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Cryptography Homework 1

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Homework 1

Due September 25, 2014. The answers can be handed in person or submitted electronically on Blackboard. All problems carry 4 points. 1. The probabilities (or frequencies) of the 26 letters of the English alphabet in English text are as follows. Letter A B C D E F G H I Prob. .082 .015 .028 .043 .127 .022 .020 .061 .070 Letter J K L M N O P Q R Prob. .002 .008 .040 .024 .067 .075 .019 .001 .060 Letter S T U V W X Y Z Prob. .063 .091 .028 .010 .023 .001 .020 .001 Using this information, decrypt the following ciphertext which was encrypted using a Shift Cipher: RUNJAWNMQXFCXLJULDUJCNCQNJVXDWCXOYJYNAWNNMNMO XAJAXXVFQNWRFJBJCBLQXXUHXDVDUCRYUHCQNBZDJANOXXC JPNXOCQNFJUUBKHCQNLDKRLLXWCNWCBXOCQNOUXXAJWMLN RURWPLXVKRWNMJWMMXDKUNRCHXDCQNWJUUXFQJUOCQNCX CJUOXAXYNWRWPBBDLQJBFRWMXFBJWMMXXABCQNWHXDJU UXFCQNXCQNAQJUOOXAVJCLQRWPCQNYJCCNAWCQNWHXDMXDKU NCQNFQXUNCQRWPJPJRWCXPRENJVJAPRWXONAAXAJWMCQNWH XDXAMNACQNYJYNA 2. In a one-time pad, if a message m of length is is encrypted with a key k = 0 (i.e., k consists of all 0s) then enck (m) = m. That is why, it is sometimes suggested to prohibit this key. In other words, the keyspace is restricted to strings which are all not zeros. Is the resulting cryptosystem perfectly secure? 3. For every string s, let s be the string formed by taking the bitwise complement of the string s. For example 101 = 010 and 0010 = 1101. Suppose that G is a psuedorandom number generator (PRG) with expansion factor . Which amongst the following functions are psuedorandom number generators? (Explain why?) (a) G1 (s) = G(s) for every string s. (b) G2 (s) = G(s) for every string s. (c) G3 (s) = G(s)G1 (s) for every string s.

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4. Are the following statements true or false? Please explain why. (a) It is perfectly secure to use the same key for encrypting two different messages when using one-time pad. (b) If I want to achieve authenticated

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