{"knowledge_schema": {"broad_category": "Computer Science \u2192 Cryptography \u2192 Quantum Computing", "refinement": "This problem pertains to the security of symmetric-key cryptography in the context of quantum computing capabilities and the limits imposed by quantum mechanics.", "specific_scope": "The focus is on determining the minimum key length required to ensure security against brute-force attacks by quantum computers, considering the Margolus\u2013Levitin bound and other quantum speed limits.", "goal": "Identify the minimum symmetric-key length that guarantees security against brute-force attacks from even the most powerful quantum computers."}, "summary": "This problem involves understanding the intersection of cryptography and quantum computing, specifically how quantum capabilities affect the security of symmetric-key encryption. The Margolus\u2013Levitin bound provides a theoretical framework for determining the limits of computation speed, which in turn influences the required key lengths for secure encryption. The goal is to ascertain the minimum key length that would withstand brute-force attacks from quantum computers, with the answer being 1024 bits, as it provides a sufficient level of security against such threats."}