[CRYPTO] lib: table driven multiplications in GF(2^128)

A lot of cypher modes need multiplications in GF(2^128). LRW, ABL, GCM...
I use functions from this library in my LRW implementation and I will
also use them in my ABL (Arbitrary Block Length, an unencumbered (correct
me if I am wrong, wide block cipher mode).

Elements of GF(2^128) must be presented as u128 *, it encourages automatic
and proper alignment.

The library contains support for two different representations of GF(2^128),
see the comment in gf128mul.h. There different levels of optimization
(memory/speed tradeoff).

The code is based on work by Dr Brian Gladman. Notable changes:
- deletion of two optimization modes
- change from u32 to u64 for faster handling on 64bit machines
- support for 'bbe' representation in addition to the, already implemented,
  'lle' representation.
- move 'inline void' functions from header to 'static void' in the
  source file
- update to use the linux coding style conventions

The original can be found at:
http://fp.gladman.plus.com/AES/modes.vc8.19-06-06.zip

The copyright (and GPL statement) of the original author is preserved.

Signed-off-by: Rik Snel <rsnel@cube.dyndns.org>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>

1 files changed, 466 insertions, 0 deletions

diff --git a/crypto/gf128mul.c b/crypto/gf128mul.c
new file mode 100644
index 000000000000..0a2aadfa1d85
--- /dev/null
+++ b/crypto/gf128mul.c
@@ -0,0 +1,466 @@
+/* gf128mul.c - GF(2^128) multiplication functions
+ *
+ * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
+ * Copyright (c) 2006, Rik Snel <rsnel@cube.dyndns.org>
+ *
+ * Based on Dr Brian Gladman's (GPL'd) work published at
+ * http://fp.gladman.plus.com/cryptography_technology/index.htm
+ * See the original copyright notice below.
+ *
+ * This program is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by the Free
+ * Software Foundation; either version 2 of the License, or (at your option)
+ * any later version.
+ */
+
+/*
+ ---------------------------------------------------------------------------
+ Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.
+
+ LICENSE TERMS
+
+ The free distribution and use of this software in both source and binary
+ form is allowed (with or without changes) provided that:
+
+   1. distributions of this source code include the above copyright
+      notice, this list of conditions and the following disclaimer;
+
+   2. distributions in binary form include the above copyright
+      notice, this list of conditions and the following disclaimer
+      in the documentation and/or other associated materials;
+
+   3. the copyright holder's name is not used to endorse products
+      built using this software without specific written permission.
+
+ ALTERNATIVELY, provided that this notice is retained in full, this product
+ may be distributed under the terms of the GNU General Public License (GPL),
+ in which case the provisions of the GPL apply INSTEAD OF those given above.
+
+ DISCLAIMER
+
+ This software is provided 'as is' with no explicit or implied warranties
+ in respect of its properties, including, but not limited to, correctness
+ and/or fitness for purpose.
+ ---------------------------------------------------------------------------
+ Issue 31/01/2006
+
+ This file provides fast multiplication in GF(128) as required by several
+ cryptographic authentication modes
+*/
+
+#include <crypto/gf128mul.h>
+#include <linux/kernel.h>
+#include <linux/module.h>
+#include <linux/slab.h>
+
+#define gf128mul_dat(q) { \
