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970 lines
26 KiB
970 lines
26 KiB
4 years ago
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// ecp.cpp - originally written and placed in the public domain by Wei Dai
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#include "pch.h"
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#ifndef CRYPTOPP_IMPORTS
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#include "ecp.h"
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#include "asn.h"
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#include "integer.h"
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#include "nbtheory.h"
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#include "modarith.h"
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#include "filters.h"
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#include "algebra.cpp"
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ANONYMOUS_NAMESPACE_BEGIN
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using CryptoPP::ECP;
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using CryptoPP::Integer;
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using CryptoPP::ModularArithmetic;
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#if defined(HAVE_GCC_INIT_PRIORITY)
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#define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 50)))
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const ECP::Point g_identity INIT_ATTRIBUTE = ECP::Point();
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#elif defined(HAVE_MSC_INIT_PRIORITY)
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#pragma warning(disable: 4075)
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#pragma init_seg(".CRT$XCU")
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const ECP::Point g_identity;
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#pragma warning(default: 4075)
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#elif defined(HAVE_XLC_INIT_PRIORITY)
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#pragma priority(290)
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const ECP::Point g_identity;
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#endif
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inline ECP::Point ToMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
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{
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return P.identity ? P : ECP::Point(mr.ConvertIn(P.x), mr.ConvertIn(P.y));
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}
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inline ECP::Point FromMontgomery(const ModularArithmetic &mr, const ECP::Point &P)
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{
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return P.identity ? P : ECP::Point(mr.ConvertOut(P.x), mr.ConvertOut(P.y));
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}
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inline Integer IdentityToInteger(bool val)
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{
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return val ? Integer::One() : Integer::Zero();
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}
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struct ProjectivePoint
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{
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ProjectivePoint() {}
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ProjectivePoint(const Integer &x, const Integer &y, const Integer &z)
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: x(x), y(y), z(z) {}
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Integer x, y, z;
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};
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/// \brief Addition and Double functions
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/// \sa <A HREF="https://eprint.iacr.org/2015/1060.pdf">Complete
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/// addition formulas for prime order elliptic curves</A>
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struct AdditionFunction
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{
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explicit AdditionFunction(const ECP::Field& field,
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const ECP::FieldElement &a, const ECP::FieldElement &b, ECP::Point &r);
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// Double(P)
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ECP::Point operator()(const ECP::Point& P) const;
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// Add(P, Q)
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ECP::Point operator()(const ECP::Point& P, const ECP::Point& Q) const;
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protected:
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/// \brief Parameters and representation for Addition
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/// \details Addition and Doubling will use different algorithms,
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/// depending on the <tt>A</tt> coefficient and the representation
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/// (Affine or Montgomery with precomputation).
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enum Alpha {
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/// \brief Coefficient A is 0
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A_0 = 1,
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/// \brief Coefficient A is -3
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A_3 = 2,
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/// \brief Coefficient A is arbitrary
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A_Star = 4,
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/// \brief Representation is Montgomery
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A_Montgomery = 8
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};
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const ECP::Field& field;
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const ECP::FieldElement &a, &b;
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ECP::Point &R;
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Alpha m_alpha;
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};
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#define X p.x
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#define Y p.y
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#define Z p.z
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#define X1 p.x
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#define Y1 p.y
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#define Z1 p.z
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#define X2 q.x
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#define Y2 q.y
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#define Z2 q.z
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#define X3 r.x
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#define Y3 r.y
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#define Z3 r.z
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AdditionFunction::AdditionFunction(const ECP::Field& field,
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const ECP::FieldElement &a, const ECP::FieldElement &b, ECP::Point &r)
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: field(field), a(a), b(b), R(r), m_alpha(static_cast<Alpha>(0))
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{
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if (field.IsMontgomeryRepresentation())
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{
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m_alpha = A_Montgomery;
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}
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else
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{
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if (a == 0)
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{
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m_alpha = A_0;
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}
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else if (a == -3 || (a - field.GetModulus()) == -3)
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{
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m_alpha = A_3;
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}
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else
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{
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m_alpha = A_Star;
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}
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}
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}
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ECP::Point AdditionFunction::operator()(const ECP::Point& P) const
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{
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if (m_alpha == A_3)
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{
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// Gyrations attempt to maintain constant-timeness
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// We need either (P.x, P.y, 1) or (0, 1, 0).
