Provide a comprehensive analysis of Shor's algorithm and its implications for modern public-key cryptography (RSA, ECC). Compare the time complexity of integer factorization using the General Number Field Sieve (classical) versus Shor's algorithm (quantum). Additionally, discuss the current state of Noisy Intermediate-Scale Quantum (NISQ) devices and the specific challenges (error rates, qubit coherence times) that prevent immediate practical implementation. Conclude with an evaluation of post-quantum cryptographic standards (e.g., Lattice-based cryptography) proposed by NIST as a defense mechanism.