+        q(0x00), q(0x01), q(0x02), q(0x03), q(0x04), q(0x05), q(0x06), q(0x07),\
+        q(0x08), q(0x09), q(0x0a), q(0x0b), q(0x0c), q(0x0d), q(0x0e), q(0x0f),\
+        q(0x10), q(0x11), q(0x12), q(0x13), q(0x14), q(0x15), q(0x16), q(0x17),\
+        q(0x18), q(0x19), q(0x1a), q(0x1b), q(0x1c), q(0x1d), q(0x1e), q(0x1f),\
+        q(0x20), q(0x21), q(0x22), q(0x23), q(0x24), q(0x25), q(0x26), q(0x27),\
+        q(0x28), q(0x29), q(0x2a), q(0x2b), q(0x2c), q(0x2d), q(0x2e), q(0x2f),\
+        q(0x30), q(0x31), q(0x32), q(0x33), q(0x34), q(0x35), q(0x36), q(0x37),\
+        q(0x38), q(0x39), q(0x3a), q(0x3b), q(0x3c), q(0x3d), q(0x3e), q(0x3f),\
+        q(0x40), q(0x41), q(0x42), q(0x43), q(0x44), q(0x45), q(0x46), q(0x47),\
+        q(0x48), q(0x49), q(0x4a), q(0x4b), q(0x4c), q(0x4d), q(0x4e), q(0x4f),\
+        q(0x50), q(0x51), q(0x52), q(0x53), q(0x54), q(0x55), q(0x56), q(0x57),\
+        q(0x58), q(0x59), q(0x5a), q(0x5b), q(0x5c), q(0x5d), q(0x5e), q(0x5f),\
+        q(0x60), q(0x61), q(0x62), q(0x63), q(0x64), q(0x65), q(0x66), q(0x67),\
+        q(0x68), q(0x69), q(0x6a), q(0x6b), q(0x6c), q(0x6d), q(0x6e), q(0x6f),\
+        q(0x70), q(0x71), q(0x72), q(0x73), q(0x74), q(0x75), q(0x76), q(0x77),\
+        q(0x78), q(0x79), q(0x7a), q(0x7b), q(0x7c), q(0x7d), q(0x7e), q(0x7f),\
+        q(0x80), q(0x81), q(0x82), q(0x83), q(0x84), q(0x85), q(0x86), q(0x87),\
+        q(0x88), q(0x89), q(0x8a), q(0x8b), q(0x8c), q(0x8d), q(0x8e), q(0x8f),\
+        q(0x90), q(0x91), q(0x92), q(0x93), q(0x94), q(0x95), q(0x96), q(0x97),\
+        q(0x98), q(0x99), q(0x9a), q(0x9b), q(0x9c), q(0x9d), q(0x9e), q(0x9f),\
+        q(0xa0), q(0xa1), q(0xa2), q(0xa3), q(0xa4), q(0xa5), q(0xa6), q(0xa7),\
+        q(0xa8), q(0xa9), q(0xaa), q(0xab), q(0xac), q(0xad), q(0xae), q(0xaf),\
+        q(0xb0), q(0xb1), q(0xb2), q(0xb3), q(0xb4), q(0xb5), q(0xb6), q(0xb7),\
+        q(0xb8), q(0xb9), q(0xba), q(0xbb), q(0xbc), q(0xbd), q(0xbe), q(0xbf),\
+        q(0xc0), q(0xc1), q(0xc2), q(0xc3), q(0xc4), q(0xc5), q(0xc6), q(0xc7),\
+        q(0xc8), q(0xc9), q(0xca), q(0xcb), q(0xcc), q(0xcd), q(0xce), q(0xcf),\
+        q(0xd0), q(0xd1), q(0xd2), q(0xd3), q(0xd4), q(0xd5), q(0xd6), q(0xd7),\
+        q(0xd8), q(0xd9), q(0xda), q(0xdb), q(0xdc), q(0xdd), q(0xde), q(0xdf),\
+        q(0xe0), q(0xe1), q(0xe2), q(0xe3), q(0xe4), q(0xe5), q(0xe6), q(0xe7),\
+        q(0xe8), q(0xe9), q(0xea), q(0xeb), q(0xec), q(0xed), q(0xee), q(0xef),\
+        q(0xf0), q(0xf1), q(0xf2), q(0xf3), q(0xf4), q(0xf5), q(0xf6), q(0xf7),\
+        q(0xf8), q(0xf9), q(0xfa), q(0xfb), q(0xfc), q(0xfd), q(0xfe), q(0xff) \
+}
+
+/*      Given the value i in 0..255 as the byte overflow when a field element
+    in GHASH is multipled by x^8, this function will return the values that
+    are generated in the lo 16-bit word of the field value by applying the
+    modular polynomial. The values lo_byte and hi_byte are returned via the
+    macro xp_fun(lo_byte, hi_byte) so that the values can be assembled into
+    memory as required by a suitable definition of this macro operating on
+    the table above
+*/
+
+#define xx(p, q)        0x##p##q
+
+#define xda_bbe(i) ( \
+        (i & 0x80 ? xx(43, 80) : 0) ^ (i & 0x40 ? xx(21, c0) : 0) ^ \
+        (i & 0x20 ? xx(10, e0) : 0) ^ (i & 0x10 ? xx(08, 70) : 0) ^ \
+        (i & 0x08 ? xx(04, 38) : 0) ^ (i & 0x04 ? xx(02, 1c) : 0) ^ \
+        (i & 0x02 ? xx(01, 0e) : 0) ^ (i & 0x01 ? xx(00, 87) : 0) \
+)
+
+#define xda_lle(i) ( \
+        (i & 0x80 ? xx(e1, 00) : 0) ^ (i & 0x40 ? xx(70, 80) : 0) ^ \