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const Integer x = P.x * IdentityToInteger(!P.identity);
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const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
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const Integer z = 1 * IdentityToInteger(!P.identity);
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ProjectivePoint p(x, y, z), r;
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ECP::FieldElement t0 = field.Square(X);
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ECP::FieldElement t1 = field.Square(Y);
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ECP::FieldElement t2 = field.Square(Z);
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ECP::FieldElement t3 = field.Multiply(X, Y);
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t3 = field.Add(t3, t3);
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Z3 = field.Multiply(X, Z);
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Z3 = field.Add(Z3, Z3);
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Y3 = field.Multiply(b, t2);
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Y3 = field.Subtract(Y3, Z3);
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X3 = field.Add(Y3, Y3);
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Y3 = field.Add(X3, Y3);
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X3 = field.Subtract(t1, Y3);
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Y3 = field.Add(t1, Y3);
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Y3 = field.Multiply(X3, Y3);
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X3 = field.Multiply(X3, t3);
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t3 = field.Add(t2, t2);
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t2 = field.Add(t2, t3);
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Z3 = field.Multiply(b, Z3);
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Z3 = field.Subtract(Z3, t2);
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Z3 = field.Subtract(Z3, t0);
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t3 = field.Add(Z3, Z3);
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Z3 = field.Add(Z3, t3);
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t3 = field.Add(t0, t0);
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t0 = field.Add(t3, t0);
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t0 = field.Subtract(t0, t2);
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t0 = field.Multiply(t0, Z3);
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Y3 = field.Add(Y3, t0);
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t0 = field.Multiply(Y, Z);
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t0 = field.Add(t0, t0);
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Z3 = field.Multiply(t0, Z3);
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X3 = field.Subtract(X3, Z3);
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Z3 = field.Multiply(t0, t1);
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Z3 = field.Add(Z3, Z3);
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Z3 = field.Add(Z3, Z3);
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const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
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X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
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// More gyrations
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R.x = X3*Z3.NotZero();
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R.y = Y3*Z3.NotZero();
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R.identity = Z3.IsZero();
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return R;
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}
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else if (m_alpha == A_0)
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{
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// Gyrations attempt to maintain constant-timeness
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// We need either (P.x, P.y, 1) or (0, 1, 0).
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const Integer x = P.x * IdentityToInteger(!P.identity);
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const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
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const Integer z = 1 * IdentityToInteger(!P.identity);
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ProjectivePoint p(x, y, z), r;
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const ECP::FieldElement b3 = field.Multiply(b, 3);
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ECP::FieldElement t0 = field.Square(Y);
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Z3 = field.Add(t0, t0);
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Z3 = field.Add(Z3, Z3);
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Z3 = field.Add(Z3, Z3);
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ECP::FieldElement t1 = field.Add(Y, Z);
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ECP::FieldElement t2 = field.Square(Z);
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t2 = field.Multiply(b3, t2);
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X3 = field.Multiply(t2, Z3);
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Y3 = field.Add(t0, t2);
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Z3 = field.Multiply(t1, Z3);
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t1 = field.Add(t2, t2);
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t2 = field.Add(t1, t2);
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t0 = field.Subtract(t0, t2);
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Y3 = field.Multiply(t0, Y3);
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Y3 = field.Add(X3, Y3);
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t1 = field.Multiply(X, Y);
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X3 = field.Multiply(t0, t1);
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X3 = field.Add(X3, X3);
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const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
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X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
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// More gyrations
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R.x = X3*Z3.NotZero();
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R.y = Y3*Z3.NotZero();
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R.identity = Z3.IsZero();
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return R;
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}
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#if 0
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// Code path disabled at the moment due to https://github.com/weidai11/cryptopp/issues/878
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else if (m_alpha == A_Star)
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{
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// Gyrations attempt to maintain constant-timeness
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// We need either (P.x, P.y, 1) or (0, 1, 0).
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const Integer x = P.x * IdentityToInteger(!P.identity);
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const Integer y = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
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const Integer z = 1 * IdentityToInteger(!P.identity);
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ProjectivePoint p(x, y, z), r;
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const ECP::FieldElement b3 = field.Multiply(b, 3);
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ECP::FieldElement t0 = field.Square(Y);
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Z3 = field.Add(t0, t0);
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Z3 = field.Add(Z3, Z3);
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Z3 = field.Add(Z3, Z3);
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ECP::FieldElement t1 = field.Add(Y, Z);
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ECP::FieldElement t2 = field.Square(Z);
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t2 = field.Multiply(b3, t2);
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X3 = field.Multiply(t2, Z3);
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Y3 = field.Add(t0, t2);
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Z3 = field.Multiply(t1, Z3);
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t1 = field.Add(t2, t2);
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t2 = field.Add(t1, t2);
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t0 = field.Subtract(t0, t2);
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Y3 = field.Multiply(t0, Y3);
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Y3 = field.Add(X3, Y3);
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t1 = field.Multiply(X, Y);
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X3 = field.Multiply(t0, t1);
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X3 = field.Add(X3, X3);
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const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
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X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
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// More gyrations
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R.x = X3*Z3.NotZero();
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R.y = Y3*Z3.NotZero();
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R.identity = Z3.IsZero();
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return R;
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}
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#endif
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else // A_Montgomery
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{
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// More gyrations
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bool identity = !!(P.identity + (P.y == field.Identity()));
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ECP::FieldElement t = field.Square(P.x);
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t = field.Add(field.Add(field.Double(t), t), a);
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t = field.Divide(t, field.Double(P.y));
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ECP::FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), P.x);
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R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
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R.x.swap(x);
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// More gyrations
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R.x *= IdentityToInteger(!identity);
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R.y *= IdentityToInteger(!identity);
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R.identity = identity;
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return R;
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}
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}
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ECP::Point AdditionFunction::operator()(const ECP::Point& P, const ECP::Point& Q) const
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{
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if (m_alpha == A_3)
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{
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// Gyrations attempt to maintain constant-timeness
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// We need either (P.x, P.y, 1) or (0, 1, 0).
