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utility.6 The company Katz created, PKWare, Inc., still exists. Tragically, Phil Katz died in 2000, a t age 37, as a result of alcohol abuse [106]. PKZIP is primarily a compression utility, but since ARC provided a n encryption option, PKZIP needed one as well. ARC encryption was trivialsimply a repeated XOR with the password-and Katz wanted something stronger. The obvious cipher choices were DES or triple-DES, but efficiency was a major issue, as were concerns over export controls, which limited the strength of encryption that could be used on products destined for non-US markets. As a result, PKZIP used its own homebrew cipher, designed by Roger Schlafly [78]. Although the PKZIP cipher is weak, it is not trivial t o break. Export controls in force at the time limited key sizes to 40 bits or less, and the work factor to break the PKZIP cipher is close t o that limit, unless a large amount of known plaintext is available, in which case the work factor can be reduced significantly. The PKZIP cipher employs a n interesting and unorthodox design. For one thing, it may be one of the first ciphers t o use mixed-mode arithmetic as an efficient way t o achieve a degree of nonlinearity. This is a common strategy today, employed in such well-known and respected ciphers as IDEA and TEA. However, it is clear that there was little, if any, peer review of the PKZIP cipher, in violation of Kerckhoffs Principle. Not surprisingly, PKZIP proved t o be weak when exposed t o the light of day. Biham and Kocher [13]developed a known plaintext attack on the PKZIP cipher which we discuss in this section. However, the paper [13]is itself difficult to decipher-Conrad s implementation [30] is the key to understanding the Biham-Kocher attack. Attacks that require slightly less known plaintext are known [143].
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We ignore the PKZIP compression process and instead focus on the encryption. Here, we are concerned with the so-called internal representation of the key, a 96-bit quantity derived from a user-supplied password [13]. We denote this key as three 32-bit words, X , Y ,and 2.The attack will recover this key, which enables us to decrypt the message, as well as any other messages encrypted under the same password. The PKZIP stream cipher generates one byte of keyst,ream a t each step. Being a stream cipher, the keystream is XORed with the plaintext t o produce the ciphertext. The same keystream is XORed with the ciphertext t o recover the plaintext.
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The success of ZIP and the rapid demise of ARC was not only due to the technical superiority of the ZIP format. Another factor was the widespread belief amongst nerds that Phil Katz had been persecuted by SEA.
STREAM CIPHERS
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Below, we follow the convention that upper case letters represent 32bit words, while lower case represent 8-bit bytes- for the one require 16-bit quantity, we also use lower case. All arithmetic is to be taken modulo 232. As in other sections of this book, we adopt the convention that bits are numbered from left-to-right, beginning with 0. In the PKZIP attack discussed below, we often need t o specify a range of bits within a byte or a 32-bit word. We use the notation (A)i,..j, where j 2 i , for the string of bits of length j - i 1 beginning with bit i and ending with bit j of A. The PKZIP encryption algorithm appears in Table 3.11. Here, p is the current plaintext byte, c the resulting ciphertext byte, and k is the keystream byte.
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Table 3.11: PKZIP Encryption encrypt plaintext byte p result is ciphertext byte c given current X ,Y , Z k = getKeystreamByte(2) c=p@k update(X, y,2, ) P The functions getKeystreamByte and update are defined in Tables 3.12 and 3.13, respectively. T h e decryption process is easily derived from these encryption routines. Table 3.12: PKZIP getKeystreamByte getKeystrciamByte( 2)
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