+        (i & 0x20 ? xx(38, 40) : 0) ^ (i & 0x10 ? xx(1c, 20) : 0) ^ \
+        (i & 0x08 ? xx(0e, 10) : 0) ^ (i & 0x04 ? xx(07, 08) : 0) ^ \
+        (i & 0x02 ? xx(03, 84) : 0) ^ (i & 0x01 ? xx(01, c2) : 0) \
+)
+
+static const u16 gf128mul_table_lle[256] = gf128mul_dat(xda_lle);
+static const u16 gf128mul_table_bbe[256] = gf128mul_dat(xda_bbe);
+
+/* These functions multiply a field element by x, by x^4 and by x^8
+ * in the polynomial field representation. It uses 32-bit word operations
+ * to gain speed but compensates for machine endianess and hence works
+ * correctly on both styles of machine.
+ */
+
+static void gf128mul_x_lle(be128 *r, const be128 *x)
+{
+        u64 a = be64_to_cpu(x->a);
+        u64 b = be64_to_cpu(x->b);
+        u64 _tt = gf128mul_table_lle[(b << 7) & 0xff];
+
+        r->b = cpu_to_be64((b >> 1) | (a << 63));
+        r->a = cpu_to_be64((a >> 1) ^ (_tt << 48));
+}
+
+static void gf128mul_x_bbe(be128 *r, const be128 *x)
+{
+        u64 a = be64_to_cpu(x->a);
+        u64 b = be64_to_cpu(x->b);
+        u64 _tt = gf128mul_table_bbe[a >> 63];
+
+        r->a = cpu_to_be64((a << 1) | (b >> 63));
+        r->b = cpu_to_be64((b << 1) ^ _tt);
+}
+
+static void gf128mul_x8_lle(be128 *x)
+{
+        u64 a = be64_to_cpu(x->a);
+        u64 b = be64_to_cpu(x->b);
+        u64 _tt = gf128mul_table_lle[b & 0xff];
+
+        x->b = cpu_to_be64((b >> 8) | (a << 56));
+        x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
+}
+
+static void gf128mul_x8_bbe(be128 *x)
+{
+        u64 a = be64_to_cpu(x->a);
+        u64 b = be64_to_cpu(x->b);
+        u64 _tt = gf128mul_table_bbe[a >> 56];
+
+        x->a = cpu_to_be64((a << 8) | (b >> 56));
+        x->b = cpu_to_be64((b << 8) ^ _tt);
+}
+
+void gf128mul_lle(be128 *r, const be128 *b)
+{
+        be128 p[8];
+        int i;
+
+        p[0] = *r;
+        for (i = 0; i < 7; ++i)
+                gf128mul_x_lle(&p[i + 1], &p[i]);
+
+        memset(r, 0, sizeof(r));
+        for (i = 0;;) {
+                u8 ch = ((u8 *)b)[15 - i];
+
+                if (ch & 0x80)
+                        be128_xor(r, r, &p[0]);
+                if (ch & 0x40)
+                        be128_xor(r, r, &p[1]);
+                if (ch & 0x20)
+                        be128_xor(r, r, &p[2]);
+                if (ch & 0x10)
+                        be128_xor(r, r, &p[3]);
+                if (ch & 0x08)
+                        be128_xor(r, r, &p[4]);
+                if (ch & 0x04)
+                        be128_xor(r, r, &p[5]);
+                if (ch & 0x02)
+                        be128_xor(r, r, &p[6]);
+                if (ch & 0x01)
+                        be128_xor(r, r, &p[7]);
+
+                if (++i >= 16)
+                        break;
+
+                gf128mul_x8_lle(r);
+        }
+}
+EXPORT_SYMBOL(gf128mul_lle);
+
+void gf128mul_bbe(be128 *r, const be128 *b)
+{
+        be128 p[8];
+        int i;
+
+        p[0] = *r;
+        for (i = 0; i < 7; ++i)
+                gf128mul_x_bbe(&p[i + 1], &p[i]);
+
+        memset(r, 0, sizeof(r));
+        for (i = 0;;) {
+                u8 ch = ((u8 *)b)[i];
+
+                if (ch & 0x80)
+                        be128_xor(r, r, &p[7]);
+                if (ch & 0x40)
+                        be128_xor(r, r, &p[6]);
+                if (ch & 0x20)
+                        be128_xor(r, r, &p[5]);
+                if (ch & 0x10)
+                        be128_xor(r, r, &p[4]);
+                if (ch & 0x08)
+                        be128_xor(r, r, &p[3]);