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const Integer x1 = P.x * IdentityToInteger(!P.identity);
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const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
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const Integer z1 = 1 * IdentityToInteger(!P.identity);
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const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
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const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
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const Integer z2 = 1 * IdentityToInteger(!Q.identity);
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ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
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ECP::FieldElement t0 = field.Multiply(X1, X2);
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ECP::FieldElement t1 = field.Multiply(Y1, Y2);
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ECP::FieldElement t2 = field.Multiply(Z1, Z2);
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ECP::FieldElement t3 = field.Add(X1, Y1);
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ECP::FieldElement t4 = field.Add(X2, Y2);
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t3 = field.Multiply(t3, t4);
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t4 = field.Add(t0, t1);
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t3 = field.Subtract(t3, t4);
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t4 = field.Add(Y1, Z1);
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X3 = field.Add(Y2, Z2);
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t4 = field.Multiply(t4, X3);
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X3 = field.Add(t1, t2);
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t4 = field.Subtract(t4, X3);
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X3 = field.Add(X1, Z1);
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Y3 = field.Add(X2, Z2);
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X3 = field.Multiply(X3, Y3);
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Y3 = field.Add(t0, t2);
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Y3 = field.Subtract(X3, Y3);
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Z3 = field.Multiply(b, t2);
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X3 = field.Subtract(Y3, Z3);
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Z3 = field.Add(X3, X3);
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X3 = field.Add(X3, Z3);
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Z3 = field.Subtract(t1, X3);
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X3 = field.Add(t1, X3);
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Y3 = field.Multiply(b, Y3);
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t1 = field.Add(t2, t2);
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t2 = field.Add(t1, t2);
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Y3 = field.Subtract(Y3, t2);
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Y3 = field.Subtract(Y3, t0);
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|
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t1 = field.Add(Y3, Y3);
|
||
|
|
Y3 = field.Add(t1, Y3);
|
||
|
|
t1 = field.Add(t0, t0);
|
||
|
|
t0 = field.Add(t1, t0);
|
||
|
|
t0 = field.Subtract(t0, t2);
|
||
|
|
t1 = field.Multiply(t4, Y3);
|
||
|
|
t2 = field.Multiply(t0, Y3);
|
||
|
|
Y3 = field.Multiply(X3, Z3);
|
||
|
|
Y3 = field.Add(Y3, t2);
|
||
|
|
X3 = field.Multiply(t3, X3);
|
||
|
|
X3 = field.Subtract(X3, t1);
|
||
|
|
Z3 = field.Multiply(t4, Z3);
|
||
|
|
t1 = field.Multiply(t3, t0);
|
||
|
|
Z3 = field.Add(Z3, t1);
|
||
|
|
|
||
|
|
const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
||
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
||
|
|
|
||
|
|
// More gyrations
|
||
|
|
R.x = X3*Z3.NotZero();
|
||
|
|
R.y = Y3*Z3.NotZero();
|
||
|
|
R.identity = Z3.IsZero();
|
||
|
|
|
||
|
|
return R;
|
||
|
|
}
|
||
|
|
else if (m_alpha == A_0)
|
||
|
|
{
|
||
|
|
// Gyrations attempt to maintain constant-timeness
|
||
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
||
|
|
const Integer x1 = P.x * IdentityToInteger(!P.identity);
|
||
|
|
const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
||
|
|
const Integer z1 = 1 * IdentityToInteger(!P.identity);
|
||
|
|
|
||
|
|
const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
|
||
|
|
const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
|
||
|
|
const Integer z2 = 1 * IdentityToInteger(!Q.identity);
|
||
|
|
|
||
|
|
ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
|
||
|
|
const ECP::FieldElement b3 = field.Multiply(b, 3);
|
||
|
|
|
||
|
|
ECP::FieldElement t0 = field.Square(Y);
|
||
|
|
Z3 = field.Add(t0, t0);
|
||
|
|
Z3 = field.Add(Z3, Z3);
|
||
|
|
Z3 = field.Add(Z3, Z3);
|
||
|
|
ECP::FieldElement t1 = field.Add(Y, Z);
|
||
|
|
ECP::FieldElement t2 = field.Square(Z);
|
||
|
|
t2 = field.Multiply(b3, t2);
|
||
|
|
X3 = field.Multiply(t2, Z3);
|
||
|
|
Y3 = field.Add(t0, t2);
|
||
|
|
Z3 = field.Multiply(t1, Z3);
|
||
|
|
t1 = field.Add(t2, t2);
|
||
|
|
t2 = field.Add(t1, t2);
|
||
|
|
t0 = field.Subtract(t0, t2);
|
||
|
|
Y3 = field.Multiply(t0, Y3);
|
||
|
|
Y3 = field.Add(X3, Y3);
|
||
|
|
t1 = field.Multiply(X, Y);
|
||
|
|
X3 = field.Multiply(t0, t1);
|
||
|
|
X3 = field.Add(X3, X3);
|
||
|
|
|
||
|
|
const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
||
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
||
|
|
|
||
|
|
// More gyrations
|
||
|
|
R.x = X3*Z3.NotZero();
|
||
|
|
R.y = Y3*Z3.NotZero();
|
||
|
|
R.identity = Z3.IsZero();
|
||
|
|
|
||
|
|
return R;
|
||
|
|
}
|
||
|
|
#if 0
|
||
|
|
// Code path disabled at the moment due to https://github.com/weidai11/cryptopp/issues/878
|
||
|
|
else if (m_alpha == A_Star)
|
||
|
|
{
|
||
|
|
// Gyrations attempt to maintain constant-timeness
|
||
|
|
// We need either (P.x, P.y, 1) or (0, 1, 0).
