Introduction to RSA Algorithm Answers 1. What aspect of RSA's implementation can lead to insecure keys? A. Using identical prime numbers for key generation B. Choosing an inappropriate modulus C. Using a public key that is too short D. Not encrypting the data properly Answer: Choosing an inappropriate modulus (B) Choosing an inappropriate modulus can compromise the security of the RSA algorithm by leading to insecure key generation. 2. Which of the following is NOT an application of RSA? A. Encryption of sensitive data in transit B. Digital certificates for endpoint authentication C. Digital signatures for message authentication D. Symmetric key encryption like AES Answer: Symmetric key encryption like AES (D) RSA is specifically a public-key cryptosystem and does not involve symmetric key encryption methods like AES. 3. What is the primary strength of RSA based on its algorithm? A. The difficulty of factoring large integers B. The speed of encryption and decryption C. The ability to use small prime numbers D. The ease of generating public keys Answer: The difficulty of factoring large integers (A) RSA's security relies on the difficulty of factoring large integers, which is essential for its effectiveness. 4. For security in RSA, what must be kept secret? A. The algorithm itself B. The public key C. The encryption method D. The prime numbers used in key generation Answer: The prime numbers used in key generation (D) The security of RSA depends on keeping the prime numbers used in key generation secret. 5. Which of the following statements about RSA key generation is most accurate? A. Keys can be generated without concern for key size. B. Public and private keys must be identical for security. C. It requires the generation of a public key and a private key. D. The same key can be reused indefinitely. Answer: It requires the generation of a public key and a private key. (C) RSA key generation involves creating both a public key and a private key, which serve different purposes in encryption and decryption. 6. What is the role of the public exponent *e* in RSA key generation? A. *e* must be a prime number between 1 and φ(n). B. *e* is the public key used for encryption. C. *e* must be coprime with φ(n) to ensure security. D. *e* is used to generate the modulus *n*. Answer: *e* must be coprime with φ(n) to ensure security. (C) *e* must be coprime with φ(n) to ensure it can be used effectively in the encryption process. 7. How is the ciphertext *c* calculated during the encryption process in RSA? A. *c* = *m**e* + *n*. B. *c* = *m* * *n* mod *e*. C. *c* = *m**e* mod *n*. D. *c* = *m* + *e* mod *n*. Answer: *c* = *m**e* mod *n*. (C) The ciphertext is calculated by raising the plaintext message *m* to the power of *e* and then taking the modulus with *n*. 8. What is the main mathematical problem that RSA security relies on? A. Finding the greatest common divisor of large integers. B. Factoring large integers into their prime components. C. Computing modular inverses efficiently. D. Solving linear equations with big integers. Answer: Factoring large integers into their prime components. (B) RSA security is based on the difficulty of factoring large integers, which is computationally hard. 9. Which of the following statements about the RSA algorithm is false? A. The modulus *n* is made public while *p* and *q* must remain secret. B. Larger values of *p* and *q* enhance RSA security. C. The private key consists of (*n*, *d*). D. RSA can utilize any integer as *e* for encryption. Answer: RSA can utilize any integer as *e* for encryption. (D) RSA requires *e* to be an integer that is coprime with φ(n), and it is typically chosen from a restricted set of values. 10. What happens if a faster algorithm to factor large numbers is developed? A. RSA would be replaced by symmetric encryption methods. B. It would have no effect on the security of RSA. C. The security of RSA would be significantly compromised. D. It would make RSA encryption slower and less efficient. Answer: The security of RSA would be significantly compromised. (C) The security of RSA heavily depends on the difficulty of factoring large numbers; hence, a faster algorithm would jeopardize its security. 11. What is the result of using small values of *p* and *q* in RSA key generation? A. Improved encryption speed without sacrificing security. B. Weaker overall security due to easier factorization. C. Larger public and private keys produced. D. Enhanced performance during decryption operations. Answer: Weaker overall security due to easier factorization. (B) Using small primes for *p* and *q* weakens the security as it makes it easier to factor *n*. 12. Why is it important to use strong random number generators in RSA? A. To prevent predictability in keys and enhance difficulty of attacks. B. To simplify the encryption and decryption computations. C. To ensure that *n* is always a prime number. D. To speed up the key generation process. Answer: To prevent predictability in keys and enhance difficulty of attacks. (A) Strong random number generators help ensure that the primes *p* and *q* are unpredictable, preventing attacks. 13. Which statement best describes the impact of larger modulus values *n* in RSA? A. They make factorization significantly more difficult. B. They enhance the performance of the algorithm. C. They increase the speed of decryption processes. D. They reduce the complexity of encryption. Answer: They make factorization significantly more difficult. (A) Larger values of *n* directly increase the difficulty of factoring it, thereby enhancing RSA security.