| /* |
| * Copyright (C) 2012 Werner Dittmann |
| * All rights reserved. For licensing and other legal details, see the file legal.c. |
| * |
| * @author Werner Dittmann <Werner.Dittmann@t-online.de> |
| * |
| */ |
| #ifndef _EC_H_ |
| #define _EC_H_ |
| |
| #include <bn.h> |
| |
| /** |
| * @file ec.h |
| * @brief Elliptic curve functions for bnlib |
| * @defgroup BNLIB_EC Elliptic curve functions |
| * @{ |
| */ |
| |
| #ifdef __cplusplus |
| extern "C" |
| { |
| #endif |
| |
| typedef struct BigNum BigNum; |
| |
| typedef enum { |
| NIST192P = 1, |
| NIST224P = 2, |
| NIST256P = 3, |
| NIST384P = 4, |
| NIST521P = 5, |
| Curve25519 = 10, |
| Curve3617 = 11 |
| } Curves; |
| |
| /** |
| * \brief This structure contains the x, y affine coordinates and the z value if we |
| * use projective coordinates during EC point arithmetic. |
| */ |
| typedef struct _EcPoint { |
| BigNum *x, *y, *z; |
| BigNum tx, ty, tz; |
| } EcPoint; |
| |
| /** |
| * @brief This structure contains the value of EC curves over Prime Fields. |
| * |
| * The for NIST curves the field names correspond to the variable names defined in |
| * NIST FIPS 186-3, E.1.2. The <b>a</b> curve parameter is the constant -3 and is |
| * computed during initialization of the curve structure. |
| * |
| * For other curves, for example curve3917 we have less parameters to fill in, mostly |
| * the prime number, the base point, etc. Refer to the curve's initialization function |
| * about the use of the fileds. |
| */ |
| struct EcCurve; |
| struct EcCurve { |
| Curves id; |
| BigNum _p; |
| BigNum _n; |
| BigNum _SEED; |
| BigNum _c; |
| BigNum _a; |
| BigNum _b; |
| BigNum _Gx; |
| BigNum _Gy; |
| /* Pointers to the BigNum structures, for better readability mainly */ |
| BigNum *p; |
| BigNum *n; |
| BigNum *SEED; |
| BigNum *c; |
| BigNum *a; |
| BigNum *b; |
| BigNum *Gx; |
| BigNum *Gy; |
| /* some scratch pad variables, the EC algorithms use them to |
| avoid to much memory allocation/deallocatio0n overhead */ |
| BigNum _S1, _U1, _H, _R, _t0, _t1, _t2, _t3; |
| BigNum *S1, *U1, *H, *R, *t0, *t1, *t2, *t3; |
| int (*affineOp)(const struct EcCurve *curve, EcPoint *R, const EcPoint *P); |
| int (*doubleOp)(const struct EcCurve *curve, EcPoint *R, const EcPoint *P); |
| int (*addOp)(const struct EcCurve *curve, EcPoint *R, const EcPoint *P, const EcPoint *Q); |
| int (*modOp)(BigNum *, const BigNum *, const BigNum *); |
| int (*checkPubOp)(const struct EcCurve *curve, const EcPoint *pub); |
| int (*randomOp)(const struct EcCurve *curve, BigNum *d); |
| int (*mulScalar)(const struct EcCurve *curve, EcPoint *R, const EcPoint *P, const BigNum *scalar); |
| |
| }; |
| |
| typedef struct EcCurve EcCurve; |
| typedef EcCurve NistECpCurve; |
| |
| /** |
| * \brief Marco to initialize a EC point structure. |
| * |
| * \param P Address of the EC point structure |
| */ |
| #define INIT_EC_POINT(P) {EcPoint *e = P; e->x = &e->tx; e->y = &e->ty; e->z = &e->tz; bnBegin(e->x); bnBegin(e->y); bnBegin(e->z);} |
| |
| /** |
| * \brief Marco to free a EC point structure. |
| * |
| * \param P Address of the EC point structure |
| */ |
| #define FREE_EC_POINT(P) {EcPoint *e = P; bnEnd(e->x); bnEnd(e->y); bnEnd(e->z);} |
| |
| /** |
| * \brief Marco to set a EC point structure to the curve's base point. |
| * |
| * \param C Address of the NistECpCurve structure. |
| * |
| * \param P Address of the EC point structure. |
| */ |
| #define SET_EC_BASE_POINT(C, P) {EcPoint *e = P; const EcCurve *c = C; bnCopy(e->x, c->Gx); bnCopy(e->y, c->Gy); bnSetQ(e->z, 1);} |
| |
| /* |
| * EC point helper functions |
| */ |
| extern void ecInitPoint(EcPoint *P); |
| |
| extern void ecFreePoint(EcPoint *P); |
| |
| extern void ecSetBasePoint(EcCurve *C, EcPoint *P); |
| |
| /** |
| * \brief Get NIST EC curve parameters. |
| * |
| * Before reusing a EC curve structure make sure to call ecFreeCurveNistECp |
| * to return memory. |
| * |
| * \param curveId Which curve to initialize |
| * |
| * \param curve Pointer to a EcCurve structure |
| * |
| * \return 0 if successful |
| * |
| * \note Call ecFreeCurveNistECp to return allocated memory. |
| */ |
| int ecGetCurveNistECp(Curves curveId, NistECpCurve *curve); |
| |
| |
| /** |
| * \brief Free EC curve parameters. |
| * |
| * \param curve Pointer to a EcCurve structure |
| * |
| * \note Curve parameters must be initialized calling ecGetCurveNistECp. |
