Explain the mathematical foundations and operational steps of Shor's algorithm for integer factorization. Your explanation should detail the quantum subroutines involved, specifically Quantum Phase Estimation and the Quantum Fourier Transform. Discuss how the algorithm reduces the problem of factoring to the problem of order-finding. Finally, analyze the implications of Shor's algorithm on current RSA encryption standards and estimate the number of logical qubits required to factor a 2048-bit integer.