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where p = (25/26) , that is, p is the probability that no consistent extension of a path exists (in the random case). Under this assumption, show that the primary phase work factor is less than 245.1 for any choice of n. 24. Write a program to generate empirical results analogous to those in Tables 2.7 and 2.8.
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25. Consider a three rotor version of Sigaba, that is, assume that there are three cipher rotors, three control rotors, and three index rotors, where the rotors are the same as the actual Sigaba rotors. Assume that the stepping maze has been modified so that from one to three of the cipher rotors step with each letter encrypted or decrypted.
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a. What is the size of the theoretical keyspace for this Sigaba variant b. Under assumptions analogous to those in Section 2.4.3, what is the size of the keyspace That is, assume that only the six rotors in the machine are available for use as cipher or control rotors, the cipher and control rotors each have two orientations, only three index rotors are available, an itnalogous keying procedure is followed, the index rotors are inserted in a fixed order, and so on. 26. Consider a three rotor version of Sigaba, as described in Problem 25. Assume that the control rotors step in the same way as the three middle Sigaba rotors. Also, assume that the active inputs to the control rotors are F, G and H (that is, three inputs are active, not four, as is the case for Sigaba) and the output of the control rotors are combined as in (2.7). Also, the output of the index rotor bank is combined according to
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With these settings, at least onc of the cipher rotors will step, and at most, all three will step. Suppose that the following cipher and control rotors are available.
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Furt,herniore, suppose the following index rotors are available.
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a. Calculate the work factor for an attack on this three rotor Sigaba, using the analogous assumptions and approach a s the Sigaba attack discussed in this chapter. Specify the primary work and the secondary work. Also estiniate the number of known plaintext letters required.
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b. Implement this three rotor Sigaba and encrypt the message below. where aiu represents a blank space. Use thc following settings: cipher rotors 233, cipher rotor orientations 101 (where 0 is the forward orientation and 1 is reverse orientation). cipher rotor initializations ABC. control rotors Ol5>control rotor orientations 110, control rotor initializations ZYX, index rotor ordering 201, index rotor initialization 965.
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i 0 1 2 3 4 5 6 7 8 9 1011121314151617181920 Plaintext I A M H E A S Y 0 U A R E H E a 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Plaintext A S Y 0 U A R E M E A N D i 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 Plaintext W E A R E A L L T 0 G E T H E R
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c. Iniplenient the attack in part a. Show that you can recover the settings used to encrypt the message given in part b.
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27. This problem deals with the secondary phase of the Sigaba attack discussed in the text.
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a. For any pair of iiiputs to the index rotors, the corresponding number of control rotor output letters ranges from 1 to 11. All pairs and their corresponding values are listed in Table 2.10. Any index
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