1. Please apply columnar transposition cipher to encrypt the message "a digital computer is a machine that can solve problems for" ignoring the space in between. If the probable word is “network", please give the corresponding ciphertext (no spaces). State the result: Provide Proof:| Solution: Proof is as the following, |N (3) E(1) T(6) W(7) O(4) R(5) K(2)

A.Given p=25, q=9, and e=7, generate the public key (n,e) and the private key (n,d) using the RSA Key generation algorithm. (Use Excel for computations) b. Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=3 to send to Bob. Show the ciphertext. c. Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertext y=2 received from Alice. Show the plaintext. d. Using the fast exponentiation method, determine 530 mod 47. Show your work.

What will be the ciphered text corresponding to “ALGORITHM” if bifid cipher is used for encryption with key as “KEY” with a period as 5? a) SBPISZTKZH b) PLNSOWGKQM c) SELFQEXBHM d) YFSGWNFBW

Many forms of cryptography are based on the following discrete log problem. Choose a cyclic group G (produced by one generator g) with finitely many elements. Alice and Bob want to set up a secret communication and need a secret key for that, which becomes a group element from G. They set up the following exchange (the so-called Diffie-Hellman protocol): 1. Alice chooses a secret group element a and sends unsecured g^a to Bob 2.Bob chooses a secret group element b and sends unsecured g^b to Alice 3. Alice calculates (g^b )^a and keeps this group element secret 4.Bob calculates (g^a )^b and keeps this group element secret Since a cyclic group is abelian, Alice and Bob now share the secret key (g^b )^a=(g^a )^b. The blue group elements are publicly known, the red elements are secret. The discrete log problem presented to an eavesdropper is computing say a from the publicly known data G,g,g^a. The naming of the problem comes from the solution a= glog⁡(ga ) which is generally difficult to…