| /* 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://gladman.plushost.co.uk/oldsite/cryptography_technology/index.php |
| * 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(2^128) 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 a value i in 0..255 as the byte overflow when a field element |
| * in GF(2^128) is multiplied by x^8, the following macro returns the |
| * 16-bit value that must be XOR-ed into the low-degree end of the |
| * product to reduce it modulo the polynomial x^128 + x^7 + x^2 + x + 1. |
| * |
| * There are two versions of the macro, and hence two tables: one for |
| * the "be" convention where the highest-order bit is the coefficient of |
| * the highest-degree polynomial term, and one for the "le" convention |
| * where the highest-order bit is the coefficient of the lowest-degree |
| * polynomial term. In both cases the values are stored in CPU byte |
| * endianness such that the coefficients are ordered consistently across |
| * bytes, i.e. in the "be" table bits 15..0 of the stored value |
| * correspond to the coefficients of x^15..x^0, and in the "le" table |
| * bits 15..0 correspond to the coefficients of x^0..x^15. |
| * |
| * Therefore, provided that the appropriate byte endianness conversions |
| * are done by the multiplication functions (and these must be in place |
| * anyway to support both little endian and big endian CPUs), the "be" |
| * table can be used for multiplications of both "bbe" and "ble" |
| * elements, and the "le" table can be used for multiplications of both |
| * "lle" and "lbe" elements. |
| */ |
| |
| #define xda_be(i) ( \ |
| (i & 0x80 ? 0x4380 : 0) ^ (i & 0x40 ? 0x21c0 : 0) ^ \ |
| (i & 0x20 ? 0x10e0 : 0) ^ (i & 0x10 ? 0x0870 : 0) ^ \ |
| (i & 0x08 ? 0x0438 : 0) ^ (i & 0x04 ? 0x021c : 0) ^ \ |
| (i & 0x02 ? 0x010e : 0) ^ (i & 0x01 ? 0x0087 : 0) \ |
| ) |
| |
| #define xda_le(i) ( \ |
| (i & 0x80 ? 0xe100 : 0) ^ (i & 0x40 ? 0x7080 : 0) ^ \ |
| (i & 0x20 ? 0x3840 : 0) ^ (i & 0x10 ? 0x1c20 : 0) ^ \ |
| (i & 0x08 ? 0x0e10 : 0) ^ (i & 0x04 ? 0x0708 : 0) ^ \ |
| (i & 0x02 ? 0x0384 : 0) ^ (i & 0x01 ? 0x01c2 : 0) \ |
| ) |
| |
| static const u16 gf128mul_table_le[256] = gf128mul_dat(xda_le); |
| static const u16 gf128mul_table_be[256] = gf128mul_dat(xda_be); |
| |
| /* |
| * The following functions multiply a field element by x^8 in |
| * the polynomial field representation. They use 64-bit word operations |
| * to gain speed but compensate for machine endianness and hence work |
| * correctly on both styles of machine. |
| */ |
| |
| 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_le[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_be[a >> 56]; |
| |
| x->a = cpu_to_be64((a << 8) | (b >> 56)); |
| x->b = cpu_to_be64((b << 8) ^ _tt); |
| } |
| |
| void gf128mul_x8_ble(le128 *r, const le128 *x) |
| { |
| u64 a = le64_to_cpu(x->a); |
| u64 b = le64_to_cpu(x->b); |
| u64 _tt = gf128mul_table_be[a >> 56]; |
| |
| r->a = cpu_to_le64((a << 8) | (b >> 56)); |
| r->b = cpu_to_le64((b << 8) ^ _tt); |
| } |
| EXPORT_SYMBOL(gf128mul_x8_ble); |
| |
| 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(2^128). If we consider a GF(2^128) 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_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_sensitive(t->t[i]); |
| kfree_sensitive(t); |
| } |
| EXPORT_SYMBOL(gf128mul_free_64k); |
| |
| void gf128mul_64k_bbe(be128 *a, const 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(2^128). If we consider a GF(2^128) 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, const 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, const 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)"); |