Bob wants to create his own Merkle-Hellman Knapsack pair of keys. If the key size = 4 and his first element of the private key = 3. Show all the steps of creating the pair of keys.Answer text Question 2Rich text editor

The Merkle-Hellman Knapsack Cryptosystem is a public key cryptosystem that is based on the subset sum problem. Here are the steps to create a pair of keys:

1. Private Key Generation: The private key in the Merkle-Hellman system is a superincreasing sequence (a sequence where each element is greater than the sum of all previous elements). Given that the key size is 4 and the first element is 3, we can generate the rest of the sequence. Let's say the sequence is {3, 7, 14, 30}.

2. Public Key Generation: To generate the public key, we need to choose two numbers: a multiplier (m) and a modulus (n). The modulus (n) must be greater than the sum of the elements in the private key, and the multiplier (m) must be coprime to n (i.e., the greatest common divisor of m and n is 1). Let's say we choose m = 11 and n = 100. The public key is then generated by multiplying each element in the private key by m mod n. So, the public key would be {33, 77, 54, 0}.

3. Encryption: To encrypt a message, we represent it as a binary string of length equal to the key size. Each bit in the string corresponds to an element in the public key. If the bit is 1, we include the corresponding element in the sum; if the bit is 0, we do not. The encrypted message is the total sum.

4. Decryption: To decrypt a message, we first multiply the encrypted message by the modular multiplicative inverse of m mod n. We then find the subset of the private key that sums to this result. The binary representation of this subset (with 1s for included elements and 0s for excluded elements) is the decrypted message.

Please note that the choice of m and n in step 2 is critical for the security of the system. If m and n are not chosen properly, the system can be broken using the continued fractions algorithm.