{"id":"9ceb5e01-0186-4172-9ba3-a635c0944470","arxiv_id":"2604.23490","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A new MA-Program for non-symmetric modular inner product in LWE decryption enables QFHE with O(lambda log^2 lambda) EPR pairs and fully classical clients.","lead":"This paper introduces a modular arithmetic program tailored to LWE decryption that reduces EPR pairs needed for quantum fully homomorphic encryption from O(lambda squared) to O(lambda log squared lambda) while moving all quantum operations to the server. A smart generalist might read it to assess whether practical secure quantum cloud computing is becoming feasible through lower resource costs.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"MA-Program claimed to have O(λ) states while tracking partial sums in state space Z_q (size q), creating inconsistency unless q=O(λ)","rationale":"Reader already flags preservation of claimed state-space size under MBQC embedding; the visible mismatch between Z_q and O(λ) is a more basic internal inconsistency in the same quantity. This is visible from the abstract text alone and directly affects whether the exponential improvement follows. No other load-bearing gap (e.g., circular security or flow functions) is as directly tied to the numeric claim.","tokens_in":1820,"tokens_out":368,"duration_ms":32855,"concrete_test":"Extract the MA-Program transition function or state set (likely § on MA-Program or LWE decryption gadget); count distinct states and compare to q and to O(λ). Recompute EPR-pair count using the measured state cardinality and encoding length; if the result exceeds O(λ log² λ) by more than a log factor, the headline resource claim does not hold.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The size reduction to O(λ log² λ) EPR pairs rests on MA-Program parameters: state count O(λ), binary encoding O(log λ), length O(λ log λ). The text states the program 'tracks partial sums modulus q with state space Z_q', which requires |states|=q. Standard LWE parameters have q polynomial or larger in λ for security; the claim 'yielding programs of state count O(λ)' is then either a mis-statement or requires q=O(λ). If the former, the gadget-size formula does not follow from the described construction. The non-symmetric-function argument and MBQC embedding are secondary to this internal accounting of states.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims to introduce a modular arithmetic program (MA-Program) for LWE decryption in QFHE. By treating LWE decryption as a non-symmetric modular inner product (unlike prior symmetric-function optimizations), it constructs programs with state count O(λ), binary encoding O(log λ), and length O(λ log λ). This purportedly reduces the quantum gadget size from O(λ²) to O(λ log² λ) EPR pairs per T-gate, transfers all quantum resources to the server for a fully classical client, and uses MBQC with flow functions for O(log λ) parallel measurements per layer.","tokens_in":1987,"tokens_out":393,"duration_ms":15725,"significance":"If the claimed resource reduction and MA-Program construction hold without hidden assumptions on q or the MBQC embedding, the result would constitute a substantial efficiency gain over Barrington-based QFHE, moving the field closer to practical quantum homomorphic encryption with classical clients and no circular security assumptions.","major_comments":[{"comment":"Abstract: The central efficiency claim rests on the MA-Program having 'state count O(λ)' while 'tracks partial sums modulus q with state space Z_q'. A state space Z_q requires q states, yet the text asserts state count O(λ) and derives O(λ log² λ) EPR pairs from program length O(λ log λ). Standard LWE parameters set q polynomial or superpolynomial in λ for security, creating an internal inconsistency that prevents the stated reduction from following. This is load-bearing for the main result.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract uses 'lambda' inline without consistent mathematical formatting; ensure uniform notation (e.g., λ) throughout the manuscript.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and for identifying the potential inconsistency in the abstract. We respond point-by-point below.","responses":[{"response":"We acknowledge that the abstract phrasing creates an ambiguity. The full manuscript constructs an MA-Program specifically for the non-symmetric modular inner product <sk, ct> mod q. This construction achieves O(λ) states (not q states) by using a binary-encoded representation and a sequence of modular additions tailored to the LWE structure, resulting in program length O(λ log λ) and binary encoding O(log λ) per state. The reference to 'state space Z_q requiring O(log q) bits' describes the per-state encoding size under standard LWE parameters where log q = O(log λ), but does not imply the program maintains q distinct states. Nevertheless, the wording is imprecise and risks misinterpretation. We will revise the abstract and introduction to explicitly state that the MA-Program uses O(λ) states via its non-symmetric structure, independent of q's magnitude, and will add a clarifying sentence on how the state count is derived. This is a presentation issue only; the underlying gadget size claim remains as stated.","revision_made":"yes","referee_comment":"[Abstract] Abstract: The central efficiency claim rests on the MA-Program having 'state count O(λ)' while 'tracks partial sums modulus q with state space Z_q'. A state space Z_q requires q states, yet the text asserts state count O(λ) and derives O(λ log² λ) EPR pairs from program length O(λ log λ). Standard LWE parameters set q polynomial or superpolynomial in λ for security, creating an internal inconsistency that prevents the stated reduction from following. This is load-bearing for the main result."}],"tokens_in":1424,"tokens_out":387,"duration_ms":28080,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's central claim is a new MA-Program for the modular inner product in LWE decryption that is not symmetric. This lets them build programs of length O(lambda log lambda) instead of relying on Barrington or symmetric-function methods, which they say cuts the EPR pairs per T-gate from O(lambda squared) to O(lambda log squared lambda).