hw4-csce-4050-5050

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Indiana Institute of Technology *

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3800

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Computer Science

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Apr 3, 2024

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Applications of Cryptography CSCE 4050/5050 (Spring 2024) Homework 4 Due on Feb 16 (Mon), 11:59pm Grading remarks: CSCE 4050 (undergraduate) students will receive extra 10 bonus points, as long as the assignment sheet (with attempted solutions) will be submitted. Total points (the actual grade will not exceed 100 points): CSCE 4050: 120 points. CSCE 5050: 110 points. 1. [ Advantage (distinguishing) ] Let G : K {0,1} n be a PRG that outputs the keystream of RC4 (stream cipher). We know from Lecture 2-2 that G has the following weakness: the probability that the second byte in the output of G takes a value 0x00 (that is an all-zero byte) is 2/256. Define a statistical test for distinguishing the output of G from a uniformly random sequence and compute the respective advantage. Hint: Follow the example of Slide 20, Lecture 3-1. [20 points]
2. [ Definition of semantic security ] Consider Slide 18 of Lecture 4-1 and suppose that the adversary B selects the messages as follows: m 0 such that lsb(m 0 ) = 1 and m 1 such that lsb(m 1 ) = 0. Compute the advantage Adv SS [B,E] in this case. Explain your answer. [20 points]
3. [ DES S-boxes ] For DES, suppose that the S-box S 1 has input “000001” and the S-box S 2 has input “100000”. Provide the respective outputs. Tip: The description of S-boxes can be found, e.g., here: https://csrc.nist.gov/csrc/media/publications/fips/46/3/archive/1999-10-25/documents/fips46-3.pdf [10 points] Rubric: 5 points for each correct answer.
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