As we have discussed, public-key cryptography can be used for encryption (EIGamal for instance) and key exchange. Furthermore, it has some properties (such as nonrepudiation) which are not offered by secret key cryptography. So why do we still use symmetric cryptography in current applications? 1. In this problem, we want to compare the computational performance of symmetric and public key algorithms. Assume a fast public-key library such as OpenSSL that can decrypt data at a rate of 100 Kbit/sec using the RSA algorithm on a modern PC. On the same machine, AES can decrypt at a rate of 17 Mbit/sec. Assume we want to decrypt a movie stored on a DVD. The movie requires 1 GByte of storage. How long does decryption take with either algorithm? 2. In the DHKE protocol, it is tempting to choose the private keys ("a" for Alice and "b" for Bob) from the set {1, . . . , p-1). However, in practice, we use set {2, . . . , p-2). Why are the values a-1 and a p-1 excluded? Describe the weakness of these two values. (i) Derive the Alice's public key "A" using her potential private key a-1 for Alice and, then, noting that public keys are public, explain how the attacker can guess this bad choice of private key (ii) Repeat this for a-p-1 and use Fermat's Little Theorem (FLT) to derive the public key A and suggest why this is a bad choice