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Ki represents the current round s 48-bit string derived from the 56-bit key, and f represents the diffusion function This function operates as follows: 1 48 bits are selected from the 56-bit key 2 The right half is expanded from 32 bits to 48 bits via an expansion permutation 3 Those 48 bits are combined via XOR with the 48-key bits 4 This result is then sent through eight S-boxes, producing 32 new bits, and then it is permuted again After all 16 rounds have been completed and the inverse permutation has been completed, the ciphertext is output as 64 bits Then the algorithm picks up the next 64 bits and starts all over again This is carried on until the entire message has been encrypted with DES As mentioned, the same algorithm and key are used to decrypt and encrypt with DES The only difference is that the sequence of key permutations are used in reverse order Over the years that DES has been a cryptographic standard, a lot of cryptanalysis has occurred, and while the algorithm has held up very well, some problems have been encountered Weak keys are keys that are less secure than the majority of keys allowed in the keyspace of the algorithm In the case of DES, because of the way the initial key is modified to get the subkey, certain keys are weak keys The weak keys equate in binary to having all 1s or all 0s, or where half the key is all 1s and the other half is all 0s, like those shown in Figure 4-4 Semi-weak keys, with which two keys will encrypt plaintext to identical ciphertext, also exist, meaning that either key will decrypt the ciphertext The total number of possibly weak keys is 64, which is very small compared with the 256 possible keys in DES.

678 Database Design Appendix A, app1tex This le is c 1977 and 1983 by McGraw-Hill and c 1986, 2001 by Gio Wiederhold

(page 679)

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In addition, multiple successful attacks against DES algorithms have used fewer rounds than 16 Any DES with fewer than 16 rounds could be analyzed more efficiently with chosen plaintext than via a brute-force attack using differential cryptanalysis With 16 rounds and not using a weak key, DES is reasonably secure and amazingly has been for more than two decades In 1999, a distributed effort consisted of a supercomputer and 100,000 PCs over the Internet to break a 56-bit DES key By attempting more than 240 billion keys per second, the effort was able to retrieve the key in less than a day This demonstrates an incredible resistance to cracking a 20-year-old algorithm, but it also demonstrates that more stringent algorithms are needed to protect data today

Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do Go to, let us go down, and confound their language, that they may not understand one another s speech Genesis 11, 6 to 7

This list is intended to provide assistance when reading about les and databases Since there is a great deal of variation of meaning of the terms used in the literature, it is impossible to make this index truly comprehensive The appropriateness of the provided cross references has to be veri ed in each case by careful reading of the source material and the corresponding section of this book Often there will be no exact match and the concept or technique described in a reference will have to be circumscribed in a few sentences Whenever references are used to present material for classroom discussion or evaluation, then it is essential to use the standard terminology which has been introduced in this book to avoid misunderstandings and the associated waste of time

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