Extra Credit 3

Due: May 7, 2018 at 11:59pm
Points: 20

Questions

1. (10 points) Alice enciphers messages m and m′ using the El Gamal cipher. Unfortunately, she uses the same random integer k. Eve intercepts the ciphers C and c′ corresponding to the two messages, respectively. She learns m through various sources. But she only has the ciphertext c′ corresponding to m′. Show how she can get m′.

2. (10 points) Assume that a cryptographic checksum function computes hashes of 128 bits. Prove that the probability is approximately 0.5 that at least one collision will occur after hashing O(2⁶⁴) randomly selected messages.

Matt Bishop Office: 2209 Watershed Sciences Phone: +1 (530) 752-8060 Email: mabishop@ucdavis.edu

ECS 153, Computer Security Version of April 26, 2018 at 7:05PM

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