+                if (ch & 0x04)
+                        be128_xor(r, r, &p[2]);
+                if (ch & 0x02)
+                        be128_xor(r, r, &p[1]);
+                if (ch & 0x01)
+                        be128_xor(r, r, &p[0]);
+
+                if (++i >= 16)
+                        break;
+
+                gf128mul_x8_bbe(r);
+        }
+}
+EXPORT_SYMBOL(gf128mul_bbe);
+
+/*      This version uses 64k bytes of table space.
+    A 16 byte buffer has to be multiplied by a 16 byte key
+    value in GF(128).  If we consider a GF(128) value in
+    the buffer's lowest byte, we can construct a table of
+    the 256 16 byte values that result from the 256 values
+    of this byte.  This requires 4096 bytes. But we also
+    need tables for each of the 16 higher bytes in the
+    buffer as well, which makes 64 kbytes in total.
+*/
+/* additional explanation
+ * t[0][BYTE] contains g*BYTE
+ * t[1][BYTE] contains g*x^8*BYTE
+ *  ..
+ * t[15][BYTE] contains g*x^120*BYTE */
+struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g)
+{
+        struct gf128mul_64k *t;
+        int i, j, k;
+
+        t = kzalloc(sizeof(*t), GFP_KERNEL);
+        if (!t)
+                goto out;
+
+        for (i = 0; i < 16; i++) {
+                t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
+                if (!t->t[i]) {
+                        gf128mul_free_64k(t);
+                        t = NULL;
+                        goto out;
+                }
+        }
+
+        t->t[0]->t[128] = *g;
+        for (j = 64; j > 0; j >>= 1)
+                gf128mul_x_lle(&t->t[0]->t[j], &t->t[0]->t[j + j]);
+
+        for (i = 0;;) {
+                for (j = 2; j < 256; j += j)
+                        for (k = 1; k < j; ++k)
+                                be128_xor(&t->t[i]->t[j + k],
+                                          &t->t[i]->t[j], &t->t[i]->t[k]);
+
+                if (++i >= 16)
+                        break;
+
+                for (j = 128; j > 0; j >>= 1) {
+                        t->t[i]->t[j] = t->t[i - 1]->t[j];
+                        gf128mul_x8_lle(&t->t[i]->t[j]);
+                }
+        }
+
+out:
+        return t;
+}
+EXPORT_SYMBOL(gf128mul_init_64k_lle);
+
+struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g)
+{
+        struct gf128mul_64k *t;
+        int i, j, k;
+
+        t = kzalloc(sizeof(*t), GFP_KERNEL);
+        if (!t)
+                goto out;
+
+        for (i = 0; i < 16; i++) {
+                t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
+                if (!t->t[i]) {
+                        gf128mul_free_64k(t);
+                        t = NULL;
+                        goto out;
+                }
+        }
+
+        t->t[0]->t[1] = *g;
+        for (j = 1; j <= 64; j <<= 1)
+                gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);
+
+        for (i = 0;;) {
+                for (j = 2; j < 256; j += j)
+                        for (k = 1; k < j; ++k)
+                                be128_xor(&t->t[i]->t[j + k],
+                                          &t->t[i]->t[j], &t->t[i]->t[k]);
+
+                if (++i >= 16)
+                        break;
+
+                for (j = 128; j > 0; j >>= 1) {
+                        t->t[i]->t[j] = t->t[i - 1]->t[j];
+                        gf128mul_x8_bbe(&t->t[i]->t[j]);
+                }
+        }
+
+out:
+        return t;
+}
+EXPORT_SYMBOL(gf128mul_init_64k_bbe);
+
+void gf128mul_free_64k(struct gf128mul_64k *t)
