3 * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
5 * (c) 2017 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 #ifndef CATACOMB_FGOLDI_H
29 #define CATACOMB_FGOLDI_H
35 /*----- Header files ------------------------------------------------------*/
37 #include <mLib/bits.h>
39 #ifndef CATACOMB_QFARITH_H
43 /*----- Data structures ---------------------------------------------------*/
50 #if !defined(FGOLDI_IMPL) && defined(HAVE_INT64)
51 # define FGOLDI_IMPL 28
55 # define FGOLDI_IMPL 12
59 typedef int32 fgoldi_piece;
62 typedef int16 fgoldi_piece;
65 /*----- Functions provided ------------------------------------------------*/
67 /* --- @fgoldi_load@ --- *
69 * Arguments: @fgoldi *z@ = where to store the result
70 * @const octet xv[56]@ = source to read
74 * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
75 * external representation from @xv@ and stores it in @z@.
77 * External representation is little-endian base-256. Some
78 * elements have multiple encodings, which are not produced by
79 * correct software; use of noncanonical encodings is not an
80 * error, and toleration of them is considered a performance
84 extern void fgoldi_load(fgoldi */*z*/, const octet /*xv*/[56]);
86 /* --- @fgoldi_store@ --- *
88 * Arguments: @octet zv[56]@ = where to write the result
89 * @const fgoldi *x@ = the field element to write
93 * Use: Stores a field element in the given octet vector in external
94 * representation. A canonical encoding is always stored.
97 extern void fgoldi_store(octet /*zv*/[56], const fgoldi */*x*/);
99 /* --- @fgoldi_set@ --- *
101 * Arguments: @fgoldi *z@ = where to write the result
102 * @int a@ = a small-ish constant
106 * Use: Sets @z@ to equal @a@.
109 extern void fgoldi_set(fgoldi */*x*/, int /*a*/);
111 /* --- @fgoldi_add@ --- *
113 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
114 * @const fgoldi *x, *y@ = two operands
118 * Use: Set @z@ to the sum %$x + y$%.
121 extern void fgoldi_add(fgoldi */*z*/,
122 const fgoldi */*x*/, const fgoldi */*y*/);
124 /* --- @fgoldi_sub@ --- *
126 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
127 * @const fgoldi *x, *y@ = two operands
131 * Use: Set @z@ to the difference %$x - y$%.
134 extern void fgoldi_sub(fgoldi */*z*/,
135 const fgoldi */*x*/, const fgoldi */*y*/);
137 /* --- @fgoldi_neg@ --- *
139 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
140 * @const fgoldi *x@ = an operand
147 extern void fgoldi_neg(fgoldi */*z*/, const fgoldi */*x*/);
149 /* --- @fgoldi_pick2@ --- *
151 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
152 * @const fgoldi *x, *y@ = two operands
153 * @uint32 m@ = a mask
157 * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
158 * @z = x@. If @m@ has some other value, then scramble @z@ in
162 extern void fgoldi_pick2(fgoldi */*z*/,
163 const fgoldi */*x*/, const fgoldi */*y*/,
166 /* --- @fgoldi_pickn@ --- *
168 * Arguments: @fgoldi *z@ = where to put the result
169 * @const fgoldi *v@ = a table of entries
170 * @size_t n@ = the number of entries in @v@
171 * @size_t i@ = an index
175 * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
176 * do something unhelpful; otherwise, if @i >= n@ then set @z@
180 extern void fgoldi_pickn(fgoldi */*z*/,
181 const fgoldi */*v*/, size_t /*n*/, size_t /*i*/);
183 /* --- @fgoldi_condswap@ --- *
185 * Arguments: @fgoldi *x, *y@ = two operands
186 * @uint32 m@ = a mask
190 * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
191 * exchange @x@ and @y@. If @m@ has some other value, then
192 * scramble @x@ and @y@ in an unhelpful way.
195 extern void fgoldi_condswap(fgoldi */*x*/, fgoldi */*y*/, uint32 /*m*/);
197 /* --- @fgoldi_condneg@ --- *
199 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
200 * @const fgoldi *x@ = an operand
201 * @uint32 m@ = a mask
205 * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
206 * @z = -x@. If @m@ has some other value then scramble @z@ in
210 extern void fgoldi_condneg(fgoldi */*z*/, const fgoldi */*x*/, uint32 /*m*/);
212 /* --- @fgoldi_mulconst@ --- *
214 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
215 * @const fgoldi *x@ = an operand
216 * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
220 * Use: Set @z@ to the product %$a x$%.
223 extern void fgoldi_mulconst(fgoldi */*z*/, const fgoldi */*x*/, long /*a*/);
225 /* --- @fgoldi_mul@ --- *
227 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
228 * @const fgoldi *x, *y@ = two operands
232 * Use: Set @z@ to the product %$x y$%.
235 extern void fgoldi_mul(fgoldi */*z*/,
236 const fgoldi */*x*/, const fgoldi */*y*/);
238 /* --- @fgoldi_sqr@ --- *
240 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
241 * @const fgoldi *x@ = an operand
245 * Use: Set @z@ to the square %$x^2$%.
248 extern void fgoldi_sqr(fgoldi */*z*/, const fgoldi */*x*/);
250 /* --- @fgoldi_inv@ --- *
252 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
253 * @const fgoldi *x@ = an operand
257 * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
258 * %$x = 0$% then @z@ is set to zero. This is considered a
262 extern void fgoldi_inv(fgoldi */*z*/, const fgoldi */*x*/);
264 /* --- @fgoldi_quosqrt@ --- *
266 * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
267 * @const fgoldi *x, *y@ = two operands
269 * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
271 * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
272 * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
273 * \ne 0$% then the operation fails. If you wanted a specific
274 * square root then you'll have to pick it yourself.
277 extern int fgoldi_quosqrt(fgoldi */*z*/,
278 const fgoldi */*x*/, const fgoldi */*y*/);
280 /*----- That's all, folks -------------------------------------------------*/