myth about wpa ( how it is done ), windows product activation technique.txt

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>>> Check digits

The rightmost digit in each of the groups is a check digit to guard
against simple errors such as the call center agent's mistyping of one
of the digits read to him or her. The value of the check digit is
calculated by adding the other five digits in the group, adding the
digits at even positions a second time, and dividing the sum by
seven. The remainder of the division is the value of the check
digit. In the above example the check digit for the first group (6) is
calculated as follows.

1 | 2 | 3 | 4 | 5 <- position
---+---+---+---+---
0 | 0 | 2 | 6 | 6 <- digits

0 + 0 + 2 + 6 + 6 = 14 (step 1: add all digits)
0 + 6 + 14 = 20 (step 2: add even digits again)

step 3: division
20 / 7 = 2, remainder is 20 - (2 * 7) = 6

=> check digit is 6

Adding the even digits twice is probably intended to guard against the
relatively frequent error of accidentally swapping two digits while
typing, as in 00626 vs. 00266, which yield different check digits.

>>> Decoding

Removing the check digits results in a 41-digit decimal number. A
decimal number of this length roughly corresponds to a 136-bit binary
number. In fact, the 41-digit number is just the decimal encoding of
such a 136-bit multi-precision integer, which is stored in little
endian byte order as a byte array. Hence, the above Installation ID
can also be represented as a sequence of 17 bytes as in

0xXX 0xXX 0xXX 0xXX 0xXX 0xXX 0xXX 0xXX
0x94 0xAA 0x46 0xD6 0x0F 0xBD 0x2C 0xC8
0x00

In this representation of the above Installation ID 'X' characters
again substitute the digits that we prefer not to disclose. The '0x'
prefix denotes hex notation throughout this paper.

>>> Decryption

When decoding arbitrary Installation IDs it can be noticed that the
most significant byte always seems to be 0x00 or 0x01, whereas the
other bytes look random. The reason for this is that the lower 16
bytes of the Installation ID are encrypted, whereas the most
significant byte is kept in plaintext.

The cryptographic algorithm employed to encrypt the Installation ID is
a proprietary four-round Feistel cipher. Since the block of input
bytes passed to a Feistel cipher is divided into two blocks of equal
size, this class of ciphers is typically applied to input blocks
consisting of an even number of bytes - in this case the lower 16 of
the 17 input bytes. The round function of the cipher is the SHA-1
message digest algorithm keyed with a four-byte sequence.

Let + denote the concatenation of two byte sequences, ^ the XOR
operation, L and R the left and right eight-byte input half for one
round, L' and R' the output halves of said round, and First-8() a
function that returns the first eight bytes of an SHA-1 message
digest. Then one round of decryption looks as follows.

L' = R ^ First-8(SHA-1(L + Key))
R' = L

The result of the decryption is 16 bytes of plaintext, which are -
together with the 17th unencrypted byte - from now on interpreted as
four double words in little endian byte order followed by a single
byte as in

name | size | offset
-----+-------------+-------
H1 | double word | 0
H2 | double word | 4
P1 | double word | 8
P2 | double word | 12
P3 | byte | 16

H1 and H2 specify the hardware configuration that the Installation ID
is linked to. P1 and P2 as well as the remaining byte P3 contain the
Product ID associated with the Installation ID.

>>> Product ID

The Product ID consists of five groups of decimal digits, as in

AAAAA-BBB-CCCCCCC-DDEEE

If you search your registry for a value named 'ProductID', you will
discover the ID that applies to your installation. The 'About' window
of Internet Explorer should also yield your Product ID.

>>>> Decoding

The mapping between the Product ID in decimal representation and its
binary encoding in the double words P1 and P2 and the byte P3 is
summarized in the following table.

digits | length | encoding
--------+---------+---------------------------------------
AAAAA | 17 bits | bit 0 to bit 16 of P1
BBB | 10 bits | bit 17 to bit 26 of P1
CCCCCCC | 28 bits | bit 27 to bit 31 of P1 (lower 5 bits)
| | bit 0 to bit 22 of P2 (upper 23 bits)
DDEEE | 17 bits | bit 23 to bit 31 of P2 (lower 9 bits)
| | bit 0 to bit 7 of P3 (upper 8 bits)

The meaning of each of the five groups of digits is documented in the
next table.

digits | meaning
--------+-------------------------------------------------
AAAAA | apparently always 55034 (in Windows XP RC1)
BBB | most significant three digits of Raw Product Key
| (see below)
CCCCCCC | least significant six digits of Raw Product Key
| plus check digit (see below)
DD | index of the public key used to verify the
| Product Key (see below)
EEE | random value

As can be seen, the (Raw) Product Key plays an important role in
generating the Product ID.

