Overview of ElGamal Encryption Answers 1. What is the primary basis for the security of ElGamal encryption? A. The use of symmetric key algorithms. B. The difficulty of the discrete logarithm problem. C. The difficulty of the prime factorization problem. D. The complexity of matrix inversion. Answer: The difficulty of the discrete logarithm problem. (B) The security of ElGamal relies on the intricate nature of the discrete logarithm problem, making it difficult to derive the private key from the public key. 2. During the encryption process in ElGamal, what is required to compute the ciphertext c1? A. The two prime numbers p and q. B. The message m and the private key x. C. The recipient's public key y and the random integer k. D. The random integer k and the generator g. Answer: The random integer k and the generator g. (D) To compute the ciphertext c1, a random integer k and the generator g are utilized according to the encryption formula. 3. What aspect of ElGamal encryption affects its overall security the most? A. The algorithm's speed in encrypting messages. B. The specific encryption and decryption formulas used. C. The prime numbers p and q used in key generation. D. The size of the public key. Answer: The prime numbers p and q used in key generation. (C) The choice of large prime numbers p and q plays a critical role in determining the overall security of the ElGamal encryption system. 4. What values are computed during the decryption process of an ElGamal ciphertext? A. Random integer k and the public key. B. c1 and c2 are transformed to recover m. C. Only the private key x is used. D. The public key y and the generator g. Answer: c1 and c2 are transformed to recover m. (B) During decryption, the recipient processes both c1 and c2 with their private key x to recover the original message m. 5. In the context of ElGamal encryption, what is the role of the random integer k? A. It is used to encrypt the message confidentiality. B. It determines the size of the private key. C. It selects the modulus p for encryption. D. It creates the public key for decryption. Answer: It is used to encrypt the message confidentiality. (A) The random integer k is integral to the encryption process, providing additional confidentiality during the message encryption. 6. Which application is NOT commonly associated with ElGamal encryption? A. Digital signatures. B. Secure online transactions. C. Image compression. D. Secure communication channels. Answer: Image compression. (C) While ElGamal is versatile in secure communication and various cryptographic applications, it is not typically associated with image compression. 7. How does ElGamal encryption compare to RSA in terms of security? A. ElGamal's security is governed by discrete logarithms, while RSA relies on prime factorization. B. ElGamal is more efficient than RSA. C. ElGamal provides less security than RSA. D. ElGamal encrypts data faster than RSA. Answer: ElGamal's security is governed by discrete logarithms, while RSA relies on prime factorization. (A) ElGamal and RSA offer comparable security; however, they are based on different mathematical problems, making them attractive for various use cases. 8. What must be ensured during the selection of the random integer k in the ElGamal encryption process? A. It should be randomly selected to prevent potential attacks. B. It must be larger than the public key y. C. It should remain constant across different encryptions. D. It must be a prime number. Answer: It should be randomly selected to prevent potential attacks. (A) The randomness in selecting k is crucial to prevent vulnerabilities and enhance the overall security of the encryption.