hw7 - 1 Two users Alice and Bob use public keys to...

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1 1. Two users, Alice and Bob, use public keys to communicate. The two public keys are: Pa+: Alice public key (n, d)=(33,7) Pa-: Alice private key (n, e)=(33,3) Pb+: Bob’s public key (33, 13) Pb-: Bob’s private key (33, 17) Assume each of the 26 letters is represented by 5 bits, as shown below: a: 00001 b: 00010 c: 00011 z: 11010 Alice sends the following message “help” to Bob. (a) Suppose we use CRC to generate the message digest. The generator is x 5 + x 3 + x + 1 Compute the digital signature of the message (b) Encrypt the entire message (message + signature) using Bob’s public key. Write down the entire binary stream. Since the remainder of 33 may be 32. Thus we need to use 6 bits to represent each encrypted letter (including the CRC). (c) When the message is received, decrypt the message using Bob’s private key. Show your procedure. 2 . In RSA, we select e and d such that ed = 1 mod z , where z = (p-1)(q-1). The first step in solving this problem is to select an e that is relatively prime to z and then find d . Prove that if e is not relatively prime to z , then d has no solutions. (note that this is true as long as z is an
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