01. Your first task is to strengthen the encryption methods used in the firm's cyber-security software by applying principles of number theory. Prime numbers and modular arithmetic are essential components of modern cryptography.
Write a detailed report on the significance of prime numbers in computing, particularly in cryptography. Explain how prime numbers form the basis of encryption algorithms.
Before this report you need to solve the following question,
a) You need to compute the modular inverse of a number in the context of cryptographic systems. Specifically, find the modular inverse of 17 modulo 3120, using the Extended Euclidean Algorithm.
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