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DES, Breaking DES, and DES Variants
The Data Encryption Standard (DES) started life in the mids, adopted by the National Bureau of Standards (NBS) [now the National Institute of Standards and Technology (NIST)] as Federal Information Processing Standard 46 (FIPS PUB ) and by the American National Standards Institute (ANSI) as X
As mentioned earlier, DES uses the Data Encryption Algorithm (DEA), a secret key block-cipher employing a bit key operating on bit blocks. FIPS PUB 81 describes four modes of DES operation: Electronic Codebook (ECB), Cipher Block Chaining (CBC), Cipher Feedback (CFB), and Output Feedback (OFB). Despite all of these options, ECB is the most commonly deployed mode of operation.
NIST finally declared DES obsolete inand withdrew FIPS PUBCircuit maker 2000 pro 2000 crack serial keygen, and 81 (Federal Register, July 26,69(), ). Although other block ciphers have replaced DES, it is still interesting to see how DES encryption is performed; not only is it sort of neat, but DES was the first crypto scheme commonly seen in non-governmental applications and was the catalyst for modern "public" cryptography and the first public Feistel cipher. DES still remains in many products IOBIT Advanced Systemcare 10 Ultimate PRO KEY crack serial keygen and cryptography students and cryptographers will continue to study DES for years to come.
DES Operational Overview
DES uses a bit key. In fact, the bit key is divided into eight 7-bit blocks and an 8th odd parity bit is added to each block (i.e., a "0" or "1" is added to the block so that there are an odd number of 1 bits in each 8-bit block). By using the 8 parity bits for rudimentary error detection, a DES key is actually 64 bits in length for computational purposes although it only has 56 bits worth of randomness, or entropy (See Section A.3 for a brief discussion of entropy and information theory).
FIGURE DES enciphering algorithm. |
DES then acts on bit blocks of the plaintext, invoking 16 rounds of permutations, swaps, and substitutes, as shown in Figure The standard includes tables describing all of the selection, Circuit maker 2000 pro 2000 crack serial keygen, permutation, and expansion operations mentioned below; these aspects of the algorithm are not secrets. The basic DES steps are:
- The bit block to be encrypted undergoes an initial permutation (IP), where each bit is moved to a new bit position; e.g., the 1st, 2nd, and 3rd bits are moved to the 58th, 50th, and 42nd position, respectively.
- The bit permuted input is divided into two bit blocks, called left and right, Circuit maker 2000 pro 2000 crack serial keygen, respectively. The initial values of the left and right blocks are denoted L_{0} and R_{0}.
- There are then 16 rounds of operation on the L and R blocks. During each iteration (where n ranges from 1 to 16), the following formulae apply:
- L_{n} = R_{n-1}
R_{n} = L_{n-1} ⊕ f(R_{n-1},K_{n})At any given step in the process, then, the new L block value is merely taken from the prior R block value, Circuit maker 2000 pro 2000 crack serial keygen. The new R block is calculated by taking the bit-by-bit exclusive-OR (XOR) of the prior L block with the results of applying the DES cipher function, f, to the prior R block and K_{n}. (K_{n} is a bit value derived from the bit DES key. Each round uses a different 48 bits according to the standard's Key Schedule algorithm.)
The cipher function, f, combines the bit R block value and the bit subkey in the following way. First, the 32 bits in the R block are expanded to 48 bits by an expansion function (E); the extra 16 bits are found by repeating the bits in 16 predefined positions. The bit expanded R-block is then ORed with the bit subkey. The result is a bit value that is then divided into eight 6-bit blocks. These are fed as input into 8 selection (S) boxes, denoted S_{1},S_{8}. Each 6-bit input yields a 4-bit output using a table lookup based on the 64 possible inputs; this results in a bit output from the S-box. The 32 bits are then rearranged by a permutation function (P), producing the results from the cipher function.
- The results from the final DES round &#; i.e., Circuit maker 2000 pro 2000 crack serial keygen, L_{16} and R_{16} &#; are recombined into a bit value and fed into an inverse initial permutation (IP^{-1}). At this step, the bits are rearranged into their original positions, so that the 58th, 50th, and 42nd bits, for example, are moved back into the 1st, 2nd, and 3rd positions, Circuit maker 2000 pro 2000 crack serial keygen, respectively. The output from IP^{-1} is the bit ciphertext block.
Consider this example using DES in CBC mode with the following bit key and input:
- Key: = 0xDB6C1A
Input character string (ASCII/IA5): +
Input string (hex): 0x2BD
Output string (hex): 0xCBB2E9FD3AD90DE2B92C6BBB6CAC43E1AFA6
Output character string (BASE64): mBLLYgsun9OtkN4rksa7tsUnU6xD4a+m
Observe that we start with a byte input message. DES acts on eight bytes at a time, so this message is padded to 24 bytes and provides three "inputs" to the cipher algorithm (we don't see the padding here; it is appended by the DES code). Since we have three input blocks, we get 24 bytes of output from the three bit (eight byte) output blocks.
If you want to test this, a really good free, online DES calculator hosted by the Information Security Group at University College London. An excellent step-by-step example of DES can also be found at J. Orlin Grabbe's The DES Algorithm Illustrated page.
NOTE: You'll notice that the output above is shown in BASE BASE64 is a character alphabet &#; i.e., a six-bit character code composed of upper- and lower-case letters, the digitsand a few punctuation characters &#; that is commonly used as a way to display binary data. A byte has eight bits, or values, but not all ASCII characters are defined and/or printable. BASE64, simply, takes a binary string (or file), divides it into six-bit blocks, and translates each block into a printable character, Circuit maker 2000 pro 2000 crack serial keygen. More information about BASE64 can be found at my BASE64 Alphabet page or Circuit maker 2000 pro 2000 crack serial keygen Wikipedia.
