1 HW #1 Information Security Course, 2023-2024 1. A small private club has only 10 members. Answers the following questions: a. How many secret keys are needed if all members of the club need to send secret messages to each other? b. How many secret keys ear needed if everyone trusts the president of the club? If a member needs to send a message to another member, she first sends it to the president; the president then sends the message to the other member. c. How many secret keys are needed if the president decides that the two members who need to communicate should contact him first. The president then creates a temporary key to be used between the two. The temporary key is encrypted and sent to both members. 2. A transposition block has 10 inputs and 10 outputs. What is the order of the permutation group? What is the key size? 3. A substitution block has 10 inputs and 10 outputs. What is the order of the permutation group? What is the key size? 4. Can you devise a meet-in-the-middle attack for a triple DES? 5. In AES, the size of the block is the same as the size of the round key (128 bits); in DES, the size of the block is 46 bits, but the size of the round key is only 48 bits. What are the advantages and disadvantages of AES over DES with respect to this difference? 6. In RC4, find a value for the secret key that does not change the state after the first and second initialization steps. 7. Alice uses Bob's RSA public key (e= 7, n = 143) to send the plaintext P = 8 encrypted as ciphertext C= 57. Show how Eve can use the chosen-ciphertext attack if she has access to Bob's computer to find the plaintext. 8. In the elliptic curve E(1, 2) over the GE(11) field: a. Find the equation of the curve. b. Generate public and private keys for Bob. c. Choose a point on the curve as a plaintext for Alice. d. Create ciphertext corresponding to the plaintext in part d for Alice. e. Decrypt the ciphertext for Bob to find the plaintext sent by Alice 2 9. Consider a Diffie-Hellman scheme with a common prime q = 17 and a primitive root a= 3. a. If user A has public key YA = 16, what is As private key XA? b. If user B has public key YB = 15, what is the shared secret key K? 10. Based on the bruteforce attack compute the full time to break the key size 2!", where we have a computer that need time 1 decryption per microsecond (1??)?

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