|
||
|
|
const Integer x1 = P.x * IdentityToInteger(!P.identity);
|
||
|
|
const Integer y1 = P.y * IdentityToInteger(!P.identity) + 1 * IdentityToInteger(P.identity);
|
||
|
|
const Integer z1 = 1 * IdentityToInteger(!P.identity);
|
||
|
|
|
||
|
|
const Integer x2 = Q.x * IdentityToInteger(!Q.identity);
|
||
|
|
const Integer y2 = Q.y * IdentityToInteger(!Q.identity) + 1 * IdentityToInteger(Q.identity);
|
||
|
|
const Integer z2 = 1 * IdentityToInteger(!Q.identity);
|
||
|
|
|
||
|
|
ProjectivePoint p(x1, y1, z1), q(x2, y2, z2), r;
|
||
|
|
const ECP::FieldElement b3 = field.Multiply(b, 3);
|
||
|
|
|
||
|
|
ECP::FieldElement t0 = field.Multiply(X1, X2);
|
||
|
|
ECP::FieldElement t1 = field.Multiply(Y1, Y2);
|
||
|
|
ECP::FieldElement t2 = field.Multiply(Z1, Z2);
|
||
|
|
ECP::FieldElement t3 = field.Add(X1, Y1);
|
||
|
|
ECP::FieldElement t4 = field.Add(X2, Y2);
|
||
|
|
t3 = field.Multiply(t3, t4);
|
||
|
|
t4 = field.Add(t0, t1);
|
||
|
|
t3 = field.Subtract(t3, t4);
|
||
|
|
t4 = field.Add(X1, Z1);
|
||
|
|
ECP::FieldElement t5 = field.Add(X2, Z2);
|
||
|
|
t4 = field.Multiply(t4, t5);
|
||
|
|
t5 = field.Add(t0, t2);
|
||
|
|
t4 = field.Subtract(t4, t5);
|
||
|
|
t5 = field.Add(Y1, Z1);
|
||
|
|
X3 = field.Add(Y2, Z2);
|
||
|
|
t5 = field.Multiply(t5, X3);
|
||
|
|
X3 = field.Add(t1, t2);
|
||
|
|
t5 = field.Subtract(t5, X3);
|
||
|
|
Z3 = field.Multiply(a, t4);
|
||
|
|
X3 = field.Multiply(b3, t2);
|
||
|
|
Z3 = field.Add(X3, Z3);
|
||
|
|
X3 = field.Subtract(t1, Z3);
|
||
|
|
Z3 = field.Add(t1, Z3);
|
||
|
|
Y3 = field.Multiply(X3, Z3);
|
||
|
|
t1 = field.Add(t0, t0);
|
||
|
|
t1 = field.Add(t1, t0);
|
||
|
|
t2 = field.Multiply(a, t2);
|
||
|
|
t4 = field.Multiply(b3, t4);
|
||
|
|
t1 = field.Add(t1, t2);
|
||
|
|
t2 = field.Subtract(t0, t2);
|
||
|
|
t2 = field.Multiply(a, t2);
|
||
|
|
t4 = field.Add(t4, t2);
|
||
|
|
t0 = field.Multiply(t1, t4);
|
||
|
|
Y3 = field.Add(Y3, t0);
|
||
|
|
t0 = field.Multiply(t5, t4);
|
||
|
|
X3 = field.Multiply(t3, X3);
|
||
|
|
X3 = field.Subtract(X3, t0);
|
||
|
|
t0 = field.Multiply(t3, t1);
|
||
|
|
Z3 = field.Multiply(t5, Z3);
|
||
|
|
Z3 = field.Add(Z3, t0);
|
||
|
|
|
||
|
|
const ECP::FieldElement inv = field.MultiplicativeInverse(Z3.IsZero() ? Integer::One() : Z3);
|
||
|
|
X3 = field.Multiply(X3, inv); Y3 = field.Multiply(Y3, inv);
|
||
|
|
|
||
|
|
// More gyrations
|
||
|
|
R.x = X3*Z3.NotZero();
|
||
|
|
R.y = Y3*Z3.NotZero();
|
||
|
|
R.identity = Z3.IsZero();
|
||
|
|
|
||
|
|
return R;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
else // A_Montgomery
|
||
|
|
{
|
||
|
|
// More gyrations
|
||
|
|
bool return_Q = P.identity;
|
||
|
|
bool return_P = Q.identity;
|
||
|
|
bool double_P = field.Equal(P.x, Q.x) && field.Equal(P.y, Q.y);
|
||
|
|
bool identity = field.Equal(P.x, Q.x) && !field.Equal(P.y, Q.y);
|
||
|
|
|
||
|
|
// This code taken from Double(P) for below
|
||
|
|
identity = !!((double_P * (P.identity + (P.y == field.Identity()))) + identity);
|
||
|
|
|
||
|
|
ECP::Point S = R;
|
||
|
|
if (double_P)
|
||
|
|
{
|
||
|
|
// This code taken from Double(P)
|
||
|
|
ECP::FieldElement t = field.Square(P.x);
|
||
|
|
t = field.Add(field.Add(field.Double(t), t), a);
|
||
|
|
t = field.Divide(t, field.Double(P.y));
|
||
|
|
ECP::FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), P.x);
|
||
|
|
R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
|
||
|
|
R.x.swap(x);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// Original Add(P,Q) code
|
||
|
|
ECP::FieldElement t = field.Subtract(Q.y, P.y);
|
||
|
|
t = field.Divide(t, field.Subtract(Q.x, P.x));
