FreeBSD/Linux Kernel Cross Reference
sys/opencrypto/gfmult.c

     /*-
      * Copyright (c) 2014 The FreeBSD Foundation
      * All rights reserved.
      *
      * This software was developed by John-Mark Gurney under
      * the sponsorship of the FreeBSD Foundation and
      * Rubicon Communications, LLC (Netgate).
      * Redistribution and use in source and binary forms, with or without
      * modification, are permitted provided that the following conditions
     * are met:
     * 1.  Redistributions of source code must retain the above copyright
     *     notice, this list of conditions and the following disclaimer.
     * 2.  Redistributions in binary form must reproduce the above copyright
     *     notice, this list of conditions and the following disclaimer in the
     *     documentation and/or other materials provided with the distribution.
     *
     * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
     * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
     * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     * SUCH DAMAGE.
     *
     *      $FreeBSD: releng/11.0/sys/opencrypto/gfmult.c 299202 2016-05-06 23:37:19Z pfg $
     *
     */
    
    #include "gfmult.h"
    
    #define REV_POLY_REDUCT 0xe1    /* 0x87 bit reversed */
    
    /* reverse the bits of a nibble */
    static const uint8_t nib_rev[] = {
            0x0, 0x8, 0x4, 0xc, 0x2, 0xa, 0x6, 0xe,
            0x1, 0x9, 0x5, 0xd, 0x3, 0xb, 0x7, 0xf,
    };
    
    /* calculate v * 2 */
    static inline struct gf128
    gf128_mulalpha(struct gf128 v)
    {
            uint64_t mask;
    
            mask = !!(v.v[1] & 1);
            mask = ~(mask - 1);
            v.v[1] = (v.v[1] >> 1) | ((v.v[0] & 1) << 63);
            v.v[0] = (v.v[0] >> 1) ^ ((mask & REV_POLY_REDUCT) << 56);
    
            return v;
    }
    
    /*
     * Generate a table for 0-16 * h.  Store the results in the table w/ indexes
     * bit reversed, and the words striped across the values.
     */
    void
    gf128_genmultable(struct gf128 h, struct gf128table *t)
    {
            struct gf128 tbl[16];
            int i;
    
            tbl[0] = MAKE_GF128(0, 0);
            tbl[1] = h;
    
            for (i = 2; i < 16; i += 2) {
                    tbl[i] = gf128_mulalpha(tbl[i / 2]);
                    tbl[i + 1] = gf128_add(tbl[i], h);
            }
    
            for (i = 0; i < 16; i++) {
                    t->a[nib_rev[i]] = tbl[i].v[0] >> 32;
                    t->b[nib_rev[i]] = tbl[i].v[0];
                    t->c[nib_rev[i]] = tbl[i].v[1] >> 32;
                    t->d[nib_rev[i]] = tbl[i].v[1];
            }
    }
    
    /*
     * Generate tables containing h, h^2, h^3 and h^4, starting at 0.
     */
    void
    gf128_genmultable4(struct gf128 h, struct gf128table4 *t)
    {
            struct gf128 h2, h3, h4;
    
            gf128_genmultable(h, &t->tbls[0]);
    
            h2 = gf128_mul(h, &t->tbls[0]);
    
            gf128_genmultable(h2, &t->tbls[1]);
    
            h3 = gf128_mul(h, &t->tbls[1]);
            gf128_genmultable(h3, &t->tbls[2]);
    
           h4 = gf128_mul(h2, &t->tbls[1]);
           gf128_genmultable(h4, &t->tbls[3]);
   }
   
   /*
    * Read a row from the table.
    */
   static inline struct gf128
   readrow(struct gf128table *tbl, unsigned bits)
   {
           struct gf128 r;
   
           bits = bits % 16;
   
           r.v[0] = ((uint64_t)tbl->a[bits] << 32) | tbl->b[bits];
           r.v[1] = ((uint64_t)tbl->c[bits] << 32) | tbl->d[bits];
   
           return r;
   }
   
   /*
    * These are the reduction values.  Since we are dealing with bit reversed
    * version, the values need to be bit reversed, AND the indexes are also
    * bit reversed to make lookups quicker.
    */
   static uint16_t reduction[] = {
           0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
           0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
   };
   
