[SOLVED] CS597 Advanced Cryptography Homework 2

CS597 Advanced Cryptography

Homework 2

Instructions:

To be turned in on paper at the beginning of class on Wednesday.

To earn points, every problem must start on a new page, and each page must have the following:

2. The answer for that problem and subproblems in your own words. from later, etc.

3. Citations or an explanation of outside sources used so that I can reproduce what you did. If you do use outside sources, you will likely learn less (not good for life, or erams).

Some notation from the book:

1. [a mod N] denotes the remainder of a divided by N, with 0< la mod N] < N. In class the brackets were dropped.

2. xlly denotes unambiguous concatenation of the strings z and y. Here “unambiguous” means that z and y can be recovered from zlly.

Three problems to turn in:

1. Consider the double (ASCII) Vigenère cipher, where we choose two keys (possibly of different lengths) ki, k2, and then encrypt a message by encrypting it first using the ASCII Vigenère cipher with ki to obtain an intermediate ciphertext c’, and then encrypting c’ using the ASCII Vigenère cipher with k2 to obtain the final ciphertext c. How would you attack this scheme?

2. Prove or refute: An encryption scheme with message space M is perfectly secret if and onlyl if for every probability distr. over M and every co,C1 EC we have Pr[C=co] = Pr[C= ci].

3. For each of the following encryption schemes, state whether the scheme is perfectly secret. Justify your answer in each case.

(a) The message space is M = {0,…,4). Algorithm Gen chooses a uniform. key from the key space {0,…,5}. Enck(m) returns [k+ m mod 5], and Deck(c) returns [c- k mod 5].

(b) The message space is M= {m E {0,1} | the last bit of m is 0}. Gen chooses a uniform. key from {0,1)-1. Enck(m) returns ciphertext m(kll0), and Deck(c) returns c(kl0).