|
||
|
|
ECP::FieldElement x = field.Subtract(field.Subtract(field.Square(t), P.x), Q.x);
|
||
|
|
R.y = field.Subtract(field.Multiply(t, field.Subtract(P.x, x)), P.y);
|
||
|
|
R.x.swap(x);
|
||
|
|
}
|
||
|
|
|
||
|
|
// More gyrations
|
||
|
|
R.x = R.x * IdentityToInteger(!identity);
|
||
|
|
R.y = R.y * IdentityToInteger(!identity);
|
||
|
|
R.identity = identity;
|
||
|
|
|
||
|
|
if (return_Q)
|
||
|
|
return (R = S), Q;
|
||
|
|
else if (return_P)
|
||
|
|
return (R = S), P;
|
||
|
|
else
|
||
|
|
return (S = R), R;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#undef X
|
||
|
|
#undef Y
|
||
|
|
#undef Z
|
||
|
|
|
||
|
|
#undef X1
|
||
|
|
#undef Y1
|
||
|
|
#undef Z1
|
||
|
|
|
||
|
|
#undef X2
|
||
|
|
#undef Y2
|
||
|
|
#undef Z2
|
||
|
|
|
||
|
|
#undef X3
|
||
|
|
#undef Y3
|
||
|
|
#undef Z3
|
||
|
|
|
||
|
|
ANONYMOUS_NAMESPACE_END
|
||
|
|
|
||
|
|
NAMESPACE_BEGIN(CryptoPP)
|
||
|
|
|
||
|
|
ECP::ECP(const ECP &ecp, bool convertToMontgomeryRepresentation)
|
||
|
|
{
|
||
|
|
if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation())
|
||
|
|
{
|
||
|
|
m_fieldPtr.reset(new MontgomeryRepresentation(ecp.GetField().GetModulus()));
|
||
|
|
m_a = GetField().ConvertIn(ecp.m_a);
|
||
|
|
m_b = GetField().ConvertIn(ecp.m_b);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
operator=(ecp);
|
||
|
|
}
|
||
|
|
|
||
|
|
ECP::ECP(BufferedTransformation &bt)
|
||
|
|
: m_fieldPtr(new Field(bt))
|
||
|
|
{
|
||
|
|
BERSequenceDecoder seq(bt);
|
||
|
|
GetField().BERDecodeElement(seq, m_a);
|
||
|
|
GetField().BERDecodeElement(seq, m_b);
|
||
|
|
// skip optional seed
|
||
|
|
if (!seq.EndReached())
|
||
|
|
{
|
||
|
|
SecByteBlock seed;
|
||
|
|
unsigned int unused;
|
||
|
|
BERDecodeBitString(seq, seed, unused);
|
||
|
|
}
|
||
|
|
seq.MessageEnd();
|
||
|
|
}
|
||
|
|
|
||
|
|
void ECP::DEREncode(BufferedTransformation &bt) const
|
||
|
|
{
|
||
|
|
GetField().DEREncode(bt);
|
||
|
|
DERSequenceEncoder seq(bt);
|
||
|
|
GetField().DEREncodeElement(seq, m_a);
|
||
|
|
GetField().DEREncodeElement(seq, m_b);
|
||
|
|
seq.MessageEnd();
|
||
|
|
}
|
||
|
|
|
||
|
|
bool ECP::DecodePoint(ECP::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
|
||
|
|
{
|
||
|
|
StringStore store(encodedPoint, encodedPointLen);
|
||
|
|
return DecodePoint(P, store, encodedPointLen);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool ECP::DecodePoint(ECP::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
|
||
|
|
{
|
||
|
|
byte type;
|
||
|
|
if (encodedPointLen < 1 || !bt.Get(type))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
switch (type)
|
||
|
|
{
|
||
|
|
case 0:
|
||
|
|
P.identity = true;
|
||
|
|
return true;
|
||
|
|
case 2:
|
||
|
|
case 3:
|
||
|
|
{
|
||
|
|
if (encodedPointLen != EncodedPointSize(true))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
Integer p = FieldSize();
|
||
|
|
|
||
|
|
P.identity = false;
|
||
|
|
P.x.Decode(bt, GetField().MaxElementByteLength());
|
||
|
|
P.y = ((P.x*P.x+m_a)*P.x+m_b) % p;
|
||
|
|
|
||
|
|
if (Jacobi(P.y, p) !=1)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
P.y = ModularSquareRoot(P.y, p);
|
||
|
|
|
||
|
|
if ((type & 1) != P.y.GetBit(0))
|
||
|
|
P.y = p-P.y;
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
case 4:
|
||
|
|
{
|
||
|
|
if (encodedPointLen != EncodedPointSize(false))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
unsigned int len = GetField().MaxElementByteLength();
|
||
|
|
P.identity = false;
|
||
|
|
P.x.Decode(bt, len);
|
||
|
|
P.y.Decode(bt, len);
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
