THE QUANTUM INTELLIGENCER

Bottom Line Up Front: Recent advances in exact, distributed quantum algorithms for the finite Abelian hidden subgroup problem (AHSP) reduce resource requirements and eliminate quantum communication needs, accelerating the timeline for cryptographically relevant quantum attacks—particularly against RSA and ECC—despite concurrent classical improvements. Threat Identification: The threat is the accelerated feasibility of quantum attacks on public-key cryptography due to a new distributed exact quantum algorithm for AHSP that leverages amplitude amplification and the Chinese Remainder Theorem to reduce qudit count and query complexity without requiring quantum communication (Liu et al., arXiv:2601.01234, 2026). The extension to certain non-Abelian groups suggests potential future applicability to broader cryptographic problems. Probability Assessment: High likelihood within 5–8 years (by 2031–2034) for experimental demonstration on small-scale cryptographic instances, assuming continued progress in quantum hardware. The removal of quantum communication makes deployment more practical than prior distributed models. Exactness of the algorithm increases reliability over probabilistic counterparts. Impact Analysis: Severe. Successful implementation would compromise widely used public-key systems (RSA, ECC, Diffie-Hellman), threatening digital signatures, TLS/SSL, blockchain, and secure communications. The distributed nature could enable modular or networked quantum devices to collaborate without high-fidelity quantum links, lowering deployment barriers. Recommended Actions: 1) Accelerate post-quantum cryptography (PQC) migration, prioritizing NIST-selected algorithms. 2) Audit cryptographic inventory to identify high-risk systems. 3) Fund research into quantum-resistant protocols and hybrid classical-quantum security models. 4) Monitor advancements in qudit-based quantum computing and distributed quantum processing. 5) Re-evaluate key rotation policies and forward secrecy mechanisms. Confidence Matrix: - Threat Identification: High confidence (based on peer-reviewed arXiv preprint with rigorous mathematical derivation) - Probability Assessment: Medium-high confidence (dependent on hardware scaling, but algorithmic efficiency improves feasibility) - Impact Analysis: High confidence (cryptographic consensus on AHSP’s role in breaking RSA) - Recommended Actions: High confidence (aligned with NSA, NIST, and CISA guidance) Citations: Liu et al., 'Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm,' arXiv:2601.01234 [quant-ph], 2026. —Ada H. Pemberley Dispatch from The Prepared E0