Crypto++  5.6.4
Free C++ class library of cryptographic schemes
ecp.h
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1 // ecp.h - written and placed in the public domain by Wei Dai
2 
3 //! \file ecp.h
4 //! \brief Classes for Elliptic Curves over prime fields
5 
6 #ifndef CRYPTOPP_ECP_H
7 #define CRYPTOPP_ECP_H
8 
9 #include "cryptlib.h"
10 #include "integer.h"
11 #include "algebra.h"
12 #include "modarith.h"
13 #include "eprecomp.h"
14 #include "smartptr.h"
15 #include "pubkey.h"
16 
17 NAMESPACE_BEGIN(CryptoPP)
18 
19 //! Elliptical Curve Point
20 struct CRYPTOPP_DLL ECPPoint
21 {
22  ECPPoint() : identity(true) {}
23  ECPPoint(const Integer &x, const Integer &y)
24  : identity(false), x(x), y(y) {}
25 
26  bool operator==(const ECPPoint &t) const
27  {return (identity && t.identity) || (!identity && !t.identity && x==t.x && y==t.y);}
28  bool operator< (const ECPPoint &t) const
29  {return identity ? !t.identity : (!t.identity && (x<t.x || (x==t.x && y<t.y)));}
30 
31 #ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
32  virtual ~ECPPoint() {}
33 #endif
34 
35  bool identity;
36  Integer x, y;
37 };
38 
39 CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<ECPPoint>;
40 
41 //! Elliptic Curve over GF(p), where p is prime
42 class CRYPTOPP_DLL ECP : public AbstractGroup<ECPPoint>
43 {
44 public:
45  typedef ModularArithmetic Field;
46  typedef Integer FieldElement;
47  typedef ECPPoint Point;
48 
49  ECP() {}
50  ECP(const ECP &ecp, bool convertToMontgomeryRepresentation = false);
51  ECP(const Integer &modulus, const FieldElement &a, const FieldElement &b)
52  : m_fieldPtr(new Field(modulus)), m_a(a.IsNegative() ? modulus+a : a), m_b(b) {}
53  // construct from BER encoded parameters
54  // this constructor will decode and extract the the fields fieldID and curve of the sequence ECParameters
56 
57  // encode the fields fieldID and curve of the sequence ECParameters
58  void DEREncode(BufferedTransformation &bt) const;
59 
60  bool Equal(const Point &P, const Point &Q) const;
61  const Point& Identity() const;
62  const Point& Inverse(const Point &P) const;
63  bool InversionIsFast() const {return true;}
64  const Point& Add(const Point &P, const Point &Q) const;
65  const Point& Double(const Point &P) const;
66  Point ScalarMultiply(const Point &P, const Integer &k) const;
67  Point CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const;
68  void SimultaneousMultiply(Point *results, const Point &base, const Integer *exponents, unsigned int exponentsCount) const;
69 
70  Point Multiply(const Integer &k, const Point &P) const
71  {return ScalarMultiply(P, k);}
72  Point CascadeMultiply(const Integer &k1, const Point &P, const Integer &k2, const Point &Q) const
73  {return CascadeScalarMultiply(P, k1, Q, k2);}
74 
75  bool ValidateParameters(RandomNumberGenerator &rng, unsigned int level=3) const;
76  bool VerifyPoint(const Point &P) const;
77 
78  unsigned int EncodedPointSize(bool compressed = false) const
79  {return 1 + (compressed?1:2)*GetField().MaxElementByteLength();}
80  // returns false if point is compressed and not valid (doesn't check if uncompressed)
81  bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const;
82  bool DecodePoint(Point &P, const byte *encodedPoint, size_t len) const;
83  void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const;
84  void EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
85 
86  Point BERDecodePoint(BufferedTransformation &bt) const;
87  void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
88 
89  Integer FieldSize() const {return GetField().GetModulus();}
90  const Field & GetField() const {return *m_fieldPtr;}
91  const FieldElement & GetA() const {return m_a;}
92  const FieldElement & GetB() const {return m_b;}
93 
94  bool operator==(const ECP &rhs) const
