@@ -44,7 +44,7 @@
---------------------------------------------------------------------------
Issue 31/01/2006
- This file provides fast multiplication in GF(128) as required by several
+ This file provides fast multiplication in GF(2^128) as required by several
cryptographic authentication modes
*/
@@ -116,9 +116,10 @@
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
+/*
+ * The following functions multiply a field element by x or 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.
*/
@@ -251,7 +252,7 @@ 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
+ 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
@@ -330,7 +331,7 @@ 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
+ 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
@@ -43,7 +43,7 @@
---------------------------------------------------------------------------
Issue Date: 31/01/2006
- An implementation of field multiplication in Galois Field GF(128)
+ An implementation of field multiplication in Galois Field GF(2^128)
*/
#ifndef _CRYPTO_GF128MUL_H
@@ -65,7 +65,7 @@
* are left and the lsb's are right. char b[16] is an array and b[0] is
* the first octet.
*
- * 80000000 00000000 00000000 00000000 .... 00000000 00000000 00000000
+ * 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
@@ -85,15 +85,17 @@
* Both of the above formats are easy to implement on big-endian
* machines.
*
- * EME (which is patent encumbered) uses 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.
+ * 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 file uses one 32bit 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.
+ * 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.
*
@@ -127,10 +129,10 @@
* machines this will automatically aligned to wordsize and on a 64-bit
* machine also.
*/
-/* Multiply a GF128 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.
+/* 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
Fix incorrect references to GF(128) instead of GF(2^128), as these are two entirely different fields, and fix a few other incorrect comments. Cc: Alex Cope <alexcope@google.com> Signed-off-by: Eric Biggers <ebiggers@google.com> --- crypto/gf128mul.c | 13 +++++++------ include/crypto/gf128mul.h | 26 ++++++++++++++------------ 2 files changed, 21 insertions(+), 18 deletions(-)