Решить задания по криптографии до 11:20 № 2275087

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Виконати 14 квітня 2021

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1. (9 points) Alice publishes her RSA public key: the modulus N = 273743 and the exponent e = 1321. (a) Bob wants to send Alice the message cup. What ciphertext does Bob send to Alice? (b) Alice knows that her modulus factors into a product of two primes, one of which is p = 457. Find the decryption exponent d for Alice. (c) Alice receives the ciphertext c = 204091 from Bob. Decrypt the message, if it is a word. 2. (6 points) Consider the Elgamal signature scheme with parameters g = 9, p = 101. Let’s Bob’s private key is d = sk = 8. (a) Calculate the Elgamal signature (r, s) and the corresponding verification for a message from Bob to Alice with the message m = 27 and ephemeral key ek = 11. (b) Verify that the messages (43, 49, 41) from Bob. 3. (3 points) Compute the two public keys and the common key for the DHKE scheme with the parameters p = 457, g = 17, and a = 26, b = 60. 4. (4 points) Let y2 = x3 + 2x + 5 be the elliptic curve defined over F17. Find P + Q, where P = (5, 2) and Q = (4, 3). 5. (3 points) Compute a session key in a DHKE protocol based on elliptic curves, if private key is a = 3 and Bob’s public key B = (5, 9). The elliptic curve being used is defined by y2 = x3 + x + 6 (mod 11).