How can quantum computing revolutionize encryption algorithms in modern software?

As quantum computing technology matures, it holds the potential to far exceed the capabilities of classical computing, particularly in the realm of encryption. Current encryption algorithms like RSA and ECDSA rely heavily on the computational difficulty of factoring large numbers or solving discrete logarithms — challenges that quantum algorithms such as Shor’s algorithm can theoretically tackle with unprecedented speed and efficiency. This raises significant concerns for software developers and cybersecurity experts about the future viability of existing encryption methods. In this context, what are the potential pathways and challenges to integrating quantum-resistant algorithms into existing software infrastructures, and how can organizations begin to prepare for this impending paradigm shift?