lib/mpi: Introduce ec implementation to MPI library

The implementation of EC is introduced from libgcrypt as the
basic algorithm of elliptic curve, which can be more perfectly
integrated with MPI implementation.
Some other algorithms will be developed based on mpi ecc, such as SM2.

Signed-off-by: Tianjia Zhang <tianjia.zhang@linux.alibaba.com>
Tested-by: Xufeng Zhang <yunbo.xufeng@linux.alibaba.com>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>

include/linux/mpi.h

@@ -157,6 +157,111 @@ void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor);
 /*-- mpi-inv.c --*/
 int mpi_invm(MPI x, MPI a, MPI n);
 
+/*-- ec.c --*/
+
+/* Object to represent a point in projective coordinates */
+struct gcry_mpi_point {
+	MPI x;
+	MPI y;
+	MPI z;
+};
+
+typedef struct gcry_mpi_point *MPI_POINT;
+
+/* Models describing an elliptic curve */
+enum gcry_mpi_ec_models {
+	/* The Short Weierstrass equation is
+	 *      y^2 = x^3 + ax + b
+	 */
+	MPI_EC_WEIERSTRASS = 0,
+	/* The Montgomery equation is
+	 *      by^2 = x^3 + ax^2 + x
+	 */
+	MPI_EC_MONTGOMERY,
+	/* The Twisted Edwards equation is
+	 *      ax^2 + y^2 = 1 + bx^2y^2
+	 * Note that we use 'b' instead of the commonly used 'd'.
+	 */
+	MPI_EC_EDWARDS
+};
+
+/* Dialects used with elliptic curves */
+enum ecc_dialects {
+	ECC_DIALECT_STANDARD = 0,
+	ECC_DIALECT_ED25519,
+	ECC_DIALECT_SAFECURVE
+};
+
+/* This context is used with all our EC functions. */
+struct mpi_ec_ctx {
+	enum gcry_mpi_ec_models model; /* The model describing this curve. */
+	enum ecc_dialects dialect;     /* The ECC dialect used with the curve. */
+	int flags;                     /* Public key flags (not always used). */
+	unsigned int nbits;            /* Number of bits.  */
+
+	/* Domain parameters.  Note that they may not all be set and if set
+	 * the MPIs may be flaged as constant.
+	 */
+	MPI p;         /* Prime specifying the field GF(p).  */
+	MPI a;         /* First coefficient of the Weierstrass equation.  */
+	MPI b;         /* Second coefficient of the Weierstrass equation.  */
+	MPI_POINT G;   /* Base point (generator).  */
+	MPI n;         /* Order of G.  */
+	unsigned int h;       /* Cofactor.  */
+
+	/* The actual key.  May not be set.  */
+	MPI_POINT Q;   /* Public key.   */
+	MPI d;         /* Private key.  */
+
+	const char *name;      /* Name of the curve.  */
+
+	/* This structure is private to mpi/ec.c! */
+	struct {
+		struct {
+			unsigned int a_is_pminus3:1;
+			unsigned int two_inv_p:1;
+		} valid; /* Flags to help setting the helper vars below.  */
+
+		int a_is_pminus3;  /* True if A = P - 3. */
+
+		MPI two_inv_p;
+
+		mpi_barrett_t p_barrett;
+
+		/* Scratch variables.  */
+		MPI scratch[11];
+
+		/* Helper for fast reduction.  */
+		/*   int nist_nbits; /\* If this is a NIST curve, the # of bits. *\/ */
+		/*   MPI s[10]; */
+		/*   MPI c; */
+	} t;
+
+	/* Curve specific computation routines for the field.  */
+	void (*addm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
+	void (*subm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ec);
+	void (*mulm)(MPI w, MPI u, MPI v, struct mpi_ec_ctx *ctx);
+	void (*pow2)(MPI w, const MPI b, struct mpi_ec_ctx *ctx);
+	void (*mul2)(MPI w, MPI u, struct mpi_ec_ctx *ctx);
+};
+
+void mpi_ec_init(struct mpi_ec_ctx *ctx, enum gcry_mpi_ec_models model,
+			enum ecc_dialects dialect,
+			int flags, MPI p, MPI a, MPI b);
+void mpi_ec_deinit(struct mpi_ec_ctx *ctx);
+MPI_POINT mpi_point_new(unsigned int nbits);
+void mpi_point_release(MPI_POINT p);
+void mpi_point_init(MPI_POINT p);
+void mpi_point_free_parts(MPI_POINT p);
+int mpi_ec_get_affine(MPI x, MPI y, MPI_POINT point, struct mpi_ec_ctx *ctx);
+void mpi_ec_add_points(MPI_POINT result,
+			MPI_POINT p1, MPI_POINT p2,
+			struct mpi_ec_ctx *ctx);
+void mpi_ec_mul_point(MPI_POINT result,
+			MPI scalar, MPI_POINT point,
+			struct mpi_ec_ctx *ctx);
+int mpi_ec_curve_point(MPI_POINT point, struct mpi_ec_ctx *ctx);
+
 /* inline functions */
 
 /**

lib/mpi/Makefile

@@ -13,6 +13,7 @@ mpi-y = \
 	generic_mpih-rshift.o		\
 	generic_mpih-sub1.o		\
 	generic_mpih-add1.o		\
+	ec.o				\
 	mpicoder.o			\
 	mpi-add.o			\
 	mpi-bit.o			\