default:
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void ECP::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
|
||
|
|
{
|
||
|
|
if (P.identity)
|
||
|
|
NullStore().TransferTo(bt, EncodedPointSize(compressed));
|
||
|
|
else if (compressed)
|
||
|
|
{
|
||
|
|
bt.Put((byte)(2U + P.y.GetBit(0)));
|
||
|
|
P.x.Encode(bt, GetField().MaxElementByteLength());
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
unsigned int len = GetField().MaxElementByteLength();
|
||
|
|
bt.Put(4U); // uncompressed
|
||
|
|
P.x.Encode(bt, len);
|
||
|
|
P.y.Encode(bt, len);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void ECP::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
|
||
|
|
{
|
||
|
|
ArraySink sink(encodedPoint, EncodedPointSize(compressed));
|
||
|
|
EncodePoint(sink, P, compressed);
|
||
|
|
CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
|
||
|
|
}
|
||
|
|
|
||
|
|
ECP::Point ECP::BERDecodePoint(BufferedTransformation &bt) const
|
||
|
|
{
|
||
|
|
SecByteBlock str;
|
||
|
|
BERDecodeOctetString(bt, str);
|
||
|
|
Point P;
|
||
|
|
if (!DecodePoint(P, str, str.size()))
|
||
|
|
BERDecodeError();
|
||
|
|
return P;
|
||
|
|
}
|
||
|
|
|
||
|
|
void ECP::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
|
||
|
|
{
|
||
|
|
SecByteBlock str(EncodedPointSize(compressed));
|
||
|
|
EncodePoint(str, P, compressed);
|
||
|
|
DEREncodeOctetString(bt, str);
|
||
|
|
}
|
||
|
|
|
||
|
|
bool ECP::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
|
||
|
|
{
|
||
|
|
Integer p = FieldSize();
|
||
|
|
|
||
|
|
bool pass = p.IsOdd();
|
||
|
|
pass = pass && !m_a.IsNegative() && m_a<p && !m_b.IsNegative() && m_b<p;
|
||
|
|
|
||
|
|
if (level >= 1)
|
||
|
|
pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive();
|
||
|
|
|
||
|
|
if (level >= 2)
|
||
|
|
pass = pass && VerifyPrime(rng, p);
|
||
|
|
|
||
|
|
return pass;
|
||
|
|
}
|
||
|
|
|
||
|
|
bool ECP::VerifyPoint(const Point &P) const
|
||
|
|
{
|
||
|
|
const FieldElement &x = P.x, &y = P.y;
|
||
|
|
Integer p = FieldSize();
|
||
|
|
return P.identity ||
|
||
|
|
(!x.IsNegative() && x<p && !y.IsNegative() && y<p
|
||
|
|
&& !(((x*x+m_a)*x+m_b-y*y)%p));
|
||
|
|
}
|
||
|
|
|
||
|
|
bool ECP::Equal(const Point &P, const Point &Q) const
|
||
|
|
{
|
||
|
|
if (P.identity && Q.identity)
|
||
|
|
return true;
|
||
|
|
|
||
|
|
if (P.identity && !Q.identity)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
if (!P.identity && Q.identity)
|
||
|
|
return false;
|
||
|
|
|
||
|
|
return (GetField().Equal(P.x,Q.x) && GetField().Equal(P.y,Q.y));
|
||
|
|
}
|
||
|
|
|
||
|
|
const ECP::Point& ECP::Identity() const
|
||
|
|
{
|
||
|
|
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
|
||
|
|
return g_identity;
|
||
|
|
#elif defined(CRYPTOPP_CXX11_STATIC_INIT)
|
||
|
|
static const ECP::Point g_identity;
|
||
|
|
return g_identity;
|
||
|
|
#else
|
||
|
|
return Singleton<Point>().Ref();
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
const ECP::Point& ECP::Inverse(const Point &P) const
|
||
|
|
{
|
||
|
|
if (P.identity)
|
||
|
|
return P;
|
||
|
|
else
|
||
|
|
{
|
||
|
|
m_R.identity = false;
|
||
|
|
m_R.x = P.x;
|
||
|
|
m_R.y = GetField().Inverse(P.y);
|
||
|
|
return m_R;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
const ECP::Point& ECP::Add(const Point &P, const Point &Q) const
|
||
|
|
{
|
||
|
|
AdditionFunction add(GetField(), m_a, m_b, m_R);
|
||
|
|
return (m_R = add(P, Q));
|
||
|
|
}
|
||
|
|
|
||
|
|
const ECP::Point& ECP::Double(const Point &P) const
|
||
|
|
{
|
||
|
|
