/* gf128mul.h - 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.
   */
  /*
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   Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.
  
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   may be distributed under the terms of the GNU General Public License (GPL),
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   Issue Date: 31/01/2006

   An implementation of field multiplication in Galois Field GF(2^128)

  */
  
  #ifndef _CRYPTO_GF128MUL_H
  #define _CRYPTO_GF128MUL_H

  #include <asm/byteorder.h>

  #include <crypto/b128ops.h>
  #include <linux/slab.h>
  
  /* Comment by Rik:
   *

   * For some background on GF(2^128) see for example: 
   * http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf 

   *
   * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can
   * be mapped to computer memory in a variety of ways. Let's examine
   * three common cases.
   *
   * Take a look at the 16 binary octets below in memory order. The msb's
   * are left and the lsb's are right. char b[16] is an array and b[0] is
   * the first octet.
   *

   * 10000000 00000000 00000000 00000000 .... 00000000 00000000 00000000

   *   b[0]     b[1]     b[2]     b[3]          b[13]    b[14]    b[15]
   *
   * Every bit is a coefficient of some power of X. We can store the bits
   * in every byte in little-endian order and the bytes themselves also in
   * little endian order. I will call this lle (little-little-endian).
   * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks
   * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.
   * This format was originally implemented in gf128mul and is used
   * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).
   *
   * Another convention says: store the bits in bigendian order and the
   * bytes also. This is bbe (big-big-endian). Now the buffer above
   * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111,
   * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe
   * is partly implemented.
   *
   * Both of the above formats are easy to implement on big-endian
   * machines.
   *

   * XTS and EME (the latter of which is patent encumbered) use the ble
   * format (bits are stored in big endian order and the bytes in little
   * endian). The above buffer represents X^7 in this case and the
   * primitive polynomial is b[0] = 0x87.

   *
   * The common machine word-size is smaller than 128 bits, so to make
   * an efficient implementation we must split into machine word sizes.

   * This implementation uses 64-bit words for the moment. Machine
   * endianness comes into play. The lle format in relation to machine
   * endianness is discussed below by the original author of gf128mul Dr
   * Brian Gladman.

   *
   * Let's look at the bbe and ble format on a little endian machine.
   *
   * bbe on a little endian machine u32 x[4]:
   *
   *  MS            x[0]           LS  MS            x[1]		  LS
   *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
   *  103..96 111.104 119.112 127.120  71...64 79...72 87...80 95...88
   *
   *  MS            x[2]           LS  MS            x[3]		  LS
   *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
   *  39...32 47...40 55...48 63...56  07...00 15...08 23...16 31...24
   *
   * ble on a little endian machine
   *
   *  MS            x[0]           LS  MS            x[1]		  LS
   *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
   *  31...24 23...16 15...08 07...00  63...56 55...48 47...40 39...32
   *
   *  MS            x[2]           LS  MS            x[3]		  LS
   *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
   *  95...88 87...80 79...72 71...64  127.120 199.112 111.104 103..96
   *
   * Multiplications in GF(2^128) are mostly bit-shifts, so you see why
   * ble (and lbe also) are easier to implement on a little-endian
   * machine than on a big-endian machine. The converse holds for bbe
   * and lle.
   *
   * Note: to have good alignment, it seems to me that it is sufficient
   * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize
   * machines this will automatically aligned to wordsize and on a 64-bit
   * machine also.
   */

  /*	Multiply a GF(2^128) field element by x. Field elements are
      held in arrays of bytes in which field bits 8n..8n + 7 are held in
      byte[n], with lower indexed bits placed in the more numerically
      significant bit positions within bytes.

  
      On little endian machines the bit indexes translate into the bit
      positions within four 32-bit words in the following way
  
      MS            x[0]           LS  MS            x[1]		  LS
      ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
      24...31 16...23 08...15 00...07  56...63 48...55 40...47 32...39
  
      MS            x[2]           LS  MS            x[3]		  LS
      ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
      88...95 80...87 72...79 64...71  120.127 112.119 104.111 96..103
  
      On big endian machines the bit indexes translate into the bit
      positions within four 32-bit words in the following way
  
      MS            x[0]           LS  MS            x[1]		  LS
      ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
      00...07 08...15 16...23 24...31  32...39 40...47 48...55 56...63
  
      MS            x[2]           LS  MS            x[3]		  LS
      ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
      64...71 72...79 80...87 88...95  96..103 104.111 112.119 120.127
  */
  
  /*	A slow generic version of gf_mul, implemented for lle and bbe
   * 	It multiplies a and b and puts the result in a */
  void gf128mul_lle(be128 *a, const be128 *b);
  
  void gf128mul_bbe(be128 *a, const be128 *b);

  /*
   * The following functions multiply a field element by x 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.
   *
   * They are defined here for performance.
   */
  
  static inline u64 gf128mul_mask_from_bit(u64 x, int which)
  {
  	/* a constant-time version of 'x & ((u64)1 << which) ? (u64)-1 : 0' */
  	return ((s64)(x << (63 - which)) >> 63);
  }
  
  static inline void gf128mul_x_lle(be128 *r, const be128 *x)
  {
  	u64 a = be64_to_cpu(x->a);
  	u64 b = be64_to_cpu(x->b);
  
  	/* equivalent to gf128mul_table_le[(b << 7) & 0xff] << 48
  	 * (see crypto/gf128mul.c): */
  	u64 _tt = gf128mul_mask_from_bit(b, 0) & ((u64)0xe1 << 56);
  
  	r->b = cpu_to_be64((b >> 1) | (a << 63));
  	r->a = cpu_to_be64((a >> 1) ^ _tt);
  }
  
  static inline void gf128mul_x_bbe(be128 *r, const be128 *x)
  {
  	u64 a = be64_to_cpu(x->a);
  	u64 b = be64_to_cpu(x->b);
  
  	/* equivalent to gf128mul_table_be[a >> 63] (see crypto/gf128mul.c): */
  	u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87;
  
  	r->a = cpu_to_be64((a << 1) | (b >> 63));
  	r->b = cpu_to_be64((b << 1) ^ _tt);
  }
  
  /* needed by XTS */

  static inline void gf128mul_x_ble(le128 *r, const le128 *x)

  {
  	u64 a = le64_to_cpu(x->a);
  	u64 b = le64_to_cpu(x->b);
  
  	/* equivalent to gf128mul_table_be[b >> 63] (see crypto/gf128mul.c): */

  	u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87;

  	r->a = cpu_to_le64((a << 1) | (b >> 63));
  	r->b = cpu_to_le64((b << 1) ^ _tt);

  }

  
  /* 4k table optimization */
  
  struct gf128mul_4k {
  	be128 t[256];
  };
  
  struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
  struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);

  void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t);
  void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t);

  void gf128mul_x8_ble(le128 *r, const le128 *x);

  static inline void gf128mul_free_4k(struct gf128mul_4k *t)
  {

  	kfree_sensitive(t);

  }

  /* 64k table optimization, implemented for bbe */

  
  struct gf128mul_64k {
  	struct gf128mul_4k *t[16];
  };

  /* First initialize with the constant factor with which you
   * want to multiply and then call gf128mul_64k_bbe with the other
   * factor in the first argument, and the table in the second.
   * Afterwards, the result is stored in *a.
   */

  struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
  void gf128mul_free_64k(struct gf128mul_64k *t);

  void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t);

  
  #endif /* _CRYPTO_GF128MUL_H */