math/fgoldi.[ch]: Implement the extra operations needed for Ed448.

[catacomb] / math / fgoldi.h

/* -*-c-*-
 *
 * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
 *
 * (c) 2017 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------*
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 *
 * Catacomb 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 Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

#ifndef CATACOMB_FGOLDI_H
#define CATACOMB_FGOLDI_H

#ifdef __cplusplus
  extern "C" {
#endif

/*----- Header files ------------------------------------------------------*/

#include <mLib/bits.h>

#ifndef CATACOMB_QFARITH_H
#  include "qfarith.h"
#endif

/*----- Data structures ---------------------------------------------------*/

typedef union {
  int32 p28[16];
  int16 p12[40];
} fgoldi;

#if !defined(FGOLDI_IMPL) && defined(HAVE_INT64)
#  define FGOLDI_IMPL 28
#endif

#ifndef FGOLDI_IMPL
#  define FGOLDI_IMPL 12
#endif

#if FGOLDI_IMPL == 28
  typedef int32 fgoldi_piece;
#endif
#if FGOLDI_IMPL == 12
  typedef int16 fgoldi_piece;
#endif

/*----- Functions provided ------------------------------------------------*/

/* --- @fgoldi_load@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to store the result
 *		@const octet xv[56]@ = source to read
 *
 * Returns:	---
 *
 * Use:		Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
 *		external representation from @xv@ and stores it in @z@.
 *
 *		External representation is little-endian base-256.  Some
 *		elements have multiple encodings, which are not produced by
 *		correct software; use of noncanonical encodings is not an
 *		error, and toleration of them is considered a performance
 *		feature.
 */

extern void fgoldi_load(fgoldi */*z*/, const octet /*xv*/[56]);

/* --- @fgoldi_store@ --- *
 *
 * Arguments:	@octet zv[56]@ = where to write the result
 *		@const fgoldi *x@ = the field element to write
 *
 * Returns:	---
 *
 * Use:		Stores a field element in the given octet vector in external
 *		representation.  A canonical encoding is always stored.
 */

extern void fgoldi_store(octet /*zv*/[56], const fgoldi */*x*/);

/* --- @fgoldi_set@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to write the result
 *		@int a@ = a small-ish constant
 *
 * Returns:	---
 *
 * Use:		Sets @z@ to equal @a@.
 */

extern void fgoldi_set(fgoldi */*x*/, int /*a*/);

/* --- @fgoldi_add@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x, *y@ = two operands
 *
 * Returns:	---
 *
 * Use:		Set @z@ to the sum %$x + y$%.
 */

extern void fgoldi_add(fgoldi */*z*/,
		       const fgoldi */*x*/, const fgoldi */*y*/);

/* --- @fgoldi_sub@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x, *y@ = two operands
 *
 * Returns:	---
 *
 * Use:		Set @z@ to the difference %$x - y$%.
 */

extern void fgoldi_sub(fgoldi */*z*/,
		       const fgoldi */*x*/, const fgoldi */*y*/);

/* --- @fgoldi_neg@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@)
 *		@const fgoldi *x@ = an operand
 *
 * Returns:	---
 *
 * Use:		Set @z = -x@.
 */

extern void fgoldi_neg(fgoldi */*z*/, const fgoldi */*x*/);

/* --- @fgoldi_pick2@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x, *y@ = two operands
 *		@uint32 m@ = a mask
 *
 * Returns:	---
 *
 * Use:		If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
 *		@z = x@.  If @m@ has some other value, then scramble @z@ in
 *		an unhelpful way.
 */

extern void fgoldi_pick2(fgoldi */*z*/,
			 const fgoldi */*x*/, const fgoldi */*y*/,
			 uint32 /*m*/);

/* --- @fgoldi_pickn@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result
 *		@const fgoldi *v@ = a table of entries
 *		@size_t n@ = the number of entries in @v@
 *		@size_t i@ = an index
 *
 * Returns:	---
 *
 * Use:		If @0 <= i < n < 32@ then set @z = v[i]@.  If @n >= 32@ then
 *		do something unhelpful; otherwise, if @i >= n@ then set @z@
 *		to zero.
 */

extern void fgoldi_pickn(fgoldi */*z*/,
			 const fgoldi */*v*/, size_t /*n*/, size_t /*i*/);

/* --- @fgoldi_condswap@ --- *
 *
 * Arguments:	@fgoldi *x, *y@ = two operands
 *		@uint32 m@ = a mask
 *
 * Returns:	---
 *
 * Use:		If @m@ is zero, do nothing; if @m@ is all-bits-set, then
 *		exchange @x@ and @y@.  If @m@ has some other value, then
 *		scramble @x@ and @y@ in an unhelpful way.
 */

extern void fgoldi_condswap(fgoldi */*x*/, fgoldi */*y*/, uint32 /*m*/);

/* --- @fgoldi_condneg@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@)
 *		@const fgoldi *x@ = an operand
 *		@uint32 m@ = a mask
 *
 * Returns:	---
 *
 * Use:		If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
 *		@z = -x@.  If @m@ has some other value then scramble @z@ in
 *		an unhelpful way.
 */

extern void fgoldi_condneg(fgoldi */*z*/, const fgoldi */*x*/, uint32 /*m*/);

/* --- @fgoldi_mulconst@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@)
 *		@const fgoldi *x@ = an operand
 *		@long a@ = a small-ish constant; %$|a| < 2^{20}$%.
 *
 * Returns:	---
 *
 * Use:		Set @z@ to the product %$a x$%.
 */

extern void fgoldi_mulconst(fgoldi */*z*/, const fgoldi */*x*/, long /*a*/);

/* --- @fgoldi_mul@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x, *y@ = two operands
 *
 * Returns:	---
 *
 * Use:		Set @z@ to the product %$x y$%.
 */

extern void fgoldi_mul(fgoldi */*z*/,
		       const fgoldi */*x*/, const fgoldi */*y*/);

/* --- @fgoldi_sqr@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x@ = an operand
 *
 * Returns:	---
 *
 * Use:		Set @z@ to the square %$x^2$%.
 */

extern void fgoldi_sqr(fgoldi */*z*/, const fgoldi */*x*/);

/* --- @fgoldi_inv@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@)
 *		@const fgoldi *x@ = an operand
 *
 * Returns:	---
 *
 * Use:		Stores in @z@ the multiplicative inverse %$x^{-1}$%.  If
 *		%$x = 0$% then @z@ is set to zero.  This is considered a
 *		feature.
 */

extern void fgoldi_inv(fgoldi */*z*/, const fgoldi */*x*/);

/* --- @fgoldi_quosqrt@ --- *
 *
 * Arguments:	@fgoldi *z@ = where to put the result (may alias @x@ or @y@)
 *		@const fgoldi *x, *y@ = two operands
 *
 * Returns:	Zero if successful, @-1@ if %$x/y$% is not a square.
 *
 * Use:		Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
 *		If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
 *		\ne 0$% then the operation fails.  If you wanted a specific
 *		square root then you'll have to pick it yourself.
 */

extern int fgoldi_quosqrt(fgoldi */*z*/,
			  const fgoldi */*x*/, const fgoldi */*y*/);

/*----- That's all, folks -------------------------------------------------*/

#ifdef __cplusplus
  }
#endif

#endif