Crypto++  8.2
Free C++ class library of cryptographic schemes
ecp.h
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1 // ecp.h - originally 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 "ecpoint.h"
14 #include "eprecomp.h"
15 #include "smartptr.h"
16 #include "pubkey.h"
17 
18 #if CRYPTOPP_MSC_VERSION
19 # pragma warning(push)
20 # pragma warning(disable: 4231 4275)
21 #endif
22 
23 NAMESPACE_BEGIN(CryptoPP)
24 
25 /// \brief Elliptic Curve over GF(p), where p is prime
26 class CRYPTOPP_DLL ECP : public AbstractGroup<ECPPoint>, public EncodedPoint<ECPPoint>
27 {
28 public:
29  typedef ModularArithmetic Field;
30  typedef Integer FieldElement;
31  typedef ECPPoint Point;
32 
33  virtual ~ECP() {}
34 
35  /// \brief Construct an ECP
36  ECP() {}
37 
38  /// \brief Construct an ECP
39  /// \param ecp the other ECP object
40  /// \param convertToMontgomeryRepresentation flag indicating if the curve
41  /// should be converted to a MontgomeryRepresentation.
42  /// \details Prior to Crypto++ 8.3 the default value for
43  /// convertToMontgomeryRepresentation was false. it was changed due to
44  /// two audit tools finding, "Signature-compatible with a copy constructor".
45  /// \sa ModularArithmetic, MontgomeryRepresentation
46  ECP(const ECP &ecp, bool convertToMontgomeryRepresentation);
47 
48  /// \brief Construct an ECP
49  /// \param modulus the prime modulus
50  /// \param a Field::Element
51  /// \param b Field::Element
52  ECP(const Integer &modulus, const FieldElement &a, const FieldElement &b)
53  : m_fieldPtr(new Field(modulus)), m_a(a.IsNegative() ? modulus+a : a), m_b(b) {}
54 
55  /// \brief Construct an ECP from BER encoded parameters
56  /// \param bt BufferedTransformation derived object
57  /// \details This constructor will decode and extract the the fields
58  /// fieldID and curve of the sequence ECParameters
60 
61  /// \brief DER Encode
62  /// \param bt BufferedTransformation derived object
63  /// \details DEREncode encode the fields fieldID and curve of the sequence
64  /// ECParameters
65  void DEREncode(BufferedTransformation &bt) const;
66 
67  /// \brief Compare two points
68  /// \param P the first point
69  /// \param Q the second point
70  /// \returns true if equal, false otherwise
71  bool Equal(const Point &P, const Point &Q) const;
72 
73  const Point& Identity() const;
74  const Point& Inverse(const Point &P) const;
75  bool InversionIsFast() const {return true;}
76  const Point& Add(const Point &P, const Point &Q) const;
77  const Point& Double(const Point &P) const;
78  Point ScalarMultiply(const Point &P, const Integer &k) const;
79  Point CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const;
80  void SimultaneousMultiply(Point *results, const Point &base, const Integer *exponents, unsigned int exponentsCount) const;
81 
82  Point Multiply(const Integer &k, const Point &P) const
83  {return ScalarMultiply(P, k);}
84  Point CascadeMultiply(const Integer &k1, const Point &P, const Integer &k2, const Point &Q) const
85  {return CascadeScalarMultiply(P, k1, Q, k2);}
86 
87  bool ValidateParameters(RandomNumberGenerator &rng, unsigned int level=3) const;
88  bool VerifyPoint(const Point &P) const;
89 
90  unsigned int EncodedPointSize(bool compressed = false) const
91  {return 1 + (compressed?1:2)*GetField().MaxElementByteLength();}
92  // returns false if point is compressed and not valid (doesn't check if uncompressed)
93  bool DecodePoint(Point &P, BufferedTransformation &bt, size_t len) const;
94  bool DecodePoint(Point &P, const byte *encodedPoint, size_t len) const;
95  void EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const;
96  void EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
97 
98  Point BERDecodePoint(BufferedTransformation &bt) const;
99  void DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const;
100 
101  Integer FieldSize() const {return GetField().GetModulus();}
102  const Field & GetField() const {return *m_fieldPtr;}
103  const FieldElement & GetA() const {return m_a;}
104  const FieldElement & GetB() const {return m_b;}
105 
106  bool operator==(const ECP &rhs) const
107  {return GetField() == rhs.GetField() && m_a == rhs.m_a && m_b == rhs.m_b;}
108 
109 private:
110  clonable_ptr<Field> m_fieldPtr;
111  FieldElement m_a, m_b;
112  mutable Point m_R;
113 };
114 
115 CRYPTOPP_DLL_TEMPLATE_CLASS DL_FixedBasePrecomputationImpl<ECP::Point>;
116 CRYPTOPP_DLL_TEMPLATE_CLASS DL_GroupPrecomputation<ECP::Point>;
117 
118 /// \brief Elliptic Curve precomputation
119 /// \tparam EC elliptic curve field
120 template <class EC> class EcPrecomputation;
121 
122 /// \brief ECP precomputation specialization
123 /// \details Implementation of <tt>DL_GroupPrecomputation<ECP::Point></tt> with input and output
124 /// conversions for Montgomery modular multiplication.