>>>> Product Key

The Raw Product Key is buried inside the Product Key that is printed
on the sticker distributed with each Windows XP CD. It consists of
five alphanumeric strings separated by '-' characters, where each
string is composed of five characters, as in

FFFFF-GGGGG-HHHHH-JJJJJ-KKKKK

Each character is one of the following 24 letters and digits:

B C D F G H J K M P Q R T V W X Y 2 3 4 6 7 8 9

Very similar to the decimal encoding of the Installation ID the 25
characters of the Product Key form a base-24 encoding of the binary
representation of the Product Key. Decoding the Product Key yields a
multi-precision integer of roughly 115 bits, which is stored - again
in little endian byte order - in an array of 15 bytes. Decoding the
above Product Key results in the following byte sequence.

0x6F 0xFA 0x95 0x45 0xFC 0x75 0xB5 0x52
0xBB 0xEF 0xB1 0x17 0xDA 0xCD 0x00

Of these 15 bytes the least significant four bytes contain the Raw
Product Key in little endian byte order. The least significant bit is
removed by shifting this 32-bit value (0x4595FA6F - remember the
little endian byte order) to the left by one bit position, resulting
in a Raw Product Key of 0x22CAFD37, or

583728439

in decimal notation.

The eleven remaining bytes form a digital signature, allowing
verification of the authenticity of the Product Key by means of a
hard-coded public key.

>>>> Product Key -> Product ID

The three most significant digits, i.e. 583, of the Raw Product Key's
nine-digit decimal representation directly map to the BBB component of
the Product ID described above.

To obtain the CCCCCCC component, a check digit is appended to the
remaining six digits 728439. The check digit is chosen such that the
sum of all digits - including the check digit - is divisible by
seven. In the given case, the sum of the six digits is

7 + 2 + 8 + 4 + 3 + 9 = 33

which results in a check digit of 2, since

7 + 2 + 8 + 4 + 3 + 9 + 2 = 33 + 2 = 35

which is divisible by seven. The CCCCCCC component of the Product ID
is therefore 7284392.

For verifying a Product Key, more than one public key is available. If
verification with the first public key fails, the second is tried,
etc. The DD component of the Product ID specifies which of the public
keys in this sequence was successfully used to verify the Product Key.

This mechanism might be intended to support several different parties
generating valid Product Keys with different individual private keys.

However, the different private keys might also represent different
versions of a product. A Product Key for the 'professional' release
could then be signed with a different key than a Product Key for the
'server' release. The DD component would then represent the product
version.

Finally, a valid Product ID derived from our example Product Key might
be

55034-583-7284392-00123

which indicates that the first public key (DD = index = 0) matched and
123 was chosen as the random number EEE.

The randomly selected EEE component is the reason for msoobe.exe
presenting a different Installation ID at each invocation. Because of
the applied encryption this small change results in a completely
different Installation ID.

So, the Product ID transmitted during activation will most probably
differ in the last three digits from your Product ID as displayed by
Internet Explorer or as stored in the registry.

>>> Hardware Information

As discussed above, the hardware configuration linked to the
Installation ID is represented by the two double words H1 and H2.

>>>> Bit-fields

For this purpose, the double words are divided into twelve
bit-fields. The relationship between the computer hardware and the
bit-fields is given in the following table.

double word | offset | length | bit-field value based on
------------+--------+--------+----------------------------
H1 | 0 | 10 | volume serial number string
| | | of system volume
H1 | 10 | 10 | network adapter MAC address
| | | string
H1 | 20 | 7 | CD-ROM drive hardware
| | | identification string
H1 | 27 | 5 | graphics adapter hardware
| | | identification string
H2 | 0 | 3 | unused, set to 001
H2 | 3 | 6 | CPU serial number string
H2 | 9 | 7 | harddrive hardware
| | | identification string
H2 | 16 | 5 | SCSI host adapter hardware
| | | identification string
H2 | 21 | 4 | IDE controller hardware
| | | identification string
H2 | 25 | 3 | processor model string
H2 | 28 | 3 | RAM size
H2 | 31 | 1 | 1 = dockable