Breaking DES
The mainstream cryptographic community has long held that DES's bit key was too short to withstand a brute-force attack Circuit maker 2000 pro 2000 crack serial keygen modern computers. Remember Moore's Law: computer power doubles every 18 months. Given that increase in power, a key that could withstand a brute-force guessing attack in could hardly be expected to withstand the same attack a quarter century later.
DES is even more vulnerable to a brute-force attack because it is often used to encrypt words, meaning that the entropy of the bit block is, effectively, greatly reduced. That is, if we are encrypting random bit streams, then a given byte might contain any one of 2^{8} () possible values and the entire bit block has 2^{64}, or about quintillion, possible values. If we are encrypting words, however, we are most likely to find a limited set of bit patterns; perhaps 70 or so if we account for upper and lower case letters, the numbers, space, and some punctuation. This means that only about &#; of the bit combinations of a given byte are likely to occur.
Despite this criticism, the U.S. government insisted throughout the mids that bit DES was secure and virtually unbreakable if appropriate precautions were taken. In response, RSA Laboratories sponsored a series of cryptographic challenges to prove that DES was no longer appropriate for use.
DES Challenge I was launched in March It was completed in 84 days by R. Verser in a collaborative effort using thousands of computers on the Internet.
The first DES Challenge II lasted 40 days in early This problem was solved by storycall.us, a worldwide distributed computing network using the spare CPU cycles of computers around the Internet (participants in storycall.us's activities load a client program that runs in the background, conceptually similar to the SETI @Home "Search for Extraterrestrial Intelligence" project). The storycall.us systems were checking 28 billion keys per second by the end of the project.
The second DES Challenge II lasted less than 3 days. On July 17,the Electronic Frontier Foundation (EFF) announced the construction of hardware that could brute-force a DES key in an average of days. Called Deep Crack, the device could check 90 billion keys per second and cost only about $, including design (it was erroneously and widely reported that subsequent devices could be built for as little as $50,). Since the design is scalable, this suggests that an organization could build a DES cracker that could break bit keys in an average of a day for as little as $1, Information about the hardware design and all software can be obtained from the EFF.
The DES Challenge III, launched in Januarywas broken is less than a day by the combined efforts of Deep Crack and storycall.us This is widely considered to have been the final nail in DES's coffin.
The Deep Crack algorithm is actually quite interesting. The general approach Circuit maker 2000 pro 2000 crack serial keygen the DES Cracker Project took was not to break the algorithm mathematically but instead to launch a brute-force attack by guessing every possible key. A bit key yields 2^{56}, or about 72 quadrillion, possible values. So the DES cracker team looked for any shortcuts they could find! First, they assumed that some recognizable plaintext would appear in the decrypted string even though they didn't have a specific known plaintext block. They then applied all 2^{56} possible key values to the bit block Circuit maker 2000 pro 2000 crack serial keygen don't mean to make this sound simple!). The system checked to see if the decrypted value of the block was "interesting," which they defined as bytes containing one of the alphanumeric characters, space, or some punctuation. Since the likelihood of a single byte being "interesting" Circuit maker 2000 pro 2000 crack serial keygen about &#;, then the likelihood of the entire 8-byte stream being "interesting" is about &#;^{8}, or 1/ (&#;^{16}). This dropped the number of possible keys that might yield positive results to about 2^{40}, or about a trillion.
They then made the assumption that an "interesting" 8-byte block would be followed by another "interesting" block. So, if the first block of ciphertext decrypted to something interesting, they decrypted the next block; otherwise, Circuit maker 2000 pro 2000 crack serial keygen, they abandoned this key. Only if the second block was also "interesting" did download hma pro vpn license key Archives examine the key closer. Looking for 16 consecutive bytes that were "interesting" meant that only 2^{24}, or 16 million, keys needed to be examined further. This further examination was primarily to see if the text made any sense. Note that possible "interesting" blocks might be 1hJ5&aB7 or DEPOSITS; the latter is more likely to produce a better result. And even a slow laptop today can search through lists of only a few million items in a relatively short period of time. (Interested readers are urged to read Cracking DES and EFF's Cracking DES page.)
It is well beyond the scope of this paper to discuss other forms of breaking DES and other codes. Nevertheless, it is worth mentioning a couple of forms of cryptanalysis that have been shown to be effective against DES. Differential cryptanalysis, invented in Circuit maker 2000 pro 2000 crack serial keygen E. Biham and A. Shamir (of RSA fame), is a chosen-plaintext attack. By selecting pairs of plaintext with particular differences, the cryptanalyst examines the differences in the resultant ciphertext pairs. Linear plaintext, invented by M. Matsui, uses a linear approximation to analyze the actions of a block cipher (including DES). Both of these attacks can be more efficient than brute force.
DES Variants
Once DES was "officially" broken, several variants appeared. But none of them came overnight; work at hardening DES had already been underway. In the early s, there was a proposal to increase the security of DES by effectively increasing the key length by using multiple keys with multiple passes. But for this scheme to work, it had to first be shown that the DES function is not a group, as defined in mathematics. If DES was a group, then we could show that for two DES keys, X1 and X2, applied to some plaintext (P), we can find a single equivalent key, X3, that would provide the same result; i.e.,
E_{X2}(E_{X1}(P)) = E_{X3}(P)
where E_{X}(P) represents DES encryption of some plaintext P using DES key X. If DES were a group, it wouldn't matter how many keys and passes we applied to some plaintext; we could always find a single bit key that would provide the same result.
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