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The half-life of short-lived 215Po was studied in a new experimental setup by means of liquid scintillation counting. The new value of 1.781 (5) ms was obtained by offline data analysis using the delayed coincidence method. Along with the half-life determination, a careful assessment of uncertainties was carried out. The result was compared with data available from the literature.
License keys are the defacto-standard as an anti-piracy measure. To be honest, this strikes me as (in)Security Through Obscurity, although I really have no idea how license keys are generated. What is a good (secure) example of license key generation? What cryptographic primitive (if any) are they using? Is it a message digest? If so, what data would they be hashing? What methods do developers employ to make it difficult for crackers to build their own key generators? How are key generators made?
For old-school CD keys, it was just a matter of making up an algorithm for which CD keys (which could be any string) are easy to generate and easy to verify, but the ratio of valid-CD-keys to invalid-CD-keys is so small that randomly guessing CD keys is unlikely to get you a valid one.
Windows XP takes quite a bit of information, encrypts it, and puts the letter/number encoding on a sticker. This allowed MS to both verify your key and obtain the product-type (Home, Professional, etc.) at the same time. Additionally, it requires online activation.
The full algorithm is rather complex, but outlined nicely in this (completely legal!) paper, published in Germany.
Of course, no matter what you do, unless you are offering an online service (like World of Warcraft), any type of copy protection is just a stall: unfortunately, if it's any game worth value, someone will break (or at least circumvent) the CD-key algorithm, and all other copyright protections.
For online-services, life is a bit simpler, since even with the binary file you need to authenticate with their servers to make any use of it (eg. have a WoW account). The CD-key algorithm for World of Warcraft - used, for instance, when buying playtime cards - probably looks something like this:
When I originally wrote this answer it was under an assumption that the question was regarding 'offline' validation of licence keys. Most of the other answers address online verification, which is significantly easier to handle (most of the logic can be done server side).
With offline verification the most difficult thing is ensuring that you can generate a huge number of unique licence keys, and still maintain a strong algorithm that isnt easily compromised (such as a simple check digit)
It is however very much security by obscurity. Anyone taking the time to disassemble the code would be able to find the graphing function and encryption keys, then mock up a key generator, but its probably quite useful for slowing down casual piracy.
Require that the number be divisible by (say) 17. Trivial to guess, if you have access to many keys, but the majority of potential strings will be invalid. Similar would be requiring that the checksum of the key match a known value.
Require that the first half of the key, when concatenated with a known value, hashes down to the second half of the key. Better, but the program still contains all the information needed to generate keys as well as to validate them.
Generate keys by encrypting (with a private key) a known value + nonce. This can be verified by decrypting using the corresponding public key and verifying the known value. The program now has enough information to verify the key without being able to generate keys.
These are still all open to attack: the program is still there and can be patched to bypass the check. Cleverer might be to encrypt part of the program using the known value from my third method, rather than storing the value in the program. That way you'd have to find a copy of the key before you could decrypt the program, but it's still vulnerable to being copied once decrypted and to having one person take their legit copy and use it to enable everyone else to access the software.
Their main use nowadays is for the Multiplayer component, where a server can verify the CD Key. For that, it's unimportant how securely it was generated as it boils down to "Lookup whatever is passed in and check if someone else is already using it".
That being said, you still want a large distribution and some randomness to avoid a pirate simply guessing a valid key (that's valid in your database but still in a box on a store shelf) and screwing over a legitimate customer who happens to buy that box.
One solution that should give you these would be to use a public key signing scheme. Start with a "system hash" (say grab the macs on any NICs, sorted, and the CPU-ID info, plus some other stuff, concatenate it all together and take an MD5 of the result (you really don't want to be handling personally identifiable information if you don't have to)) append the CD's serial number and refuse to boot unless some registry key (or some datafile) has a valid signature for the blob. The user activates the program by shipping the blob to you and you ship back the signature.
Potential issues include that you are offering to sign practically anything so you need to assume someone will run a chosen plain text and/or chosen ciphertext attacks. That can be mitigated by checking the serial number provided and refusing to handle request from invalid ones as well as refusing to handle more than a given number of queries from a given s/n in an interval (say 2 per year)
I should point out a few things: First, a skilled and determined attacker will be able to bypass any and all security in the parts that they have unrestricted access to (i.e. everything on the CD), the best you can do on that account is make it harder to get illegitimate access than it is to get legitimate access. Second, I'm no expert so there could be serious flaws in this proposed scheme.
The only major down side is that your CD keys will be quite long when using private / public keys 1024-bit in size. You also need to choose a nonce long enough so you aren't encrypting a trivial amount of information.
A good software license key/serial number generator consists of more than just a string of random characters or a value from some curve generator. Using a limited alphanumeric alphabet, data can be embedded into a short string (e.g. XXXX-XXXX-XXXX-XXXX) that includes all kinds of useful information such as:
The license key data is then encrypted and then encoded using the limited alphanumeric alphabet. For online validation, the license server holds the secrets for decrypting the information. For offline validation, the decryption secret(s) are included with the software itself along with the decryption/validation code. Obviously, offline validation means the software isn't secure against someone making a keygen.
Probably the hardest part about creating a license key is figuring out how to cram as much data as possible into as few bytes as possible. Remember that users will be entering in their license keys by hand, so every bit counts and users don't want to type extremely long, complex strings in. 16 to 25 character license keys are the most common and balance how much data can be placed into a key vs. user tolerance for entering the key to unlock the software. Slicing up bytes into chunks of bits allows for more information to be included but does increase code complexity of both the generator and validator.
Encryption is a complex topic. In general, standard encryption algorithms like AES have block sizes that don't align with the goal of keeping license key lengths short. Therefore, most developers making their own license keys end up writing their own encryption algorithms (an activity which is frequently discouraged) or don't encrypt keys at all, which guarantees that someone will write a keygen. Suffice it to say that good encryption is hard to do right and a decent understanding of how Feistel networks and existing ciphers work are prerequisites.
Verifying a key is a matter of decoding and decrypting the string, verifying the hash/checksum, checking the product ID and major and minor version numbers in the data, verifying that the license hasn't expired, and doing whatever other checks need to be performed.
Writing a keygen is a matter of knowing what a license key consists of and then producing the same output that the original key generator produces. If the algorithm for license key verification is included in and used by the software, then it is just a matter of creating software that does the reverse of the verification process.
To see what the entire process looks like, here is a blog post I recently wrote that goes over choosing the license key length, the data layout, the encryption algorithm, and the final encoding scheme:
The above license server supports both online and offline validation modes. A software product might start its existence with online only validation. When the software product is ready to retire and no longer supported, it can easily move to offline validation where all existing keys continue to work once the user upgrades to the very last version of the software that switches over to offline validation.
A live demo of how the above license server can be integrated into a website to sell software licenses plus an installable demo application can be found here (both the website and demo app are open source too):
There are also DRM behaviors that incorporate multiple steps to the process. One of the most well known examples is one of Adobe's methods for verifying an installation of their Creative Suite. The traditional CD Key method discussed here is used, then Adobe's support line is called. The CD key is given to the Adobe representative and they give back an activation number to be used by the user.
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