125 /// \sa DL_GroupPrecomputation, ModularArithmetic, MontgomeryRepresentation
126 template<> class EcPrecomputation<ECP> : public DL_GroupPrecomputation<ECP::Point>
127 {
128 public:
129  typedef ECP EllipticCurve;
130 
131  virtual ~EcPrecomputation() {}
132 
133  // DL_GroupPrecomputation
134  bool NeedConversions() const {return true;}
135  Element ConvertIn(const Element &P) const
136  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertIn(P.x), m_ec->GetField().ConvertIn(P.y));};
137  Element ConvertOut(const Element &P) const
138  {return P.identity ? P : ECP::Point(m_ec->GetField().ConvertOut(P.x), m_ec->GetField().ConvertOut(P.y));}
139  const AbstractGroup<Element> & GetGroup() const {return *m_ec;}
140  Element BERDecodeElement(BufferedTransformation &bt) const {return m_ec->BERDecodePoint(bt);}
141  void DEREncodeElement(BufferedTransformation &bt, const Element &v) const {m_ec->DEREncodePoint(bt, v, false);}
142 
143  /// \brief Set the elliptic curve
144  /// \param ec ECP derived class
145  /// \details SetCurve() is not inherited
146  void SetCurve(const ECP &ec)
147  {
148  m_ec.reset(new ECP(ec, true));
149  m_ecOriginal = ec;
150  }
151 
152  /// \brief Get the elliptic curve
153  /// \returns ECP curve
154  /// \details GetCurve() is not inherited
155  const ECP & GetCurve() const {return *m_ecOriginal;}
156 
157 private:
158  value_ptr<ECP> m_ec, m_ecOriginal;
159 };
160 
161 NAMESPACE_END
162 
163 #if CRYPTOPP_MSC_VERSION
164 # pragma warning(pop)
165 #endif
166 
167 #endif
Elliptical Curve Point over GF(p), where p is prime.
Definition: ecpoint.h:20
This file contains helper classes/functions for implementing public key algorithms.
const char * Identity()
ConstByteArrayParameter.
Definition: argnames.h:94
Elliptic Curve over GF(p), where p is prime.
Definition: ecp.h:26
Abstract base classes that provide a uniform interface to this library.
bool InversionIsFast() const
Determine if inversion is fast.
Definition: ecp.h:75
Classes for automatic resource management.
Ring of congruence classes modulo n.
Definition: modarith.h:43
Interface for random number generators.
Definition: cryptlib.h:1412
Element ConvertIn(const Element &P) const
Converts an element between representations.
Definition: ecp.h:135
Classes for Elliptic Curve points.
Classes for performing mathematics over different fields.
Interface for buffered transformations.
Definition: cryptlib.h:1627
bool operator==(const OID &lhs, const OID &rhs)
Compare two OIDs for equality.
void DEREncodeElement(BufferedTransformation &bt, const Element &v) const
Encodes element in DER format.
Definition: ecp.h:141
A pointer which can be copied and cloned.
Definition: smartptr.h:103
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
const AbstractGroup< Element > & GetGroup() const
Retrieves AbstractGroup interface.
Definition: ecp.h:139
Element BERDecodeElement(BufferedTransformation &bt) const
Decodes element in DER format.
Definition: ecp.h:140
Abstract group.
Definition: algebra.h:26
Classes for precomputation in a group.
Abstract class for encoding and decoding ellicptic curve points.
Definition: ecpoint.h:90
Elliptic Curve precomputation.
Definition: ec2n.h:99
ECP()
Construct an ECP.
Definition: ecp.h:36
Multiple precision integer with arithmetic operations.
bool NeedConversions() const
Determines if elements needs conversion.
Definition: ecp.h:134
unsigned int EncodedPointSize(bool compressed=false) const
Determines encoded point size.
Definition: ecp.h:90
Class file for performing modular arithmetic.
Crypto++ library namespace.
ECP(const Integer &modulus, const FieldElement &a, const FieldElement &b)
Construct an ECP.
Definition: ecp.h:52
const ECP & GetCurve() const
Get the elliptic curve.
Definition: ecp.h:155
Element ConvertOut(const Element &P) const
Converts an element between representations.
Definition: ecp.h:137
DL_FixedBasePrecomputation adapter class.
Definition: eprecomp.h:126
void SetCurve(const ECP &ec)
Set the elliptic curve.
Definition: ecp.h:146