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 k-i 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 ....
View Full Document
- Fall '10
- Cryptography, Oscar, Extended Euclidean algorithm