AdditionFunction add(GetField(), m_a, m_b, m_R);
|
||
|
|
return (m_R = add(P));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class Iterator> void ParallelInvert(const AbstractRing<T> &ring, Iterator begin, Iterator end)
|
||
|
|
{
|
||
|
|
size_t n = end-begin;
|
||
|
|
if (n == 1)
|
||
|
|
*begin = ring.MultiplicativeInverse(*begin);
|
||
|
|
else if (n > 1)
|
||
|
|
{
|
||
|
|
std::vector<T> vec((n+1)/2);
|
||
|
|
unsigned int i;
|
||
|
|
Iterator it;
|
||
|
|
|
||
|
|
for (i=0, it=begin; i<n/2; i++, it+=2)
|
||
|
|
vec[i] = ring.Multiply(*it, *(it+1));
|
||
|
|
if (n%2 == 1)
|
||
|
|
vec[n/2] = *it;
|
||
|
|
|
||
|
|
ParallelInvert(ring, vec.begin(), vec.end());
|
||
|
|
|
||
|
|
for (i=0, it=begin; i<n/2; i++, it+=2)
|
||
|
|
{
|
||
|
|
if (!vec[i])
|
||
|
|
{
|
||
|
|
*it = ring.MultiplicativeInverse(*it);
|
||
|
|
*(it+1) = ring.MultiplicativeInverse(*(it+1));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
std::swap(*it, *(it+1));
|
||
|
|
*it = ring.Multiply(*it, vec[i]);
|
||
|
|
*(it+1) = ring.Multiply(*(it+1), vec[i]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (n%2 == 1)
|
||
|
|
*it = vec[n/2];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
class ProjectiveDoubling
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
ProjectiveDoubling(const ModularArithmetic &m_mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q)
|
||
|
|
: mr(m_mr)
|
||
|
|
{
|
||
|
|
CRYPTOPP_UNUSED(m_b);
|
||
|
|
if (Q.identity)
|
||
|
|
{
|
||
|
|
sixteenY4 = P.x = P.y = mr.MultiplicativeIdentity();
|
||
|
|
aZ4 = P.z = mr.Identity();
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
P.x = Q.x;
|
||
|
|
P.y = Q.y;
|
||
|
|
sixteenY4 = P.z = mr.MultiplicativeIdentity();
|
||
|
|
aZ4 = m_a;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void Double()
|
||
|
|
{
|
||
|
|
twoY = mr.Double(P.y);
|
||
|
|
P.z = mr.Multiply(P.z, twoY);
|
||
|
|
fourY2 = mr.Square(twoY);
|
||
|
|
S = mr.Multiply(fourY2, P.x);
|
||
|
|
aZ4 = mr.Multiply(aZ4, sixteenY4);
|
||
|
|
M = mr.Square(P.x);
|
||
|
|
M = mr.Add(mr.Add(mr.Double(M), M), aZ4);
|
||
|
|
P.x = mr.Square(M);
|
||
|
|
mr.Reduce(P.x, S);
|
||
|
|
mr.Reduce(P.x, S);
|
||
|
|
mr.Reduce(S, P.x);
|
||
|
|
P.y = mr.Multiply(M, S);
|
||
|
|
sixteenY4 = mr.Square(fourY2);
|
||
|
|
mr.Reduce(P.y, mr.Half(sixteenY4));
|
||
|
|
}
|
||
|
|
|
||
|
|
const ModularArithmetic &mr;
|
||
|
|
ProjectivePoint P;
|
||
|
|
Integer sixteenY4, aZ4, twoY, fourY2, S, M;
|
||
|
|
};
|
||
|
|
|
||
|
|
struct ZIterator
|
||
|
|
{
|
||
|
|
ZIterator() {}
|
||
|
|
ZIterator(std::vector<ProjectivePoint>::iterator it) : it(it) {}
|
||
|
|
Integer& operator*() {return it->z;}
|
||
|
|
int operator-(ZIterator it2) {return int(it-it2.it);}
|
||
|
|
ZIterator operator+(int i) {return ZIterator(it+i);}
|
||
|
|
ZIterator& operator+=(int i) {it+=i; return *this;}
|
||
|
|
std::vector<ProjectivePoint>::iterator it;
|
||
|
|
};
|
||
|
|
|
||
|
|
ECP::Point ECP::ScalarMultiply(const Point &P, const Integer &k) const
|
||
|
|
{
|
||
|
|
Element result;
|
||
|
|
if (k.BitCount() <= 5)
|
||
|
|
AbstractGroup<ECPPoint>::SimultaneousMultiply(&result, P, &k, 1);
|
||
|
|
else
|
||
|
|
ECP::SimultaneousMultiply(&result, P, &k, 1);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
void ECP::SimultaneousMultiply(ECP::Point *results, const ECP::Point &P, const Integer *expBegin, unsigned int expCount) const
|
||
|
|
{
|
||
|
|
if (!GetField().IsMontgomeryRepresentation())
|
||
|
|
{
|
||
|
|
ECP ecpmr(*this, true);
|
||
|
|
const ModularArithmetic &mr = ecpmr.GetField();
|
||
|
|
ecpmr.SimultaneousMultiply(results, ToMontgomery(mr, P), expBegin, expCount);
