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Researchers from NTT Labs and the Chinese University of Hong Kong have demonstrated that deriving provably quantum-hard problems from unstructured assumptions is fundamentally limited, challenging simple pathways to establishing quantum advantage in cryptography. This work extends the classical Bennett-Gill question to the quantum realm, revealing a substantial barrier where Shor's algorithms invalidate traditional number-theoretic hardness proofs while current cryptographic tools fail to offer robust alternatives for quantum computers. The findings highlight the critical distinction between structured and unstructured sources of computational difficulty, underscoring the complexity required to secure post-quantum cryptography.
NTT Labs rules out simple paths to quantum hardness proofs
NTT Social Informatics Laboratories and The Chinese University of Hong Kong researchers are addressing the difficulty of establishing quantum hardness proofs, finding that simple paths from unstructured assumptions to proving quantum advantage are unlikely. Xiao Liang, Takashi Yamakawa, and Chak Fai Yung are investigating structured quantum hardness, a complex area of quantum computing research.
Whether useful structured hardness can arise from unstructured assumptions is a fundamental question in complexity and cryptography. The longstanding Bennett-Gill question asks whether NP∩coNP remains hard relative to a random oracle; recently gave a conditional affirmative answer in the classical setting. They establish the quantum analogue: if, then with probability 1 over a random oracle O. This finding is significant because Shor’s algorithms invalidate traditional methods for establishing computational difficulty, while current cryptography doesn’t readily offer provably hard problems for quantum computers. Random oracles, essentially black boxes that provide random responses to queries, is a framework for investigating this question, offering computational difficulty without imposing specific algebraic structures. The team’s work builds upon the Bennett-Gill question, which originally asked if NP∩coNP remains hard relative to a random oracle, and extends it to the…
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