text: /*
   * RELIC is an Efficient LIbrary for Cryptography
   * Copyright (C) 2007-2017 RELIC Authors
   *
   * This file is part of RELIC. RELIC is legal property of its developers,
   * whose names are not listed here. Please refer to the COPYRIGHT file
   * for contact information.
   *
   * RELIC is free software; you can redistribute it and/or
   * modify it under the terms of the GNU Lesser General Public
   * License as published by the Free Software Foundation; either
   * version 2.1 of the License, or (at your option) any later version.
   *
   * RELIC is distributed in the hope that it will be useful,
   * but WITHOUT ANY WARRANTY; without even the implied warranty of
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
   * Lesser General Public License for more details.
   *
   * You should have received a copy of the GNU Lesser General Public License
   * along with RELIC. If not, see <http://www.gnu.org/licenses/>.
   */
  
  /**
   * @file
   *
   * Implementation of point doubling on binary elliptic curves.
   *
   * @ingroup eb
   */
  
  #include <string.h>
  
  #include <relic_core.h>
  #include <relic_eb.h>
  
  /*============================================================================*/
  /* Private definitions                                                        */
  /*============================================================================*/
  
  #if EB_ADD == BASIC || !defined(STRIP)
  
  /**
   * Doubles a point represented in affine coordinates on an ordinary binary
   * elliptic curve.
   *
   * @param[out] r				- the result.
   * @param[in] p					- the point to double.
   */
  static void eb_dbl_basic_imp(eb_t r, const eb_t p) {
  	fb_t t0, t1, t2;
  
  	fb_null(t0);
  	fb_null(t1);
  	fb_null(t2);
  
  	TRY {
  		fb_new(t0);
  		fb_new(t1);
  		fb_new(t2);
  
  		/* t0 = 1/x1. */
  		fb_inv(t0, p->x);
  		/* t0 = y1/x1. */
  		fb_mul(t0, t0, p->y);
  		/* t0 = lambda = x1 + y1/x1. */
  		fb_add(t0, t0, p->x);
  		/* t1 = lambda^2. */
  		fb_sqr(t1, t0);
  		/* t2 = lambda^2 + lambda. */
  		fb_add(t2, t1, t0);
  
  		/* t2 = lambda^2 + lambda + a2. */
  		switch (eb_curve_opt_a()) {
  			case OPT_ZERO:
  				break;
  			case OPT_ONE:
  				fb_add_dig(t2, t2, (dig_t)1);
  				break;
  			case OPT_DIGIT:
  				fb_add_dig(t2, t2, eb_curve_get_a()[0]);
  				break;
  			default:
  				fb_add(t2, t2, eb_curve_get_a());
  				break;
  		}
  
  		/* t1 = x1 + x3. */
  		fb_add(t1, t2, p->x);
  
  		/* t1 = lambda * (x1 + x3). */
  		fb_mul(t1, t0, t1);
  
  		fb_copy(r->x, t2);
  		/* y3 = lambda * (x1 + x3) + x3 + y1. */
  		fb_add(t1, t1, r->x);
  		fb_add(r->y, t1, p->y);
  
  		fb_copy(r->z, p->z);
  
  		r->norm = 1;
  	}
  	CATCH_ANY {
  		THROW(ERR_CAUGHT);
  	}
  	FINALLY {
  		fb_free(t0);
  		fb_free(t1);
  		fb_free(t2);
  	}
  }
  
  #endif /* EB_ADD == BASIC */
  
  #if EB_ADD == PROJC || !defined(STRIP)
  
  /**
   * Doubles a point represented in projective coordinates on an ordinary binary
   * elliptic curve.
   *
   * @param[out] r				- the result.
   * @param[in] p					- the point to double.
   */
  static void eb_dbl_projc_imp(eb_t r, const eb_t p) {
  	fb_t t0, t1;
  
  	fb_null(t0);
  	fb_null(t1);
  
  	TRY {
  		fb_new(t0);
  		fb_new(t1);
  
  		/* t0 = B = x1^2. */
  		fb_sqr(t0, p->x);
  		/* C = B + y1. */
  		fb_add(r->y, t0, p->y);
  
  		if (!p->norm) {
  			/* A = x1 * z1. */
  			fb_mul(t1, p->x, p->z);
  			/* z3 = A^2. */
  			fb_sqr(r->z, t1);
  		} else {
  			/* if z1 = 1, A = x1. */
  			fb_copy(t1, p->x);
  			/* if z1 = 1, z3 = x1^2. */
  			fb_copy(r->z, t0);
  		}
  
  		/* t1 = D = A * C. */
  		fb_mul(t1, t1, r->y);
  
  		/* C^2 + D. */
  		fb_sqr(r->y, r->y);
  		fb_add(r->x, t1, r->y);
  
  		/* C^2 + D + a2 * z3. */
  		switch (eb_curve_opt_a()) {
  			case OPT_ZERO:
  				break;
  			case OPT_ONE:
  				fb_add(r->x, r->z, r->x);
  				break;
  			case OPT_DIGIT:
  				fb_mul_dig(r->y, r->z, eb_curve_get_a()[0]);
  				fb_add(r->x, r->y, r->x);
  				break;
  			default:
  				fb_mul(r->y, r->z, eb_curve_get_a());
  				fb_add(r->x, r->y, r->x);
  				break;
  		}
  
  		/* t1 = (D + z3). */
  		fb_add(t1, t1, r->z);
  		/* t0 = B^2. */
  		fb_sqr(t0, t0);
  		/* t0 = B^2 * z3. */
  		fb_mul(t0, t0, r->z);
  		/* y3 = (D + z3) * r3 + B^2 * z3. */
  		fb_mul(r->y, t1, r->x);
  		fb_add(r->y, r->y, t0);
  
  		r->norm = 0;
  	}
  	CATCH_ANY {
  		THROW(ERR_CAUGHT);
  	}
  	FINALLY {
  		fb_free(t0);
  		fb_free(t1);
  	}
  }
  
  #endif /* EB_ADD == PROJC */
  
  /*============================================================================*/
  /* Public definitions                                                         */
  /*============================================================================*/
  
  #if EB_ADD == BASIC || !defined(STRIP)
  
  void eb_dbl_basic(eb_t r, const eb_t p) {
  	if (eb_is_infty(p)) {
  		eb_set_infty(r);
  		return;
  	}
  
  	eb_dbl_basic_imp(r, p);
  }
  
  #endif
  
  #if EB_ADD == PROJC || !defined(STRIP)
  
  void eb_dbl_projc(eb_t r, const eb_t p) {
  
  	if (eb_is_infty(p)) {
  		eb_set_infty(r);
  		return;
  	}
  
  	eb_dbl_projc_imp(r, p);
  }
  
  #endif
  