how to solve this problems in cryptography?   

Problems 1. (15 Points) There is nothing exclusively special about strings and XOR in one-time pad. We can get the same properties using integers mod n and addition mod n. This problem considers a variant of one-time pad, in which the keys, plaintexts, and ciphertexts are all elements of Zn instead of {0, 1}. (a) What is the decryption algorithm that corresponds to the following encryption algo- rithm? Enc(k, m) : c= (k + m) mod n Show that the resulting scheme satisfies correctness (b) Show that the above scheme satisfies one-time uniform ciphertext security (c) It's not just the distribution of keys that is important. The way that the key is combined with the plaintext is also important. Show that a scheme with the following encryption algorithm does not satisfy one-time uniform ciphertext security Enc(k, m) : c= (km) mod n 2. (10 Points) Alice is using one-time pad and notices that when her key is the all-zeroes string k = 0", then Enc(k, m) = m and her message is sent in the clear! To avoid this problem, she decides to modify KeyGen to exclude the all-zeroes key. She modifies KeyGen to choose a key uniformly from {0,1}"\{0"}, the set of all n-bit strings except on. In this way, she guarantees that her plaintext is never sent in the clear. (a) Describe an attack demonstrating that the modified scheme does not satisfy one-time uniform ciphertext security 1-1