
PointGFp()
Definition: point_gfp.h:53
Botan::PointGFp::negate
PointGFp & negate()
Definition: point_gfp.h:117
Botan::operator*
BigInt operator*(const BigInt &x, const BigInt &y)
Definition: big_ops3.cpp:83
Botan::Exception
std::runtime_error Exception
Definition: exceptn.h:19
Botan::MemoryRegion< byte >
Botan::operator+=
MemoryRegion< T > & operator+=(MemoryRegion< T > &out, const MemoryRegion< T > &in)
Definition: secmem.h:386
Botan
Definition: algo_base.h:14
Botan::CT::is_zero
T is_zero(T x)
Definition: ct_utils.h:57
Botan::MemoryRegion::size
size_t size() const
Definition: secmem.h:29
Botan::Illegal_Transformation
Definition: point_gfp.h:22
Botan::PointGFp::is_zero
bool is_zero() const
Definition: point_gfp.h:146
std::swap
void swap(Botan::MemoryRegion< T > &x, Botan::MemoryRegion< T > &y)
Definition: secmem.h:438
Botan::Illegal_Point
Definition: point_gfp.h:32
Botan::PointGFp::get_curve
const CurveGFp & get_curve() const
Definition: point_gfp.h:128
Botan::operator-
BigInt operator-(const BigInt &x, const BigInt &y)
Definition: big_ops3.cpp:48
Botan::multi_exponentiate
PointGFp multi_exponentiate(const PointGFp &p1, const BigInt &z1, const PointGFp &p2, const BigInt &z2)
Definition: point_gfp.cpp:265
Botan::CurveGFp
Definition: curve_gfp.h:20