From Win95, Microsoft's product installation Key is changed from the original 10 digits to 25 characters. This change represents Microsoft bid farewell to simple verification, and has put into an elliptical curve. From the perspective of cryptography, this is definitely a milestone, because the elliptical curve method is still in the stage of research, Microsoft is the first manufacturer of commercial products. So what is it in this 25 characters? 1.Base24 This 25 characters actually be 114bits' data with base24 for UUCODE, as installing Key, this base must absolutely avoid misiapping, so Microsoft chooses the following 24 characters as uucode: bcdfghjkmpqrtvwxy2346789, So, if your installation Key has the characters other than these 24 characters, you can throw it into the garbage cartridge, you don't have to try it. 2.114 Bits Uudecode received 114 bits according to the INTEL high in the format as follows: [xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx] Total 114 Bits | | | / 55 BISH | / 30 BITS Serial / 31 Bits Data / 1 bits flag / flag: Unknown marker, this bit is always 0 in all kinds of KEY you have seen. Serial: User serial number, transferred into a decimal representation as aaaabbbbb, corresponding to: Retail Edition: xxxxx-aaa-bbbbbbbX-xxxxx OEM version: XXXXX-OEM-0AAAAabX-BBBBBB 51BITS is always called DATA, is the basic part of CDKey. Hash: DATA is obtained by specific processing, see later. Sign: The ellipse sign of the HASH value, see later. 3. Elliptic curve signing algorithm to indicate that the elliptic curve signing algorithm is not an easy task, interested in using the "elliptic curve" or "Elliptic Curve" to find related information in search engines, here is simple This section describes how to use Microsoft.
The so-called elliptic curve refers to such a class of curve equations: Y ^ 2 A1 * XY A3 * Y = x ^ 3 A2 * x ^ 2 A4 * x A6 in password learning is its two special cases And Microsoft uses the special case of these two special examples: Y ^ 2 = x ^ 3 a * x b (MOD P) When A, B, P is selected, you can determine an elliptic curve, and then Select a generated point G (GX, GY), and there is a minimum integer Q such that Q * g = O, then, then arbitrarily select an integer KK (KX, KY) = k * g, so the elliptical curve signing algorithm Key is fully generated: public key is: A, B, P, G (GX, GY), K (KX, KY) private key is: A, B, P, G (GX, GY), Q, k When signing the DATA: a. First, choose an integer R b. SHA-1 in the total 100 bytes of DATA, RX, RY, to get the 28 bits in the result to beh; c. seek Sign = r - Hash * K (MOD Q); D. After the three numbers of Data, Hash, SIGN get 25 cdKey. When you verify CDKey: a. Remove the 25 cdkey Uudecode and then remove DATA, HASH, SIGN; B. Seek point R (RX, RY) = Sing * G Hash * k (MOD P); c. DATA, RX, RY a total of 100 bytes of SHA-1, and 28 gets Hash '; d. If Hash = hash', the cdkey is a valid Key. 4. BINK can be seen from the previous description, in order to verify the cdkey, Microsoft must disclose the public key in the elliptical curve signature algorithm, then where is this public key? The answer is in the BINK resource in Pidgen.dll (other products such as Office is packaged in * .msi), and there are two groups, from the current known Key combination, the first set of keys is used to retail Version, the second group is used for OEM versions. Whether the Key of the two products can be generous is whether the corresponding key is the same, such as the second set of keys of the Chinese version of Windows 2000 Pro / SRV / ADVSRV is also the same, the OEM version of a PWindows 2000 PRO, The OEM version of PWindows 2000 SRV / ADV can be used simultaneously. 5. Crack and its difficulty To crack the generating algorithm of CDKey, the corresponding private key must be obtained from the key disclosed in Microsoft, that is, Q and K are required. From the key disclosed in Bink, P is a prime number of 384 bits, which looks like to be at least O (2 ^ 168), but a defect in Microsoft design (?) Reduces actual workload to Only O (2 ^ 28) is ok.
