# hw409 - 5. (5 points) Bob acts as a trusted user to collect...

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CS346 Cryptography, Fall 2009 Homework 4, Due November 5 1. (5 points) Problem 4 (Chapter 8.8) 2. (10 points) Problem 10 (Chapter 8.8) 3. (10 points) Using the Diﬃe-Lamport signature scheme (see class notes) with encryption e ( x,K ) = x K mod n , Alice chooses in advance the four keys a 1 = 2 ,a 2 = 5 ,b 1 = 7 ,b 2 = 3 . A. If n = 13, give an example of what could be the validation parameters sent by Alice to Bob. B. What is Alice’s signature on the message 10? C. If Bob receives the signed message m 1 m 2 73, and the message is genuine, what are the message bits m 1 and m 2 ? 4. (10 points) Suppose Alice’s public modulus is n A = 2773, her public exponent is b A = 17, her private exponent is a A = 157. Bob’s public modulus is n B = 35, his public exponent is b B = 5. A. Compute Alice’s signature of the message 1111. B. Explain how would Alice send the plaintext 1111 signed and encrypted. Explain what Bob has to do to decrypt the message and verify the signature.
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Unformatted text preview: 5. (5 points) Bob acts as a trusted user to collect information from various people. Each person sends his/her data to Bob, encrypted with Bobs public key. However, before sending the actual message, each user authenticates Bob, using a standard authentica-tion protocol. Before sending their encrypted information, each person would choose some random message R, enrypt it with Bobs public key, and send E B ( R ) to Bob. Bob is supposed to answer by applying his private key to the message received, thus sending back the value R to the given person. After verifying that Bob responded with the correct R, the person will send his/her encrypted information using Bobs public key. Explain how Oscar can obtain someone elses data in this setup, without knowing anybodys private key. (Of course Oscar knows Bobs public key.)...
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## This note was uploaded on 10/07/2010 for the course C S 52475 taught by Professor Gal during the Fall '10 term at University of Texas at Austin.

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