| */ |
| void ecFreeCurveNistECp(EcCurve *curve); |
| |
| /** |
| * \brief Double an EC point. |
| * |
| * This function uses affine coordinates to perform the computations. For |
| * further reference see RFC 6090 or the standard work <i>Guide to Elliptic |
| * Curve Cryptography</i>. |
| * |
| * \param curve Address of EC curve structure |
| * \param R Address of resulting EC point structure |
| * \param P Address of the EC point structure |
| * |
| * \return 0 if successful |
| */ |
| int ecDoublePoint(const EcCurve *curve, EcPoint *R, const EcPoint *P); |
| |
| /** |
| * \brief Add two EC points. |
| * |
| * This function uses affine coordinates to perform the computations. For |
| * further reference see RFC 6090 or the standard work <i>Guide to Elliptic |
| * Curve Cryptography</i>. |
| * |
| * \param curve Address of EC curve structure |
| * \param R Address of resulting EC point structure |
| * \param P Address of the first EC point structure |
| * \param Q Address of the second EC point structure |
| * |
| * \return 0 if successful |
| */ |
| int ecAddPoint(const EcCurve *curve, EcPoint *R, const EcPoint *P, const EcPoint *Q); |
| |
| /** |
| * \brief Mulitply an EC point with a scalar value. |
| * |
| * \param curve Address of EC curve structure |
| * \param R Address of resulting EC point structure |
| * \param P Address of the EC point structure |
| * \param scalar Address of the scalar multi-precision integer value |
| * |
| * \return 0 if successful |
| */ |
| int ecMulPointScalar(const EcCurve *curve, EcPoint *R, const EcPoint *P, const BigNum *scalar); |
| |
| /** |
| * \brief Convert an EC point from Jacobian projective coordinates to normal affine x/y coordinates. |
| * |
| * \param curve Address of EC curve structure |
| * \param R Address of EC point structure that receives the x/y coordinates |
| * \param P Address of the EC point structure that contains the jacobian x/y/z coordinates. |
| * |
| * \return 0 if successful |
| */ |
| int ecGetAffine(const EcCurve *curve, EcPoint *R, const EcPoint *P); |
| |
| /** |
| * @brief Generate a random number. |
| * |
| * The method generates a random number and checks if it matches the curve restricitions. |
| * Use this number as ECDH private key. |
| * |
| * @param curve the NIST curve to use. |
| * |
| * @param d receives the generated random number. |
| */ |
| int ecGenerateRandomNumber(const NistECpCurve *curve, BigNum *d); |
| |
| /** |
| * @brief Check a public key. |
| * |
| * The method checks if a public key is valid. For NIST curves it uses the |
| * ECC Partial Validation, NIST SP800-56A section 5.6.2.6 |
| * |
| * For other curves it computes the equation and compares the left hand and |
| * the right handresults. If they are equal the point is on the curve. |
| * |
| * @param curve the curve to use. |
| * |
| * @param pub the public key to check. |
| * |
| * @returns true (!0) if the check was ok, false (0) otherwise. |
| * |
| * @note The function uses some scratch pad variable of the NistECpCurve structure. |
| */ |
| int ecCheckPubKey(const EcCurve *curve, const EcPoint *pub); |
| |
| int ecGetCurvesCurve(Curves curveId, EcCurve *curve); |
| |
| void ecFreeCurvesCurve(EcCurve *curve); |
| |
| /** |
| * This is a special function for DJB's curve 25519. Actually it's the scalar multiplication |
| * mypublic = basepoint * secret |
| */ |
| int curve25519_donna(unsigned char *mypublic, const unsigned char *secret, const unsigned char *basepoint); |
| |
| /* |
| * Some additional functions that are not available in bnlib |
| */ |
| int bnAddMod_ (struct BigNum *rslt, struct BigNum *n1, struct BigNum *mod); |
| |
| int bnAddQMod_ (struct BigNum *rslt, unsigned n1, struct BigNum *mod); |
| |
| int bnSubMod_ (struct BigNum *rslt, struct BigNum *n1, struct BigNum *mod); |
| |
| int bnSubQMod_ (struct BigNum *rslt, unsigned n1, struct BigNum *mod); |
| |
| int bnMulMod_ (struct BigNum *rslt, struct BigNum *n1, struct BigNum *n2, struct BigNum *mod, const EcCurve *curve); |
| |
| int bnMulQMod_ (struct BigNum *rslt, struct BigNum *n1, unsigned n2, struct BigNum *mod, const EcCurve *curve); |
| |
| int bnSquareMod_ (struct BigNum *rslt, struct BigNum *n1, struct BigNum *mod, const EcCurve *curve); |
| |
| #ifdef __cplusplus |
| } |
| #endif |
| |
| /** |
| * @} |
| */ |
| |
| #endif |