Unformatted text preview: of n-bit words: 8-bit words, 16-bit words, 32-bit words, whatever: X1, X2, X3,..., Xm. This initial state is the key. The ith word of the generator is Xi = (Xi-a + Xi-b + Xi-c +...+ Xi-m) mod 2n If the coefficients a, b, c,..., m are chosen right, the period of this generator is at least 2n - 1. One of the requirements on the coefficients is that the least significant bit forms a maximal-length LFSR. For example, (55,24,0) is a primitive polynomial mod 2 from Table 16.2. This means that the following additive generator is maximal length. Xi = (Xi-55 + Xi-24) mod 2n This works because the primitive polynomial has three coefficients. If it has more than three, you need some additional requirements to make it maximal length. See  for details. Fish
Fish is an additive generator based on techniques used in the shrinking generator . It produces a stream of 32-bit words which can be XORed with a plaintext stream to produce ciphertext, or XORed with a ciphertext stream to produce plaintext. The algorithm is named as it is because it is a Fibonacci shrinking generator. First, use these two additive generators. The key is the initial values of these generators. Ai = (Ai-55 + Ai-24) mod 232 Bi = (Bi-52 + Bi-19) mod 232 These sequences are shrunk, as a pair, depending on the least significant bit of Bi: if it is 1, use the pair; if it is 0, ignore the pair. Cj is the sequence of used words from Ai, and Dj is the sequence of used words from Bi. These words are used in pairs—C2j, C2j+1, D2j, and D2j+1—to generate two 32-bit output words: K2j and K2j+1. E2j = C2j • (D2j ^ D2j+1) F2j = D2j+1 ^ (E2j ^ C2j+1) K2j = E2j • F2j K2i+1 = C2i+1 • F2j This algorithm is fast. On a 33 megahertz 486, a C implementation of Fish encrypts data at 15 megabits per second. Unfortunately, it is also insecure; an attack has a work factor of about 240 . Pike
Pike is a leaner, meaner version of Fish, brought to you by Ross Anderson, the man who broke Fish . It uses three additive gene...
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- Fall '10
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