Crypto++
ecp.h
1 #ifndef CRYPTOPP_ECP_H
2 #define CRYPTOPP_ECP_H
3 
4 #include "modarith.h"
5 #include "eprecomp.h"
6 #include "smartptr.h"
7 #include "pubkey.h"
8 
9 NAMESPACE_BEGIN(CryptoPP)
10 
11 //! Elliptical Curve Point
12 struct CRYPTOPP_DLL ECPPoint
13 {
14  ECPPoint() : identity(true) {}
15  ECPPoint(const Integer &x, const Integer &y)
16  : identity(false), x(x), y(y) {}
17 
18  bool operator==(const ECPPoint &t) const
19  {return (identity && t.identity) || (!identity && !t.identity && x==t.x && y==t.y);}
20  bool operator< (const ECPPoint &t) const
21  {return identity ? !t.identity : (!t.identity && (x<t.x || (x==t.x && y<t.y)));}
22 
23  bool identity;
24  Integer x, y;
25 };
26 
27 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<ECPPoint>;
28 
29 //! Elliptic Curve over GF(p), where p is prime
30 class CRYPTOPP_DLL ECP : public AbstractGroup<ECPPoint>
31 {
32 public:
33  typedef ModularArithmetic Field;
34  typedef Integer FieldElement;
35  typedef ECPPoint Point;
36 
37  ECP() {}
38  ECP(const ECP &ecp, bool convertToMontgomeryRepresentation = false);
39  ECP(const Integer &modulus, const FieldElement &a, const FieldElement &b)
40  : m_fieldPtr(new Field(modulus)), m_a(a.IsNegative() ? modulus+a : a), m_b(b) {}
41  // construct from BER encoded parameters
42  // this constructor will decode and extract the the fields fieldID and curve of the sequence ECParameters
44 
45  // encode the fields fieldID and curve of the sequence ECParameters
46  void DEREncode(BufferedTransformation &bt) const;
47 
48  bool Equal(const Point &P, const Point &Q) const;
49  const Point& Identity() const;
50  const Point& Inverse(const Point &P) const;
51  bool InversionIsFast() const {return true;}
52  const Point& Add(const Point &P, const Point &Q) const;
53  const Point& Double(const Point &P) const;
54  Point ScalarMultiply(const Point &P, const Integer &k) const;
55  Point CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const;
56  void SimultaneousMultiply(Point *results, const Point &base, const Integer *exponents, unsigned int exponentsCount) const;
57 
58  Point Multiply(const Integer &k, const Point &P) const
59  {return ScalarMultiply(P, k);}
60  Point CascadeMultiply(const Integer &k1, const Point &P, const Integer &k2, const Point &Q) const
61  {return CascadeScalarMultiply(P, k1, Q, k2);}
62 
63  bool ValidateParameters(RandomNumberGenerator &rng, unsigned int level=3) const;
64  bool VerifyPoint(const Point &P) const;
65 
66  unsigned int EncodedPointSize(bool compressed = false) const
67  {return 1 + (compressed?1:2)*GetField().MaxElementByteLength();}
68  // returns false if point is compressed and not valid (doesn't check if uncompressed)
69  bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const;
70  bool DecodePoint(Point &P, const byte *encodedPoint, size_t len) const;
71  void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const;
72  void EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
73 
74  Point BERDecodePoint(BufferedTransformation &bt) const;
75  void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
76 
77  Integer FieldSize() const {return GetField().GetModulus();}
78  const Field & GetField() const {return *m_fieldPtr;}
79  const FieldElement & GetA() const {return m_a;}
80  const FieldElement & GetB() const {return m_b;}
81 
82  bool operator==(const ECP &rhs) const
83  {return GetField() == rhs.GetField() && m_a == rhs.m_a && m_b == rhs.m_b;}
84 
85 private:
86  clonable_ptr<Field> m_fieldPtr;
87  FieldElement m_a, m_b;
88  mutable Point m_R;
89 };
90 
91 CRYPTOPP_DLL_TEMPLATE_CLASS DL_FixedBasePrecomputationImpl<ECP::Point>;
92 CRYPTOPP_DLL_TEMPLATE_CLASS DL_GroupPrecomputation<ECP::Point>;
93 
94 template <class T> class EcPrecomputation;
95 
96 //! ECP precomputation
97 template<> class EcPrecomputation<ECP> : public DL_GroupPrecomputation<ECP::Point>
98 {
99 public:
100  typedef ECP EllipticCurve;
101 
102  // DL_GroupPrecomputation
103  bool NeedConversions() const {return true;}
104  Element ConvertIn(const Element &P) const
105  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertIn(P.x), m_ec->GetField().ConvertIn(P.y));};
106  Element ConvertOut(const Element &P) const
107  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertOut(P.x), m_ec->GetField().ConvertOut(P.y));}
108  const AbstractGroup<Element> & GetGroup() const {return *m_ec;}
109  Element BERDecodeElement(BufferedTransformation &bt) const {return m_ec->BERDecodePoint(bt);}
110  void DEREncodeElement(BufferedTransformation &bt, const Element &v) const {m_ec->DEREncodePoint(bt, v, false);}
111 
112  // non-inherited
113  void SetCurve(const ECP &ec)
114  {
115  m_ec.reset(new ECP(ec, true));
116  m_ecOriginal = ec;
117  }
118  const ECP & GetCurve() const {return *m_ecOriginal;}
119 
120 private:
121  value_ptr<ECP> m_ec, m_ecOriginal;
122 };
123 
124 NAMESPACE_END
125 
126 #endif
Elliptical Curve Point.
Definition: ecp.h:12
This file contains helper classes/functions for implementing public key algorithms.
Elliptic Curve over GF(p), where p is prime.
Definition: ecp.h:30
ring of congruence classes modulo n
Definition: modarith.h:19
interface for random number generators
Definition: cryptlib.h:668
interface for buffered transformations
Definition: cryptlib.h:770
multiple precision integer and basic arithmetics
Definition: integer.h:26
bool operator<(const ::PolynomialMod2 &a, const ::PolynomialMod2 &b)
compares degree
Definition: gf2n.h:252