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Blowfish: A symmetric 64-bit block cipher invented by Bruce Schneier; optimized for 32-bit processors with large data caches, it is significantly faster than DES on a Pentium/PowerPC-class machine. Key lengths can vary from 32 to 448 bits in length. Blowfish, available freely and intended as a substitute for DES or IDEA, is in use in a large number of products.
GPRS (General Packet Radio Service) encryption: GSM mobile phone systems use GPRS for data applications, and GPRS uses a number of encryption methods, offering different levels of data protection. GEA/0 offers no encryption at all. GEA/1 and GEA/2 are proprietary stream ciphers, employing a 64-bit key and a 96-bit or 128-bit state, respectively. GEA/1 and GEA/2 are most widely used by network service providers today although both have been reportedly broken. GEA/3 is a 128-bit block cipher employing a 64-bit key that is used by some carriers; GEA/4 is a 128-bit clock cipher with a 128-bit key, but is not yet deployed.
RSA: The first, and still most common, PKC implementation, named for the three MIT mathematicians who developed it — Ronald Rivest, Adi Shamir, and Leonard Adleman. RSA today is used in hundreds of software products and can be used for key exchange, digital signatures, or encryption of small blocks of data. RSA uses a variable size encryption block and a variable size key. The key-pair is derived from a very large number, n, that is the product of two prime numbers chosen according to special rules; these primes may be 100 or more digits in length each, yielding an n with roughly twice as many digits as the prime factors. The public key information includes n and a derivative of one of the factors of n; an attacker cannot determine the prime factors of n (and, therefore, the private key) from this information alone and that is what makes the RSA algorithm so secure. (Some descriptions of PKC erroneously state that RSA's safety is due to the difficulty in factoring large prime numbers. In fact, large prime numbers, like small prime numbers, only have two factors!) The ability for computers to factor large numbers, and therefore attack schemes such as RSA, is rapidly improving and systems today can find the prime factors of numbers with more than 200 digits. Nevertheless, if a large number is created from two prime factors that are roughly the same size, there is no known factorization algorithm that will solve the problem in a reasonable amount of time; a 2005 test to factor a 200-digit number took 1.5 years and over 50 years of compute time. In 2009, Kleinjung et al. reported that factoring a 768-bit (232-digit) RSA-768 modulus utilizing hundreds of systems took two years and they estimated that a 1024-bit RSA modulus would take about a thousand times as long. Even so, they suggested that 1024-bit RSA be phased out by 2013. (See the Wikipedia article on integer factorization.) Regardless, one presumed protection of RSA is that users can easily increase the key size to always stay ahead of the computer processing curve. As an aside, the patent for RSA expired in September 2000 which does not appear to have affected RSA's popularity one way or the other. A detailed example of RSA is presented below in Section 5.3.
Table 2 — from a 1996 article discussing both why exporting 40-bit keys was, in essence, no crypto at all and why DES' days were numbered — shows what DES key sizes were needed to protect data from attackers with different time and financial resources. This information was not merely academic; one of the basic tenets of any security system is to have an idea of what you are protecting and from whom are you protecting it! The table clearly shows that a 40-bit key was essentially worthless against even the most unsophisticated attacker. On the other hand, 56-bit keys were fairly strong unless you might be subject to some pretty serious corporate or government espionage. But note that even 56-bit keys were clearly on the decline in their value and that the times in the table were worst cases.
Using the LanMan scheme, the client system then encrypts the challenge using DES. Recall that DES employs a 56-bit key, acts on a 64-bit block of data, and produces a 64-bit output. In this case, the 64-bit data block is the random number. The client actually uses three different DES keys to encrypt the random number, producing three different 64-bit outputs. The first key is the first seven bytes (56 bits) of the password's hash value, the second key is the next seven bytes in the password's hash, and the third key is the remaining two bytes of the password's hash concatenated with five zero-filled bytes. (So, for the example above, the three DES keys would be 60771b22d73c34, bd4a290a79c8b0, and 9f180000000000.) Each key is applied to the random number resulting in three 64-bit outputs, which comprise the response. Thus, the server's 8-byte challenge yields a 24-byte response from the client and this is all that would be seen on the network. The server, for its part, does the same calculation to ensure that the values match.
Unlike Diffie-Hellman, RSA can be used for key exchange as well as digital signatures and the encryption of small blocks of data. Today, RSA is primarily used to encrypt the session key used for secret key encryption (message integrity) or the message's hash value (digital signature). RSA's mathematical hardness comes from the ease in calculating large numbers and the difficulty in finding the prime factors of those large numbers. Although employed with numbers using hundreds of digits, the math behind RSA is relatively straight-forward.
Having nothing to do with TrueCrypt, but having something to do with plausible deniability and devious crypto schemes, is a new approach to holding password cracking at bay dubbed Honey Encryption. With most of today's crypto systems, decrypting with a wrong key produces digital gibberish while a correct key produces something recognizable, making it easy to know when a correct key has been found. Honey Encryption produces fake data that resembles real data for every key that is attempted, making it significantly harder for an attacker to determine whether they have the correct key or not; thus, if an attacker has a credit card file and tries thousands of keys to crack it, they will obtain thousands of possibly legitimate credit card numbers. See "'Honey Encryption' Will Bamboozle Attackers with Fake Secrets" (Simonite) for some general information or "Honey Encryption: Security Beyond the Brute-Force Bound" (Juels & Ristenpart) for a detailed paper.
Files in an NTFS file system maintain a number of attributes that contain the system metadata (e.g., the $STANDARD_INFORMATION attribute maintains the file timestamps and the $FILE_NAME attribute contains the file name). Files encrypted with EFS store the keys, as stated above, in a data stream named $EFS within the $LOGGED_UTILITY_STREAM attribute. Figure 29 shows the partial contents of the Master File Table (MFT) attributes for an EFS encrypted file.
LRCs are very weak error detection mechanisms. If there is a single bit error, it will certainly be detected by an LRC. But an even number of errors in the same bit position within multiple bytes will escape detection by an XOR LRC. And a burst of errors might even escape detection by an additive LRC. The point is, it is trivial to create syndromes of bit errors that won't be found by an LRC code. (This is not to say that they are not used in some data transmission systems!)
One of the key concepts of information theory is that of entropy. In physics, entropy is a quantification of the disorder in a system; in information theory, entropy describes the uncertainty of a random variable or the randomness of an information symbol. As an example, consider a file that has been compressed using PKZip. The original file and the compressed file have the same information content but the smaller (i.e., compressed) file has more entropy because the content is stored in a smaller space (i.e., with fewer symbols) and each data unit has more randomness than in the uncompressed version. In fact, a perfect compression algorithm would result in compressed files with the maximum possible entropy; i.e., the files would contain the same number of 0s and 1s, and they would be distributed within the file in a totally unpredictable, random fashion. 2ff7e9595c