95  {return GetField() == rhs.GetField() && m_a == rhs.m_a && m_b == rhs.m_b;}
96 
97 #ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
98  virtual ~ECP() {}
99 #endif
100 
101 private:
102  clonable_ptr<Field> m_fieldPtr;
103  FieldElement m_a, m_b;
104  mutable Point m_R;
105 };
106 
107 CRYPTOPP_DLL_TEMPLATE_CLASS DL_FixedBasePrecomputationImpl<ECP::Point>;
108 CRYPTOPP_DLL_TEMPLATE_CLASS DL_GroupPrecomputation<ECP::Point>;
109 
110 template <class T> class EcPrecomputation;
111 
112 //! ECP precomputation
113 template<> class EcPrecomputation<ECP> : public DL_GroupPrecomputation<ECP::Point>
114 {
115 public:
116  typedef ECP EllipticCurve;
117 
118  // DL_GroupPrecomputation
119  bool NeedConversions() const {return true;}
120  Element ConvertIn(const Element &P) const
121  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertIn(P.x), m_ec->GetField().ConvertIn(P.y));};
122  Element ConvertOut(const Element &P) const
123  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertOut(P.x), m_ec->GetField().ConvertOut(P.y));}
124  const AbstractGroup<Element> & GetGroup() const {return *m_ec;}
125  Element BERDecodeElement(BufferedTransformation &bt) const {return m_ec->BERDecodePoint(bt);}
126  void DEREncodeElement(BufferedTransformation &bt, const Element &v) const {m_ec->DEREncodePoint(bt, v, false);}
127 
128  // non-inherited
129  void SetCurve(const ECP &ec)
130  {
131  m_ec.reset(new ECP(ec, true));
132  m_ecOriginal = ec;
133  }
134  const ECP & GetCurve() const {return *m_ecOriginal;}
135 
136 #ifndef CRYPTOPP_MAINTAIN_BACKWARDS_COMPATIBILITY_562
137  virtual ~EcPrecomputation() {}
138 #endif
139 
140 private:
141  value_ptr<ECP> m_ec, m_ecOriginal;
142 };
143 
144 NAMESPACE_END
145 
146 #endif
virtual void SimultaneousMultiply(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
Multiplies a base to multiple exponents in a group.
Definition: algebra.cpp:256
Elliptical Curve Point.
Definition: ecp.h:20
This file contains helper classes/functions for implementing public key algorithms.
bool InversionIsFast() const
Determine if inversion is fast.
Definition: ecp.h:63
Elliptic Curve over GF(p), where p is prime.
Definition: ecp.h:42
virtual Element ScalarMultiply(const Element &a, const Integer &e) const
Performs a scalar multiplication.
Definition: algebra.cpp:90
Abstract base classes that provide a uniform interface to this library.
Classes for automatic resource management.
Ring of congruence classes modulo n.
Definition: modarith.h:34
Interface for random number generators.
Definition: cryptlib.h:1193
Classes for performing mathematics over different fields.
Interface for buffered transformations.
Definition: cryptlib.h:1359
bool operator==(const OID &lhs, const OID &rhs)
Compare two OIDs for equality.
virtual const Element & Identity() const =0
Provides the Identity element.
virtual const Element & Double(const Element &a) const
Doubles an element in the group.
Definition: algebra.cpp:15
bool operator<(const OID &lhs, const OID &rhs)
Compare two OIDs for ordering.
bool IsNegative() const
Determines if the Integer is negative.
Definition: integer.h:332
A pointer which can be copied and cloned.
Definition: smartptr.h:108
Multiple precision integer with arithmetic operations.
Definition: integer.h:45
virtual const Element & Add(const Element &a, const Element &b) const =0
Adds elements in the group.
virtual bool Equal(const Element &a, const Element &b) const =0
Compare two elements for equality.
Classes for precomputation in a group.
virtual const Element & Inverse(const Element &a) const =0
Inverts the element in the group.
Multiple precision integer with arithmetic operations.
Class file for performing modular arithmetic.
Crypto++ library namespace.
virtual Element CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
TODO.
Definition: algebra.cpp:97