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# sol3 - CS346 Cryptography Fall 2009 Homework 3 SOLUTIONS...

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CS346 Cryptography, Fall 2009 Homework 3, SOLUTIONS 1. (8 points) Suppose that for using RSA, Bob has chosen a large public modulus n for which the factorization cannot be found in a reasonable amount of time. Suppose Alice sends a message to Bob representing each alphabetic character as an integer between 0 and 25, and encrypting each as a separate plaintext character. Describe how Oscar can easily decrypt a message which is encrypted this way. Solution: Oscar can generate a table of the encrypted values corresponding to the 26 alphabetic characters, since he knows the encryption key. Then Oscar can decrypt the ciphertext character by character comparing the ciphertext with the entries of the table. 2. (8 points) If an RSA user’s public key is n = 17 · 43 and b = 29, what is the private exponent a ? Explain what you do and include the partial results of your calculations. HINT: Use the extended Euclidean algorithm. It will only take a few steps, you can do it by hand.

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sol3 - CS346 Cryptography Fall 2009 Homework 3 SOLUTIONS...

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