CIS3360: Security in Computing Homework 5 1. ( 15 points) Knowledge - based Question: a. What are the differences between public/symmetric key cryptography? The advantage and disadvantage of each? a. For English alphabet based texts regardless of upper or lower case (i.e., assuming each letter has only 26 possible value), if the length of the key using Vigenere Cipher is 4, how many possible encryption keys exist? (hint: we all know that Caesar cipher has 26 possible encryption keys) b. What is the usage of a cryptographic hash function? Can two documents have the same hash value? Answer: 1. Public vs Symmetric Key Cryptography • Public Key (Asymmetric) : o Uses two keys : public (shared) and private (secret). o Advantages : Easier key distribution, non - repudiation. o Disadvantages : Slower, more computationally intensive. • Symmetric Key : o Uses one key for both encryption and decryption. o Advantages : Faster, simpler. o Disadvantages : Key distribution is harder, not scalable. 2. Vigenère Cipher with Key Length 4 • There are 26^4 = 456,976 possible encryption keys. 3. Cryptographic Hash Function • Usage : Ensures data integrity, stores passwords securely, creates digital signatures. • Collisions : While rare, two documents can technically have the same hash value (this is called a collision). 2. (10 points) Determine whether a statement is True or False. If a statement is false, you must explain why. a. Digital signature of a message m is H(m), where H() represent a cryptographic hash function such as MD5 or SHA - 1. b. Cesar cipher is a kind of substitution cipher, while Vigenere cipher is a kind of transposition cipher. Answer: Let's go through each statement: a. Digital signature of a message m is H(m), where H() represents a cryptographic hash function such as MD5 or SHA - 1. • False . A digital signature is not just the hash of a message (H(m)). Instead, it is the result of applying a private key to the hash of the message (H(m)) using a signing algorithm (like RSA or ECDSA). The process involves signing the hash (H(m)) to create the signature, not just computing the hash itself. So, a digital signature typically involves hashing the message and then encrypting the hash with a private key, not just the hash alone. b. Caesar cipher is a kind of substitution cipher, while Vigenère cipher is a kind of transposition cipher. • False . Both the Caesar cipher and Vigenère cipher are types of substitution ciphers , not transposition ciphers. o Caesar cipher shifts each letter by a fixed number of positions in the alphabet (a simple form of substitution). o Vigenère cipher uses a keyword to shift letters in the plaintext by different amounts, effectively creating a more complex substitution cipher. A transposition cipher involves rearranging the positions of characters in the plaintext, which is not what the Vigenère cipher does. 3. (20 points) Cipher Generation: a. What are the substitutions for the (decimal) numbers 12, 7, and 2 using the S - box shown in the textbook as Figure 8.3. b. What is the encryption of the following string “THELAZYFOX” using the Caesar cipher with a key of “3 c. What is the Hill cipher key matrix K that can realize the following permutation: π : (1,2,3,4,5) → (3,5,1,4,2)