Introduction to Elliptic Curve Cryptography Answers 1. What problem does ECC rely on for its security? A. Elliptic curve discrete logarithm problem B. Symmetric key distribution problem C. Prime number generation problem D. Integer factorization problem Answer: Elliptic curve discrete logarithm problem (A) ECC's security is based on the difficulty of solving the elliptic curve discrete logarithm problem. 2. Which of the following best describes an elliptic curve? A. A family of smooth, algebraic curves B. A simple polynomial with real coefficients C. A type of polygon used in geometry D. A linear equation in two-variable Answer: A family of smooth, algebraic curves (A) Elliptic curves are defined by a specific equation and are a family of smooth, algebraic curves. 3. What is the significance of the coefficients 'a' and 'b' in the elliptic curve equation? A. They are elements in a finite field that define the curve. B. They determine the encryption key length. C. They represent points on the curve. D. They define the dimension of the curve. Answer: They are elements in a finite field that define the curve. (A) The coefficients 'a' and 'b' are elements in a finite field and are critical for defining the elliptic curve. 4. What is the fundamental task in solving the ECDLP? A. Calculating the sum of two points on the curve B. Identifying the elliptic curve parameters C. Finding the private key given the public key D. Determining the scalar 'k' that transforms point P to point Q Answer: Determining the scalar 'k' that transforms point P to point Q (D) The ECDLP revolves around the challenge of finding the scalar 'k' that relates two points on the elliptic curve. 5. How is a public key generated in the ECC key generation process? A. By hashing the private key B. By squaring the private key C. By adding the private key to the generator point D. By multiplying the private key with a generator point Answer: By multiplying the private key with a generator point (D) A public key is produced by multiplying the private key 'd' with a generator point 'G' on the elliptic curve. 6. Which statement accurately describes the efficiency of ECC? A. It requires more computational power than traditional algorithms. B. It has higher key sizes compared to RSA. C. It offers the same security with significantly smaller key sizes. D. It is only suitable for large-scale computing environments. Answer: It offers the same security with significantly smaller key sizes. (C) ECC provides comparable security to other algorithms like RSA while using much smaller key sizes. 7. What role does an ephemeral shared secret play in ECC encryption? A. It is used to create a persistent public key. B. It is a temporary key that is chosen for individual encryption sessions. C. It is a constant key utilized across multiple encryptions. D. It is used to encrypt the private key. Answer: It is a temporary key that is chosen for individual encryption sessions. (B) In ECC encryption, an ephemeral shared secret is a temporary key chosen for each encryption process. 8. Why is ECC particularly useful for resource-constrained devices? A. It uses larger key sizes than alternative cryptosystems. B. It relies only on symmetric key operations. C. It does not require any computational resources. D. It offers reduced computational complexity and smaller key storage requirements. Answer: It offers reduced computational complexity and smaller key storage requirements. (D) The smaller key sizes and reduced computational needs of ECC make it ideal for devices with limited resources. 9. What is the primary advantage of using ECC over RSA? A. ECC can process larger key sizes more efficiently. B. ECC is incompatible with mobile devices. C. ECC is based on integer factorization security. D. ECC requires smaller key sizes for equivalent security levels. Answer: ECC requires smaller key sizes for equivalent security levels. (D) ECC achieves equivalent security levels with smaller key sizes compared to RSA, making it more efficient. 10. In ECC decryption, what is used to recover the original data from the message? A. An integer factorization method. B. The recipient's private key 'd'. C. The common generator point 'G'. D. The sender's private key. Answer: The recipient's private key 'd'. (B) The recipient's private key 'd' is necessary to derive the ephemeral shared secret used for data recovery. 11. What makes the security of ECC Diffie-Hellman key exchange robust? A. The simplicity of the elliptic curve equations. B. The reliance on RSA factors for decryption. C. The use of large integer prime numbers. D. The difficulty of the ECDLP (Elliptic Curve Discrete Logarithm Problem). Answer: The difficulty of the ECDLP (Elliptic Curve Discrete Logarithm Problem). (D) The security of ECC lies in the difficulty of solving the ECDLP, which is more complex than integer factorization. 12. Which of the following is NOT an application of ECC? A. Integer factorization. B. Cryptocurrencies. C. Smart cards. D. Digital signatures. Answer: Integer factorization. (A) ECC is utilized in smart cards, digital signatures, and cryptocurrencies, but does not apply to integer factorization. 13. In ECC key exchange, what role does the common generator 'G' play? A. It is used for hashing data. B. It acts as a point of reference for generating keys. C. It ensures the security of the shared secret key. D. It encrypts the messages being exchanged. Answer: It acts as a point of reference for generating keys. (B) The common generator 'G' serves as a specified point in the elliptic curve parameters used by the participating parties.