   /*
    * Calculate:
    * (x*2^4 + word[3,0]*h) *
    * 2^4 + word[7,4]*h) *
    * ...
    * 2^4 + word[63,60]*h
    */
   static struct gf128
   gfmultword(uint64_t word, struct gf128 x, struct gf128table *tbl)
   {
           struct gf128 row;
           unsigned bits;
           unsigned redbits;
           int i;
   
           for (i = 0; i < 64; i += 4) {
                   bits = word % 16;
   
                   /* fetch row */
                   row = readrow(tbl, bits);
   
                   /* x * 2^4 */
                   redbits = x.v[1] % 16;
                   x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
                   x.v[0] >>= 4;
                   x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
   
                   word >>= 4;
   
                   x = gf128_add(x, row);
           }
   
           return x;
   }
   
   /*
    * Calculate
    * (x*2^4 + worda[3,0]*h^4+wordb[3,0]*h^3+...+wordd[3,0]*h) *
    * ...
    * 2^4 + worda[63,60]*h^4+ ... + wordd[63,60]*h
    *
    * Passing/returning struct is .5% faster than passing in via pointer on
    * amd64.
    */
   static struct gf128
   gfmultword4(uint64_t worda, uint64_t wordb, uint64_t wordc, uint64_t wordd,
       struct gf128 x, struct gf128table4 *tbl)
   {
           struct gf128 rowa, rowb, rowc, rowd;
           unsigned bitsa, bitsb, bitsc, bitsd;
           unsigned redbits;
           int i;
   
           /*
            * XXX - nibble reverse words to save a shift? probably not as
            * nibble reverse would take 20 ops (5 * 4) verse 16
            */
   
           for (i = 0; i < 64; i += 4) {
                   bitsa = worda % 16;
                   bitsb = wordb % 16;
                   bitsc = wordc % 16;
                   bitsd = wordd % 16;
   
                   /* fetch row */
                   rowa = readrow(&tbl->tbls[3], bitsa);
                   rowb = readrow(&tbl->tbls[2], bitsb);
                   rowc = readrow(&tbl->tbls[1], bitsc);
                   rowd = readrow(&tbl->tbls[0], bitsd);
   
                   /* x * 2^4 */
                   redbits = x.v[1] % 16;
                   x.v[1] = (x.v[1] >> 4) | (x.v[0] % 16) << 60;
                   x.v[0] >>= 4;
                   x.v[0] ^= (uint64_t)reduction[redbits] << (64 - 16);
   
                   worda >>= 4;
                   wordb >>= 4;
                   wordc >>= 4;
                   wordd >>= 4;
   
                   x = gf128_add(x, gf128_add(rowa, gf128_add(rowb,
                       gf128_add(rowc, rowd))));
           }
   
           return x;
   }
   
   struct gf128
   gf128_mul(struct gf128 v, struct gf128table *tbl)
   {
           struct gf128 ret;
   
           ret = MAKE_GF128(0, 0);
   
           ret = gfmultword(v.v[1], ret, tbl);
           ret = gfmultword(v.v[0], ret, tbl);
   
           return ret;
   }
   
   /*
    * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
    * (((a*h+b)*h+c)*h+d)*h
    */
   struct gf128
   gf128_mul4(struct gf128 a, struct gf128 b, struct gf128 c, struct gf128 d,
       struct gf128table4 *tbl)
   {
           struct gf128 tmp;
   
           tmp = MAKE_GF128(0, 0);
   
           tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
           tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
   
           return tmp;
   }
   
   /*
    * a = data[0..15] + r
    * b = data[16..31]
    * c = data[32..47]
    * d = data[48..63]
    *
    * Calculate a*h^4 + b*h^3 + c*h^2 + d*h, or:
    * (((a*h+b)*h+c)*h+d)*h
    */
   struct gf128
   gf128_mul4b(struct gf128 r, const uint8_t *v, struct gf128table4 *tbl)
   {
           struct gf128 a, b, c, d;
           struct gf128 tmp;
   
           tmp = MAKE_GF128(0, 0);
   
           a = gf128_add(r, gf128_read(&v[0*16]));
           b = gf128_read(&v[1*16]);
           c = gf128_read(&v[2*16]);
           d = gf128_read(&v[3*16]);
   
           tmp = gfmultword4(a.v[1], b.v[1], c.v[1], d.v[1], tmp, tbl);
           tmp = gfmultword4(a.v[0], b.v[0], c.v[0], d.v[0], tmp, tbl);
   
           return tmp;
   }

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