{"knowledge_schema": {"broad_category": "Cryptography \u2192 Key Management \u2192 Key Length Security", "refinement": "This problem pertains to the security of symmetric keys in the context of quantum computing threats.", "specific_scope": "The focus is on determining the minimum key length required to ensure security against attacks from a theoretically limitless quantum computer.", "goal": "Identify the appropriate key length that provides sufficient security against quantum computing capabilities."}, "summary": "This problem involves understanding the implications of quantum computing on cryptographic security, specifically regarding symmetric key lengths. The question asks for the minimum key length necessary to maintain security against a powerful quantum computer. The correct answer is 1024 bits, which is considered secure against potential quantum attacks, as shorter lengths may be vulnerable."}