+{
+        int i;
+
+        for (i = 0; i < 16; i++)
+                kfree(t->t[i]);
+        kfree(t);
+}
+EXPORT_SYMBOL(gf128mul_free_64k);
+
+void gf128mul_64k_lle(be128 *a, struct gf128mul_64k *t)
+{
+        u8 *ap = (u8 *)a;
+        be128 r[1];
+        int i;
+
+        *r = t->t[0]->t[ap[0]];
+        for (i = 1; i < 16; ++i)
+                be128_xor(r, r, &t->t[i]->t[ap[i]]);
+        *a = *r;
+}
+EXPORT_SYMBOL(gf128mul_64k_lle);
+
+void gf128mul_64k_bbe(be128 *a, struct gf128mul_64k *t)
+{
+        u8 *ap = (u8 *)a;
+        be128 r[1];
+        int i;
+
+        *r = t->t[0]->t[ap[15]];
+        for (i = 1; i < 16; ++i)
+                be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
+        *a = *r;
+}
+EXPORT_SYMBOL(gf128mul_64k_bbe);
+
+/*      This version uses 4k bytes of table space.
+    A 16 byte buffer has to be multiplied by a 16 byte key
+    value in GF(128).  If we consider a GF(128) value in a
+    single byte, we can construct a table of the 256 16 byte
+    values that result from the 256 values of this byte.
+    This requires 4096 bytes. If we take the highest byte in
+    the buffer and use this table to get the result, we then
+    have to multiply by x^120 to get the final value. For the
+    next highest byte the result has to be multiplied by x^112
+    and so on. But we can do this by accumulating the result
+    in an accumulator starting with the result for the top
+    byte.  We repeatedly multiply the accumulator value by
+    x^8 and then add in (i.e. xor) the 16 bytes of the next
+    lower byte in the buffer, stopping when we reach the
+    lowest byte. This requires a 4096 byte table.
+*/
+struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g)
+{
+        struct gf128mul_4k *t;
+        int j, k;
+
+        t = kzalloc(sizeof(*t), GFP_KERNEL);
+        if (!t)
+                goto out;
+
+        t->t[128] = *g;
+        for (j = 64; j > 0; j >>= 1)
+                gf128mul_x_lle(&t->t[j], &t->t[j+j]);
+
+        for (j = 2; j < 256; j += j)
+                for (k = 1; k < j; ++k)
+                        be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
+
+out:
+        return t;
+}
+EXPORT_SYMBOL(gf128mul_init_4k_lle);
+
+struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g)
+{
+        struct gf128mul_4k *t;
+        int j, k;
+
+        t = kzalloc(sizeof(*t), GFP_KERNEL);
+        if (!t)
+                goto out;
+
+        t->t[1] = *g;
+        for (j = 1; j <= 64; j <<= 1)
+                gf128mul_x_bbe(&t->t[j + j], &t->t[j]);
+
+        for (j = 2; j < 256; j += j)
+                for (k = 1; k < j; ++k)
+                        be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);
+
+out:
+        return t;
+}
+EXPORT_SYMBOL(gf128mul_init_4k_bbe);
+
+void gf128mul_4k_lle(be128 *a, struct gf128mul_4k *t)
+{
+        u8 *ap = (u8 *)a;
+        be128 r[1];
+        int i = 15;
+
+        *r = t->t[ap[15]];
+        while (i--) {
+                gf128mul_x8_lle(r);
+                be128_xor(r, r, &t->t[ap[i]]);
+        }
+        *a = *r;
+}
+EXPORT_SYMBOL(gf128mul_4k_lle);
+
+void gf128mul_4k_bbe(be128 *a, struct gf128mul_4k *t)
+{
+        u8 *ap = (u8 *)a;
+        be128 r[1];
+        int i = 0;
+
+        *r = t->t[ap[0]];
+        while (++i < 16) {
+                gf128mul_x8_bbe(r);
+                be128_xor(r, r, &t->t[ap[i]]);
+        }
+        *a = *r;
+}
+EXPORT_SYMBOL(gf128mul_4k_bbe);
+
+MODULE_LICENSE("GPL");
+MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");