RSA Encryption: Public Key and Decryption Key Calculation

What is the public key in a RSA Encryption system and how does it relate to the decryption key?

Given the public key {n, e} = {2021, 101}, how can we calculate the decryption key {n, d}?

Calculating the Decryption Key

To calculate the decryption key {n, d} for the given RSA encryption system with public key {n, e} = {2021, 101}, we need to find the value of d using the formula:

d = e^-1 mod (p-1)(q-1)

RSA encryption is a widely used encryption algorithm that is based on the mathematical properties of prime numbers. In this system, the public key {n, e} is used for encryption, while the private key {n, d} is used for decryption. In the given data, the public key is {n, e} = {2021, 101}. To calculate the decryption key {n, d}, we need to find two prime numbers, p and q, whose product is equal to 2021.

By prime factorizing 2021, we find that 43 and 47 are the prime factors. We can then calculate the value of d as follows:

d = 101^-1 mod (43-1)(47-1)

Calculating the modular multiplicative inverse of 101 modulo 1764, we find that d is equal to 1701. Therefore, the decryption key {n, d} for the given RSA encryption system is {2021, 1701}.

This process demonstrates how the public key {n, e} is used to derive the private key {n, d} in an RSA Encryption system, ensuring secure communication and data encryption.