Unformatted text preview: A to calculate inverses? Explain. 4. (8 points) Suppose that Oscar intercepts a message encoded with the RSA encryption, but he does not know the private key. Assume that n = p · q is the public modulus, and b is the public exponent. Suppose someone tells Oscar, that one of the plaintext blocks has a common factor with n . Explain how Oscar can use this information to decrypt the message. 5. (8 points) Prove that ( x b mod n ) a mod n = x ab mod n HINT: The binomial theorem will be helpful: ( s + t ) k = k X i =0 k i ! s i t ki EXTRA CREDIT (10 points) Describe the most eﬃcient algorithm you can for computing x b mod n , if b is an arbitrary integer. Your solution should be eﬃcient enough to use for RSA encoding. HINT: We have already seen in class how to do this if b is of the form b = 2 l for some integer l ....
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 Fall '10
 GAL
 Cryptography, Oscar, Extended Euclidean algorithm

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