| #ifndef ECP_ZZZ_H |
| #define ECP_ZZZ_H |
| |
| #include "fp_YYY.h" |
| #include "config_curve_ZZZ.h" |
| |
| using namespace amcl; |
| |
| namespace ZZZ { |
| |
| /* Curve Params - see rom.c */ |
| extern const int CURVE_A; /**< Elliptic curve A parameter */ |
| extern const int CURVE_B_I; |
| extern const int CURVE_Cof_I; |
| extern const XXX::BIG CURVE_B; /**< Elliptic curve B parameter */ |
| extern const XXX::BIG CURVE_Order; /**< Elliptic curve group order */ |
| extern const XXX::BIG CURVE_Cof; /**< Elliptic curve cofactor */ |
| |
| /* Generator point on G1 */ |
| extern const XXX::BIG CURVE_Gx; /**< x-coordinate of generator point in group G1 */ |
| extern const XXX::BIG CURVE_Gy; /**< y-coordinate of generator point in group G1 */ |
| |
| |
| /* For Pairings only */ |
| |
| /* Generator point on G2 */ |
| extern const XXX::BIG CURVE_Pxa; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxb; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pya; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyb; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| |
| /*** needed for BLS24 curves ***/ |
| |
| extern const XXX::BIG CURVE_Pxaa; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxab; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxba; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxbb; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyaa; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyab; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyba; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pybb; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| |
| /*** needed for BLS48 curves ***/ |
| |
| extern const XXX::BIG CURVE_Pxaaa; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxaab; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxaba; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxabb; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxbaa; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxbab; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxbba; /**< real part of x-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pxbbb; /**< imaginary part of x-coordinate of generator point in group G2 */ |
| |
| extern const XXX::BIG CURVE_Pyaaa; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyaab; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyaba; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pyabb; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pybaa; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pybab; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pybba; /**< real part of y-coordinate of generator point in group G2 */ |
| extern const XXX::BIG CURVE_Pybbb; /**< imaginary part of y-coordinate of generator point in group G2 */ |
| |
| |
| |
| extern const XXX::BIG CURVE_Bnx; /**< BN curve x parameter */ |
| |
| extern const XXX::BIG CURVE_Cru; /**< BN curve Cube Root of Unity */ |
| |
| extern const XXX::BIG Fra; /**< real part of BN curve Frobenius Constant */ |
| extern const XXX::BIG Frb; /**< imaginary part of BN curve Frobenius Constant */ |
| |
| |
| extern const XXX::BIG CURVE_W[2]; /**< BN curve constant for GLV decomposition */ |
| extern const XXX::BIG CURVE_SB[2][2]; /**< BN curve constant for GLV decomposition */ |
| extern const XXX::BIG CURVE_WB[4]; /**< BN curve constant for GS decomposition */ |
| extern const XXX::BIG CURVE_BB[4][4]; /**< BN curve constant for GS decomposition */ |
| |
| |
| /** |
| @brief ECP structure - Elliptic Curve Point over base field |
| */ |
| |
| typedef struct |
| { |
| // int inf; /**< Infinity Flag - not needed for Edwards representation */ |
| |