|
||
|
|
for (unsigned int i=0; i<expCount; i++)
|
||
|
|
results[i] = FromMontgomery(mr, results[i]);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
ProjectiveDoubling rd(GetField(), m_a, m_b, P);
|
||
|
|
std::vector<ProjectivePoint> bases;
|
||
|
|
std::vector<WindowSlider> exponents;
|
||
|
|
exponents.reserve(expCount);
|
||
|
|
std::vector<std::vector<word32> > baseIndices(expCount);
|
||
|
|
std::vector<std::vector<bool> > negateBase(expCount);
|
||
|
|
std::vector<std::vector<word32> > exponentWindows(expCount);
|
||
|
|
unsigned int i;
|
||
|
|
|
||
|
|
for (i=0; i<expCount; i++)
|
||
|
|
{
|
||
|
|
CRYPTOPP_ASSERT(expBegin->NotNegative());
|
||
|
|
exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 5));
|
||
|
|
exponents[i].FindNextWindow();
|
||
|
|
}
|
||
|
|
|
||
|
|
unsigned int expBitPosition = 0;
|
||
|
|
bool notDone = true;
|
||
|
|
|
||
|
|
while (notDone)
|
||
|
|
{
|
||
|
|
notDone = false;
|
||
|
|
bool baseAdded = false;
|
||
|
|
for (i=0; i<expCount; i++)
|
||
|
|
{
|
||
|
|
if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
|
||
|
|
{
|
||
|
|
if (!baseAdded)
|
||
|
|
{
|
||
|
|
bases.push_back(rd.P);
|
||
|
|
baseAdded =true;
|
||
|
|
}
|
||
|
|
|
||
|
|
exponentWindows[i].push_back(exponents[i].expWindow);
|
||
|
|
baseIndices[i].push_back((word32)bases.size()-1);
|
||
|
|
negateBase[i].push_back(exponents[i].negateNext);
|
||
|
|
|
||
|
|
exponents[i].FindNextWindow();
|
||
|
|
}
|
||
|
|
notDone = notDone || !exponents[i].finished;
|
||
|
|
}
|
||
|
|
|
||
|
|
if (notDone)
|
||
|
|
{
|
||
|
|
rd.Double();
|
||
|
|
expBitPosition++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// convert from projective to affine coordinates
|
||
|
|
ParallelInvert(GetField(), ZIterator(bases.begin()), ZIterator(bases.end()));
|
||
|
|
for (i=0; i<bases.size(); i++)
|
||
|
|
{
|
||
|
|
if (bases[i].z.NotZero())
|
||
|
|
{
|
||
|
|
bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
|
||
|
|
bases[i].z = GetField().Square(bases[i].z);
|
||
|
|
bases[i].x = GetField().Multiply(bases[i].x, bases[i].z);
|
||
|
|
bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
std::vector<BaseAndExponent<Point, Integer> > finalCascade;
|
||
|
|
for (i=0; i<expCount; i++)
|
||
|
|
{
|
||
|
|
finalCascade.resize(baseIndices[i].size());
|
||
|
|
for (unsigned int j=0; j<baseIndices[i].size(); j++)
|
||
|
|
{
|
||
|
|
ProjectivePoint &base = bases[baseIndices[i][j]];
|
||
|
|
if (base.z.IsZero())
|
||
|
|
finalCascade[j].base.identity = true;
|
||
|
|
else
|
||
|
|
{
|
||
|
|
finalCascade[j].base.identity = false;
|
||
|
|
finalCascade[j].base.x = base.x;
|
||
|
|
if (negateBase[i][j])
|
||
|
|
finalCascade[j].base.y = GetField().Inverse(base.y);
|
||
|
|
else
|
||
|
|
finalCascade[j].base.y = base.y;
|
||
|
|
}
|
||
|
|
finalCascade[j].exponent = Integer(Integer::POSITIVE, 0, exponentWindows[i][j]);
|
||
|
|
}
|
||
|
|
results[i] = GeneralCascadeMultiplication(*this, finalCascade.begin(), finalCascade.end());
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
ECP::Point ECP::CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const
|
||
|
|
{
|
||
|
|
if (!GetField().IsMontgomeryRepresentation())
|
||
|
|
{
|
||
|
|
ECP ecpmr(*this, true);
|
||
|
|
const ModularArithmetic &mr = ecpmr.GetField();
|
||
|
|
return FromMontgomery(mr, ecpmr.CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));
|
||
|
|
}
|
||
|
|
else
|
||
|
|
return AbstractGroup<Point>::CascadeScalarMultiply(P, k1, Q, k2);
|
||
|
|
}
|
||
|
|
|
||
|
|
NAMESPACE_END
|
||
|
|
|
||
|
|
#endif
|