Lab: Asymmetric Encryption

By Drs. Anthony Vance and Dave Eargle

Part 1. Understanding Asymmetric Keys

  1. Key Exchange Problem. Imagine 200 people wish to communicate securely using symmetric keys, one symmetric key for each pair of people. (See Metcalf’s Law).

    Question: How many symmetric keys would this system use in total?
  2. RSA keys vs AES keys

    Question: Does a 256-bit RSA key (a key with a 256-bit modulus) provide strength similar to that of a 256-bit AES key? Explain.

    Note: www.keylength.com gives estimates for good key lengths. Here’s a tip for interpreting that site: If you were to select “Compare all methods”, and then enter the year “2030”, the “Method” column means “group that makes recommendations using their method” (recall that NIST held the competition that resulted in the AES winner being selected). “Date” means how long you’ll be secure until. “Symmetric” means the minimum keysize you would need to be secure for that long using a symmetric method such as AES. “Factoring Modulus” means the minimum keysize you would need to be secure for that long using an asymmetric method such as RSA.

Part 2. Calculating RSA keys

Note: To help you answer the following questions, view this “RSA Algorithm” video. Also, you can review the RSA wikipedia page example.
  1. Complete encryption and decryption using the RSA algorithm, for the following data (show all work): p = 5, q = 11, e = 3, M = 9. Also:

    Question: What is the ciphertext when performing RSA encryption with p=5, q=11, e=3, M=9?
    Question: Show all work for encryption and decryption
  2. You are Eve. In a public-key system using RSA, you intercept the ciphertext, C=10, sent to a user whose public key is e=5, n=35.

    Question: What is the plaintext `M`?