| YYY::FP x; /**< x-coordinate of point */ |
| #if CURVETYPE_ZZZ!=MONTGOMERY |
| YYY::FP y; /**< y-coordinate of point. Not needed for Montgomery representation */ |
| #endif |
| YYY::FP z;/**< z-coordinate of point */ |
| } ECP; |
| |
| |
| /* ECP E(Fp) prototypes */ |
| /** @brief Tests for ECP point equal to infinity |
| * |
| @param P ECP point to be tested |
| @return 1 if infinity, else returns 0 |
| */ |
| extern int ECP_isinf(ECP *P); |
| /** @brief Tests for equality of two ECPs |
| * |
| @param P ECP instance to be compared |
| @param Q ECP instance to be compared |
| @return 1 if P=Q, else returns 0 |
| */ |
| extern int ECP_equals(ECP *P,ECP *Q); |
| /** @brief Copy ECP point to another ECP point |
| * |
| @param P ECP instance, on exit = Q |
| @param Q ECP instance to be copied |
| */ |
| extern void ECP_copy(ECP *P,ECP *Q); |
| /** @brief Negation of an ECP point |
| * |
| @param P ECP instance, on exit = -P |
| */ |
| extern void ECP_neg(ECP *P); |
| /** @brief Set ECP to point-at-infinity |
| * |
| @param P ECP instance to be set to infinity |
| */ |
| extern void ECP_inf(ECP *P); |
| /** @brief Calculate Right Hand Side of curve equation y^2=f(x) |
| * |
| Function f(x) depends on form of elliptic curve, Weierstrass, Edwards or Montgomery. |
| Used internally. |
| @param r BIG n-residue value of f(x) |
| @param x BIG n-residue x |
| */ |
| extern void ECP_rhs(YYY::FP *r,YYY::FP *x); |
| /** @brief Set ECP to point(x,y) given just x and sign of y |
| * |
| Point P set to infinity if no such point on the curve. If x is on the curve then y is calculated from the curve equation. |
| The correct y value (plus or minus) is selected given its sign s. |
| @param P ECP instance to be set (x,[y]) |
| @param x BIG x coordinate of point |
| @param s an integer representing the "sign" of y, in fact its least significant bit. |
| */ |
| extern int ECP_setx(ECP *P,XXX::BIG x,int s); |
| |
| #if CURVETYPE_ZZZ==MONTGOMERY |
| /** @brief Set ECP to point(x,[y]) given x |
| * |
| Point P set to infinity if no such point on the curve. Note that y coordinate is not needed. |
| @param P ECP instance to be set (x,[y]) |
| @param x BIG x coordinate of point |
| @return 1 if point exists, else 0 |
| */ |
| extern int ECP_set(ECP *P,XXX::BIG x); |
| /** @brief Extract x coordinate of an ECP point P |
| * |
| @param x BIG on exit = x coordinate of point |
| @param P ECP instance (x,[y]) |
| @return -1 if P is point-at-infinity, else 0 |
| */ |
| extern int ECP_get(XXX::BIG x,ECP *P); |
| /** @brief Adds ECP instance Q to ECP instance P, given difference D=P-Q |
| * |
| Differential addition of points on a Montgomery curve |
| @param P ECP instance, on exit =P+Q |
| @param Q ECP instance to be added to P |
| @param D Difference between P and Q |
| */ |
| extern void ECP_add(ECP *P,ECP *Q,ECP *D); |
| #else |
| /** @brief Set ECP to point(x,y) given x and y |
| * |
| Point P set to infinity if no such point on the curve. |
| @param P ECP instance to be set (x,y) |
| @param x BIG x coordinate of point |
| @param y BIG y coordinate of point |
| @return 1 if point exists, else 0 |
| */ |
| extern int ECP_set(ECP *P,XXX::BIG x,XXX::BIG y); |
| /** @brief Extract x and y coordinates of an ECP point P |
| * |
| If x=y, returns only x |
| @param x BIG on exit = x coordinate of point |
| @param y BIG on exit = y coordinate of point (unless x=y) |
| @param P ECP instance (x,y) |
| @return sign of y, or -1 if P is point-at-infinity |
| */ |
| extern int ECP_get(XXX::BIG x,XXX::BIG y,ECP *P); |
| /** @brief Adds ECP instance Q to ECP instance P |
| * |
| @param P ECP instance, on exit =P+Q |
| @param Q ECP instance to be added to P |
