# Sally Silly makes up her own version of RSA She doesn’t...

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MATH 470 Homework 5 Solutions [1] Sally Silly makes up her own version of RSA. She doesn’t want to mess with two primes so she just takes the modulus n to be a prime p but everything else is the same. Why is this not a good idea? d . [2] Bob spent some time making sure he had a selection of “strong primes” for his RSA parameters. Since Alice and Bob are very friendly, Alice decided to use some of this research. She in fact chose one of Bob’s primes p A = p B (but used a different q A ) in forming her modulus n A . Just to “be safe,” Bob and Alice chose different prime values for the exponents e A and e B . If Eve suspects something like this and of course she has access to the publicly available n A , n B and e A , e B , can she exploit this information and if so how? 2 . What would happen if you ran the Euclidean algorithm on n 1 and n 2 2 . What a bad idea. Never share your primes even with your best girlfriend. [3] If instead, Alice used the same modulus as Bob n A = n B , (but with different prime exponents) is there now a weakness? If, for example, Eve intercepted the same message m encrypted as c A and c B using Alice and Bob’s RSA public keys would this help to determine m ? [Hint: the Euclidean algorithm will help here.]