Hill Cipher Overview Answers 1. What vulnerability does the Hill cipher have? A. It uses asymmetric key encryption. B. It cannot handle larger block sizes. C. It is vulnerable to known plaintext attacks. D. It is easily decipherable with a brute-force attack. Answer: It is vulnerable to known plaintext attacks. (C) The Hill cipher can be compromised if enough plaintext-ciphertext pairs are known. 2. How does the block size (n) affect the Hill cipher's security? A. Larger block sizes typically enhance security. B. Smaller block sizes make the cipher stronger. C. Block size does not affect security. D. Block size only impacts speed, not security. Answer: Larger block sizes typically enhance security. (A) A larger block size in the Hill cipher generally leads to greater strength against cryptanalysis. 3. Why is the Hill cipher not suitable for modern applications? A. It is dependent on simple substitution methods. B. It is primarily used for symmetric key encryption. C. It has historical value but lacks practical robustness. D. It requires extensive computational resources. Answer: It has historical value but lacks practical robustness. (C) While educational, the Hill cipher does not provide sufficient robustness against modern cryptanalysis. 4. Which of the following statements about the Hill cipher is true? A. It serves primarily as a historical learning tool. B. It effectively uses asymmetric key cryptography. C. It uses advanced techniques and offers strong security. D. It is more secure than modern symmetric-key ciphers. Answer: It serves primarily as a historical learning tool. (A) The Hill cipher has educational value in cryptography, especially for learning about polygraphic substitution. 5. What can be concluded about the key matrix of the Hill cipher? A. Its determination requires complex algorithms. B. It can be easily determined through linear algebra if enough data is available. C. It is never identifiable from plaintext-ciphertext pairs. D. It is larger than that of any modern cipher. Answer: It can be easily determined through linear algebra if enough data is available. (B) If enough plaintext-ciphertext pairs are known, the key matrix of the Hill cipher can be derived using linear algebra. 6. What is the primary advantage of the Hill cipher over monoalphabetic ciphers? A. It uses a fixed key for encryption. B. It requires no mathematical operations. C. It encrypts one letter at a time. D. It encrypts multiple letters simultaneously. Answer: It encrypts multiple letters simultaneously. (D) The Hill cipher encrypts multiple letters at a time, increasing complexity and security compared to monoalphabetic ciphers. 7. What determines the size of the key matrix in the Hill cipher? A. The length of the ciphertext. B. The type of encryption algorithm used. C. The total number of letters in the alphabet. D. The number of plaintext letters to be encrypted at one time. Answer: The number of plaintext letters to be encrypted at one time. (D) The key matrix is a square matrix of size n x n, where n represents the number of letters encrypted simultaneously. 8. Which condition must be satisfied for the key matrix to ensure unique decryption? A. The elements must be larger than 26. B. The entries must be all positive integers. C. The key matrix must be invertible. D. The determinant of the key matrix must be even. Answer: The key matrix must be invertible. (C) Invertibility of the key matrix is crucial for ensuring that unique decryption is possible. 9. During encryption in the Hill cipher, how is the plaintext processed? A. It is randomized before encryption. B. It is converted to binary format. C. It is divided into blocks and converted into vectors. D. It is encrypted letter by letter. Answer: It is divided into blocks and converted into vectors. (C) The plaintext is divided into blocks of n letters and treated as vectors before multiplication with the key matrix. 10. What mathematical operation is performed on the ciphertext vector for decryption? A. Determinant calculation B. Addition with the key matrix C. Subtraction of plaintext values D. Matrix inverse multiplication Answer: Matrix inverse multiplication (D) The inverse of the key matrix is used to multiply the ciphertext vector during decryption. 11. Why is it important that the determinant of the key matrix is relatively prime to 26? A. To allow encryption of larger blocks of text. B. To ensure all entries in the matrix are unique. C. To guarantee the existence of a multiplicative inverse modulo 26. D. To ensure the key matrix can be multiplied by vectors. Answer: To guarantee the existence of a multiplicative inverse modulo 26. (C) The determinant's relative primeness to 26 ensures that a multiplicative inverse exists, allowing for effective decryption. 12. In a 2x2 Hill cipher example with a key matrix [2 5; 3 7], what would the inverse matrix need to satisfy for decryption? A. It must have a determinant less than 26. B. It must exist and be valid under mod 26. C. It must be the same size as the ciphertext. D. It should be equal to the original key matrix. Answer: It must exist and be valid under mod 26. (B) The inverse matrix must exist and be valid under mod 26 to correctly decrypt the ciphertext. 13. What happens if the key matrix is not invertible? A. All ciphertext will be random. B. The encryption process fails. C. Some plaintext blocks may not be uniquely decrypted. D. Only the first letter of plaintext can be decrypted. Answer: Some plaintext blocks may not be uniquely decrypted. (C) If the key matrix is not invertible, some plaintext blocks might not be uniquely decrypted, affecting the decryption process.