| */ |
| extern void ECP_add(ECP *P,ECP *Q); |
| /** @brief Subtracts ECP instance Q from ECP instance P |
| * |
| @param P ECP instance, on exit =P-Q |
| @param Q ECP instance to be subtracted from P |
| */ |
| extern void ECP_sub(ECP *P,ECP *Q); |
| #endif |
| /** @brief Converts an ECP point from Projective (x,y,z) coordinates to affine (x,y) coordinates |
| * |
| @param P ECP instance to be converted to affine form |
| */ |
| extern void ECP_affine(ECP *P); |
| /** @brief Formats and outputs an ECP point to the console, in projective coordinates |
| * |
| @param P ECP instance to be printed |
| */ |
| extern void ECP_outputxyz(ECP *P); |
| /** @brief Formats and outputs an ECP point to the console, converted to affine coordinates |
| * |
| @param P ECP instance to be printed |
| */ |
| extern void ECP_output(ECP * P); |
| |
| /** @brief Formats and outputs an ECP point to the console |
| * |
| @param P ECP instance to be printed |
| */ |
| extern void ECP_rawoutput(ECP * P); |
| |
| /** @brief Formats and outputs an ECP point to an octet string |
| * |
| The octet string is normally in the standard form 0x04|x|y |
| Here x (and y) are the x and y coordinates in left justified big-endian base 256 form. |
| For Montgomery curve it is 0x06|x |
| If c is true, only the x coordinate is provided as in 0x2|x if y is even, or 0x3|x if y is odd |
| @param c compression required, true or false |
| @param S output octet string |
| @param P ECP instance to be converted to an octet string |
| */ |
| extern void ECP_toOctet(octet *S,ECP *P,bool c); |
| /** @brief Creates an ECP point from an octet string |
| * |
| The octet string is normally in the standard form 0x04|x|y |
| Here x (and y) are the x and y coordinates in left justified big-endian base 256 form. |
| For Montgomery curve it is 0x06|x |
| If in compressed form only the x coordinate is provided as in 0x2|x if y is even, or 0x3|x if y is odd |
| @param P ECP instance to be created from the octet string |
| @param S input octet string |
| return 1 if octet string corresponds to a point on the curve, else 0 |
| */ |
| extern int ECP_fromOctet(ECP *P,octet *S); |
| /** @brief Doubles an ECP instance P |
| * |
| @param P ECP instance, on exit =2*P |
| */ |
| extern void ECP_dbl(ECP *P); |
| /** @brief Multiplies an ECP instance P by a small integer, side-channel resistant |
| * |
| @param P ECP instance, on exit =i*P |
| @param i small integer multiplier |
| @param b maximum number of bits in multiplier |
| */ |
| extern void ECP_pinmul(ECP *P,int i,int b); |
| /** @brief Multiplies an ECP instance P by a BIG, side-channel resistant |
| * |
| Uses Montgomery ladder for Montgomery curves, otherwise fixed sized windows. |
| @param P ECP instance, on exit =b*P |
| @param b BIG number multiplier |
| |
| */ |
| extern void ECP_mul(ECP *P,XXX::BIG b); |
| /** @brief Calculates double multiplication P=e*P+f*Q, side-channel resistant |
| * |
| @param P ECP instance, on exit =e*P+f*Q |
| @param Q ECP instance |
| @param e BIG number multiplier |
| @param f BIG number multiplier |
| */ |
| extern void ECP_mul2(ECP *P,ECP *Q,XXX::BIG e,XXX::BIG f); |
| |
| /** @brief Multiplies random point by co-factor |
| * |
| @param Q ECP multiplied by co-factor |
| */ |
| extern void ECP_cfp(ECP *Q); |
| |
| /** @brief Maps random BIG to curve point of correct order |
| * |
| @param Q ECP instance of correct order |
| @param w OCTET byte array to be mapped |
| */ |
| extern void ECP_mapit(ECP *Q,octet *w); |
| |
| /** @brief Get Group Generator from ROM |
| * |
| @param G ECP instance |
| */ |
| extern void ECP_generator(ECP *G); |
| |
| } |
| |
| #endif |