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How to Create an Invoice Template in Excel! dc`5.4. DES, Breaking DES, and DES Variants
The Data Encryption Standard (DES) started life in the mid-1970s, 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 46-3) and by the American National EFT Dongle 2.7 crack latest Archives Institute (ANSI) as X3.92.
As mentioned earlier, DES uses the Data Encryption Algorithm (DEA), a secret key block-cipher employing a 56-bit key operating on 64-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 in 2004, and withdrew FIPS PUB 46-3, 74, and 81 (Federal Register, July 26, 2004, 69(142), 44509-44510). 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 Wolfram Mathematica 12 Full Crack With Activation Key [ 2021] Feistel cipher. DES still remains in many products — and cryptography students and cryptographers will continue to study DES for years to come.
DES Operational Overview
DES uses a 1 Form Proposal - Invoice 1.5 crack serial keygen key. In fact, the 56-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 11: DES enciphering algorithm. |
DES then acts on 64-bit blocks of the plaintext, invoking 16 rounds of permutations, swaps, and substitutes, as shown in Figure 11. The standard includes tables describing all of the selection, permutation, and expansion operations mentioned below; these aspects of the algorithm are not secrets. The basic DES steps are:
- The 64-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 64-bit permuted input is divided into two 32-bit blocks, called left and right, 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. 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 48-bit value derived from the 64-bit DES key. Each round uses a different 48 bits according to the standard's Key Schedule algorithm.)
The cipher function, f, combines the 32-bit R block value and the 48-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 48-bit expanded R-block is then ORed with the 48-bit subkey. The result is a 48-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 32-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., L_{16} and R_{16} — are recombined into a 64-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, respectively. The output from IP^{-1} is the 64-bit ciphertext block.
Consider this example using DES in CBC mode with the following 56-bit key and input:
- Key: 1100101 0100100 1001001 0011101 0110101 0101011 1101100 0011010 = 0x6424491D352B6C1A
Input character string (ASCII/IA5): +2903015-08091765
Input string (hex): 0x2B323930333031352D3038303931373635
Output string (hex): 0x9812CB620B2E9FD3AD90DE2B92C6BBB6C52753AC43E1AFA6
Output character string (BASE64): mBLLYgsun9OtkN4rksa7tsUnU6xD4a+m
Observe that we start with a 17-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 64-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 RevisionFX REflex v2.3.6 for Adobe After Effects crack serial keygen London. An excellent step-by-step example 1 Form Proposal - Invoice 1.5 crack serial keygen 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 BASE64. BASE64 is a 64-character alphabet — i.e., a six-bit character code composed of upper- and lower-case 1 Form Proposal - Invoice 1.5 crack serial keygen, the digits 0-9, and a few punctuation characters — that is commonly used as a way to display binary data. A byte has eight bits, or 256 values, but not all 256 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. More information about BASE64 can be found at my BASE64 Alphabet page or at Wikipedia.
Breaking DES
The mainstream cryptographic community has long held that DES's 56-bit key was too short to withstand a brute-force attack from 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 1975 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 64-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} (256) possible values and the entire 64-bit block has 2^{64}, or about 18.5 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 ¼ of the bit combinations of a given byte are likely to occur.
Despite this criticism, the U.S. government insisted throughout the mid-1990s that 56-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 1997. 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 1998. This problem was solved by distributed.net, a worldwide distributed computing network using the spare CPU cycles of computers around the Internet (participants in distributed.net's activities load a client program that runs in the background, conceptually similar to the SETI @Home "Search for Extraterrestrial Intelligence" project). The distributed.net 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, 1998, the Electronic Frontier Foundation (EFF) announced the construction of hardware that could brute-force a DES key in an average of 4.5 days. Called Deep Crack, the device could check 90 billion keys per second and cost only about $220,000 including design (it was erroneously and widely reported that subsequent devices could be built for as little as $50,000). Since the design is scalable, this suggests that an organization could build a DES cracker that could break 56-bit keys in an average of a day for as little as $1,000,000. Information about the hardware design and all software can be obtained from the EFF.
The DES Challenge III, launched in January 1999, was broken is less than a day by the combined efforts of Deep Crack and distributed.net. 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 that 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 56-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 1 Form Proposal - Invoice 1.5 crack serial keygen possible key values to the 64-bit block (I 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" is about ¼, then the likelihood of the entire 8-byte stream being "interesting" is about ¼^{8}, or 1/65536 (½^{16}). This dropped the number of possible keys that might yield positive results to about 2^{40}, 1 Form Proposal - Invoice 1.5 crack serial keygen, 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, they abandoned this key. Only if the second block was also "interesting" did they 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, 1 Form Proposal - Invoice 1.5 crack serial keygen. 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 1990 by 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 1990s, 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 56-bit key that would provide the same result.
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