RakNet/DependentExtensions/cat/math/BigTwistedEdwards.hpp

/*
	Copyright (c) 2009-2010 Christopher A. Taylor.  All rights reserved.

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/*
    Addition and doubling formulas using Extended Twisted Edwards coordinates from
    Hisil–Wong–Carter–Dawson paper "Twisted Edwards Curves Revisited" (Asiacrypt 2008)

    w-MOF scalar multiplication from http://www.sdl.hitachi.co.jp/crypto/mof/index-e.html

    Scalar multiplication precomputation with "conjugate addition" inspired by
    Longa-Gebotys paper "Novel Precomputation Schemes for Elliptic Curve Cryptosystems" (2008)
*/

/*
    Twisted Edwards E(p) Curve: a * x^2 + y^2 = 1 + d * x^2 * y^2, a = -1, p = 2^256 - c, c small

    Edwards coordinates: (X : Y : Z)
    Extended Edwards coordinates: (X : Y : T : Z), T = XY
    Edwards to Extended Edwards: (X : Y : Z) -> (XZ : YZ : XY : ZZ)
    Extended Edwards to Edwards: (X : Y : T : Z) -> (X : Y : Z)

    -(X : Y : T : Z) = (-X : Y : -T : Z)

    Additive Identity element: X = 0

    When Z = 1, a multiplication can be omitted

    Mixing operations for more speed:
        doubling, doubling -> E = 2E
        doubling, add      -> Ee = 2E, E = Ee + Ee
*/

#ifndef CAT_BIG_TWISTED_EDWARDS_HPP
#define CAT_BIG_TWISTED_EDWARDS_HPP

#include <cat/math/BigPseudoMersenne.hpp>
#include <cat/rand/IRandom.hpp>

namespace cat {


class BigTwistedEdwards : public BigPseudoMersenne
{
    static const int POINT_REGS = 4;
    static const int XOFF = 0;
    int YOFF, TOFF, ZOFF, POINT_STRIDE;

    // Point multiplication default window
    static const int WINDOW_BITS = 6;
    static const int PRECOMP_POINTS = 1 << (WINDOW_BITS-1);
    static const int PRECOMP_NEG_OFFSET = PRECOMP_POINTS / 2;

    static const int TE_OVERHEAD = (1 + PRECOMP_POINTS) * POINT_REGS + 9 + POINT_REGS * 2;
    int te_regs;

    // Local workspace
    Leg *A, *B, *C, *D, *E, *F, *G, *H, *CurveQ, *Generator;
    Leg *TempPt;

protected:
    Leg curve_d;

    // Simultaneous Add and Subtract for efficient precomputation (A +/- B) in 14M 1D 11a (versus 16M 2D 16a)
    void PtPrecompAddSub(const Leg *in_a, const Leg *in_b, Leg *sum, Leg *diff, int neg_offset);

public:
    BigTwistedEdwards(int regs, int bits, int C, int D, const u8 *Q, const u8 *GenPt);

    int PtLegs() { return Legs() * POINT_REGS; }

	Leg GetCurveD() { return curve_d; }
	const Leg *GetCurveQ() { return CurveQ; }
	const Leg *GetGenerator() { return Generator; }

public:
    // Unpack an Extended Projective point (X,Y,T,Z) from affine point (x,y)
    void PtUnpack(Leg *inout);

	// Set a point to the identity
	void PtIdentity(Leg *inout);

	// Check if the affine point (x,y) is the additive identity x=0
	bool IsAffineIdentity(const Leg *in);

public:
    void PtCopy(const Leg *in, Leg *out);

    // Fill the X coordinate of the point with a random value
    void PtFillRandomX(IRandom *prng, Leg *out);

    // Generate a random point on the curve that is not part of a small subgroup
    void PtGenerate(IRandom *prng, Leg *out);

public:
    // Solve for Y given the X point on a curve
    void PtSolveAffineY(Leg *inout);

    // Verify that the point (x,y) exists on the given curve
    bool PtValidAffine(const Leg *in);

public:
    // out(x) = X/Z
    void SaveAffineX(const Leg *in, void *out_x);

    // out(x,y) = (X/Z,Y/Z)
    void SaveAffineXY(const Leg *in, void *out_x, void *out_y);

    // out(X,Y) = (X,Y) without attempting to convert to affine from projective
    void SaveProjectiveXY(const Leg *in, void *out_x, void *out_y);

    // out(X,Y,Z,T) = (in_x,in_y), returns false if the coordinates are invalid
    bool LoadVerifyAffineXY(const void *in_x, const void *in_y, Leg *out);

    // Compute affine coordinates for (X,Y), set Z=1, and compute T = xy
    void PtNormalize(const Leg *in, Leg *out);

public:
    // Extended Twisted Edwards Negation Formula
    void PtNegate(const Leg *in, Leg *out);

    // Extended Twisted Edwards Unified Addition Formula (works when both inputs are the same) in 8M 1D 9a
    void PtEAdd(const Leg *in_a, const Leg *in_b, Leg *out);
    void PtAdd(const Leg *in_a, const Leg *in_b, Leg *out); // -1M, cannot be followed by PtAdd

    // Extended Twisted Edwards Unified Subtraction Formula (works when both inputs are the same) in 8M 1D 9a
    void PtESubtract(const Leg *in_a, const Leg *in_b, Leg *out);
    void PtSubtract(const Leg *in_a, const Leg *in_b, Leg *out); // -1M, cannot be followed by PtAdd

    // Extended Twisted Edwards Dedicated Doubling Formula in 4M 4S 5a
    void PtEDouble(const Leg *in, Leg *out);
    void PtDouble(const Leg *in, Leg *out); // -1M, cannot be followed by PtAdd

    // Extended Twisted Edwards Dedicated Doubling Formula Assuming Z=1, in 4M 3S 4a
    void PtEDoubleZ1(const Leg *in, Leg *out);
    void PtDoubleZ1(const Leg *in, Leg *out); // -1M, cannot be followed by PtAdd

public:
    // Allocate a table for use with PtMultiplyPrecomp()
    // Free the table with Aligned::Delete()
    Leg *PtMultiplyPrecompAlloc(int w);

    // Precompute odd multiples of input point
    void PtMultiplyPrecomp(const Leg *in, int w, Leg *table);

public:
    // Extended Twisted Edwards Scalar Multiplication k*p
    // Requires precomputation with PtMultiplyPrecomp()
    // CAN *NOT* BE followed by a Pt[E]Add()
    void PtMultiply(const Leg *in_precomp, int w, const Leg *in_k, u8 msb_k, Leg *out);

    // Extended Twisted Edwards Scalar Multiplication k*p
    // Uses default precomputation
    // CAN *NOT* BE followed by a Pt[E]Add()
    void PtMultiply(const Leg *in_p, const Leg *in_k, u8 msb_k, Leg *out);

    // A reference multiplier to verify that PtMultiply() is functionally the same
    void RefMul(const Leg *in_p, const Leg *in_k, u8 msb_k, Leg *out);

public:
    // Extended Twisted Edwards Simultaneous Scalar Multiplication k*P + l*Q
    // Requires precomputation with PtMultiplyPrecomp()
    // CAN *NOT* BE followed by a Pt[E]Add()
    void PtSiMultiply(const Leg *precomp_p, const Leg *precomp_q, int w,
					  const Leg *in_k, u8 msb_k, const Leg *in_l, u8 msb_l, Leg *out);
};


} // namespace cat

#endif // CAT_BIG_TWISTED_EDWARDS_HPP