Provide a step-by-step mathematical walkthrough of generating RSA public and private keys using the prime numbers 61 and 53. Show the calculation for 'n' (modulus), 'phi(n)' (Euler's totient), 'e' (public exponent), and 'd' (private exponent). Then, take the plaintext message '19' and demonstrate the encryption and decryption processes using the derived keys, explaining the modular arithmetic involved at each step.