\n\nThey also move all quantum resources to the server so the client stays classical, use layered keys to sidestep circularity, and embed the program in MBQC for some parallelism. That package is the actual new piece.\n\nThe soft spot is the state accounting. The description says the program tracks partial sums mod q with state space Z_q, yet claims O(lambda) states and O(log lambda) binary encoding. Standard LWE parameters have q polynomial or larger in lambda, so the state count does not line up unless q is artificially small. The resource reduction is derived directly from those program parameters, so this needs to be resolved before the numbers can be trusted.\n\nThe MBQC realization and gadget details are only sketched, which is normal at abstract level but leaves the correctness of the embedding uncheckable here.\n\nThis is for people already working on quantum delegated computation and homomorphic encryption. The tailoring of the program to LWE decryption is a reasonable direction even if the current accounting has a gap. It deserves a serious referee to check whether the state-space claim can be made consistent with the security parameters.","headline":"The efficiency gain rests on an MA-Program claiming O(lambda) states while using a Z_q state space whose size is typically much larger.","tokens_in":2458,"tokens_out":370,"would_cite":false,"duration_ms":18008,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A modular arithmetic program for LWE decryption reduces EPR pairs in quantum fully homomorphic encryption from O(lambda squared) to O(lambda log squared lambda).","keywords":["quantum fully homomorphic encryption","LWE decryption","modular arithmetic program","MBQC framework","EPR pairs","classical client","parallel measurements","T-gate evaluation"],"falsifier":"A concrete construction or lower-bound proof showing that any correct MA-Program for LWE decryption requires length omega(lambda log lambda) or that the resulting gadget uses more than O(lambda log squared lambda) EPR pairs would falsify the efficiency claim.","tokens_in":2735,"feed_emoji":"🔐","tokens_out":711,"duration_ms":15511,"temperature":0.7,"pith_summary":"The paper establishes a framework for quantum fully homomorphic encryption that improves on prior Barrington-based methods by introducing a modular arithmetic program tailored to LWE decryption. Because LWE decryption computes a modular inner product that is not symmetric, existing symmetric-function optimizations cannot be used directly. The new program tracks partial sums modulo q in a state space of size q, producing programs with O(lambda) states, binary encoding of O(log lambda), and length O(lambda log lambda). This construction transfers all quantum operations to the server, leaving the client with only classical operations, while supporting parallel measurements through the MBQC framework.","feed_headline":"Modular program cuts QFHE EPR pairs to O(lambda log^2 lambda)","feed_subtitle":"Tracking partial sums modulo q produces O(lambda log lambda)-length programs and moves all quantum work to the server.","key_machinery":"The MA-Program, which tracks partial sums modulus q with state space Z_q to produce short programs for non-symmetric modular inner products.","core_discovery":"LWE decryption is realized as a modular inner product via an MA-Program whose state space is Z_q, yielding programs of state count O(lambda) and length O(lambda log lambda) that reduce the required EPR pairs from O(lambda squared) to O(lambda log squared lambda) while enabling a fully classical client and parallel evaluation.","pith_inferences":["The same modular-tracking idea might apply to other lattice-based schemes whose decryption involves non-symmetric modular arithmetic.","If the offline EPR preparation can be made reusable across multiple evaluations, the amortized cost per computation could drop further.","The reduction in per-gate quantum resources could be combined with classical FHE batching techniques to handle larger circuits.","Testing whether the MBQC flow functions preserve the exact O(lambda) state count under realistic noise models would be a direct next measurement."],"forward_implications":["QFHE evaluation of each T-gate now consumes only O(lambda log squared lambda) EPR pairs instead of O(lambda squared).","The client performs solely classical LWE key generation and encryption under classical FHE, with no quantum operations required.","A layered key structure removes the need for circular security assumptions.","Up to O(log lambda) parallel measurements per layer are supported while keeping evaluation deterministic.","Offline EPR preparation is separated from online adaptive measurements."],"fun_headline_variants":["MA-Program reduces QFHE EPR pairs to O(lambda log^2 lambda)","MA-Program enables fully classical QFHE client","LWE MA-Program yields O(lambda log lambda) program length","Z_q MA-Program cuts QFHE gadget to O(lambda log^2 lambda) EPR pairs"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The MA-Program can be embedded in the MBQC framework without increasing the stated state-space size or breaking correctness, and LWE decryption cannot exploit prior symmetric-function shortcuts.","fun_headline_variants_meta":{"raw":{"variants":["MA-Program reduces QFHE EPR pairs to O(lambda log^2 lambda)","MA-Program enables fully classical QFHE client","LWE MA-Program yields O(lambda log lambda) program length","Z_q MA-Program cuts QFHE gadget to O(lambda log^2 lambda) EPR pairs"]},"model":"grok-4.3","cost_usd":0.006992,"raw_usage":{"total_tokens":3271,"prompt_tokens":733,"num_sources_used":0,"completion_tokens":80,"cost_in_usd_ticks":69924500,"prompt_tokens_details":{"text_tokens":733,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2458,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":733,"tokens_out":80,"duration_ms":20019,"temperature":1.0,"reasoning_tokens":2458,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-01T09:51:52.294396+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A concrete construction or lower-bound proof showing that any correct MA-Program for LWE decryption requires length omega(lambda log lambda) or that the resulting gadget uses more than O(lambda log squared lambda) EPR pairs would falsify the efficiency claim.","supporting_citations":[],"review_version":2}