Cryptography: Theory and Practice

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ICS 268: Cryptography and Communication Security 9/28/2004 Homework 1 Due Tuesday, 10/5/2004, at the beginning of the class 1 Substitution cipher Have a look at the substitution cipher in Lecture Notes 1 (section 3.3) and recall the definition of perfect secrecy. Prove that the substitution cipher is perfectly secure for the special case of = 1, and that it it is not perfectly secure if 2. 2 OTP cipher variations Notation: We will denote by A n a set of n -long sequences of symbols A 1 A 2 . . . A n where each A i is an element of A . For example, taking A = { 0 , 1 } , we will write { 0 , 1 } n to denote a set of all n -long binary strings. We showed that One-Time Pad encryption satisfies perfect secrecy if M = K = { 0 , 1 } , for any . In this exercise we will look at variations of the OTP cipher, where the messages and/or keys are not any binary strings. For example, consider set S of three 2-bit strings, S = { 00 , 01 , 10 } . Consider the following three variations on the OTP cipher. In all these variations the key generation algorithm chooses k
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