{"id":"fcb48192-fbd1-44c0-bcc6-70f928a97972","arxiv_id":"2602.09707","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"upTPM achieves unbounded preprocessing for Schnorr multi-signatures on TPM hardware by deriving commitments deterministically from a constant-size seed with hardware attestation.","lead":"upTPM lets TPM devices generate unlimited nonce commitments for Schnorr multi-signatures from one 32-byte seed, keeping storage constant. This solves the bounded preprocessing problem on devices with tiny secure memory and spotty connections.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Security reduction assumes TPM state machine prevents nonce reuse without formal modeling of all host-TPM interactions","rationale":"The reader's weakest assumption directly identifies the hardware-state reliance. The full text does not appear to strengthen this into a machine-checked or exhaustive command-sequence model, so the concern remains load-bearing for the unbounded claim.","tokens_in":1804,"tokens_out":290,"duration_ms":24265,"concrete_test":"In the security game of §4, enumerate all valid TPM command sequences that could be issued by a malicious host (including any reset or counter-manipulation paths permitted by the TPM 2.0 spec); check whether the reduction still extracts the DL solution when the adversary forces a nonce reuse; if extraction fails on any sequence, the one-time invariant is not reduction-preserving.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The EU-CMA proof treats the one-time-use invariant as an external assumption on TPM hardware state (seed + monotonic counter). The construction derives nonces via PRF(seed, ctr) and publishes commitments, but the reduction does not explicitly model the full TPM command interface (e.g., possible reset, counter read, or attestation bypass sequences). If any sequence allows the host to force reuse of a previously committed nonce scalar, the discrete-log reduction fails because the simulator can no longer extract the secret from a forgery that re-uses a known commitment.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper presents upTPM, a framework for unbounded preprocessing in Schnorr multi-signature schemes on TPM 2.0 devices. Each TPM stores a single 32-byte secret seed from which an unlimited sequence of nonce commitments is derived deterministically via a PRF; commitments are published to an untrusted coordinator while nonce scalars remain inside the TPM. The construction claims three new properties: unbounded deterministic preprocessing with constant storage, asynchronous commitment refill, and TPM-attested commitments. It proves EU-CMA security in the random oracle model under the discrete-logarithm and PRF assumptions, with one-time-use enforced by TPM hardware state, and extends the scheme to (t,n)-threshold signatures while analyzing coordinator trust, crash recovery, and performance.","tokens_in":1922,"tokens_out":575,"duration_ms":24629,"significance":"If the security reduction is valid and the TPM state-machine assumptions hold, the result removes a fundamental storage bound that has limited practical deployment of offline-preprocessed Schnorr multi-signatures on resource-constrained hardware. Constant signer storage and unilateral asynchronous refill would be a meaningful engineering improvement for TPM-based wallets and threshold protocols.","major_comments":[{"comment":"Security Proof section: The EU-CMA reduction treats the one-time-use invariant as an external assumption on TPM hardware state (seed + monotonic counter) but does not explicitly model the full host-TPM command interface. Sequences such as counter reset, counter read without attestation, or attestation bypass are not analyzed; any such sequence would allow a host to force reuse of a previously committed nonce scalar, breaking the discrete-log extraction in the simulator.","section":"Security Proof"},{"comment":"Threshold Extension: The extension to (t,n)-threshold signatures is stated but the security argument is only sketched by reduction to the single-signer case. No separate game sequence or simulator is provided for the threshold setting, leaving open whether the one-time-use invariant and coordinator interactions compose correctly under t-out-of-n corruption.","section":"Threshold Extension"}],"minor_comments":[{"comment":"The abstract and introduction use 'TPM-attested commitments' without a forward reference to the precise TPM command sequence or attestation format used; a short table or figure would clarify the binding.","section":"Introduction"},{"comment":"Performance evaluation reports only aggregate timings; per-operation breakdown (seed derivation, commitment generation, attestation) would help readers assess the overhead of the unbounded mechanism.","section":"Performance Evaluation"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a good fit for a cryptography venue focused on applied hardware security. The full proof appendix is referenced but not reproduced in the provided text; its absence makes independent verification of the reduction difficult."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback on the security proof and threshold extension. We address each major comment below and will revise the manuscript to strengthen the presentation while preserving the core contributions.","responses":[{"response":"We agree that explicitly modeling the host-TPM command interface would improve clarity. In the revision we will add a dedicated subsection describing the relevant TPM 2.0 commands (e.g., TPM2_GetRandom, TPM2_Hash, TPM2_Quote for attestation, and monotonic counter operations) and formally state the one-time-use invariant as a hardware-enforced property. Under the standard trusted-hardware assumption, any counter reset or attestation bypass requires breaking the TPM's own security guarantees, which lies outside the adversary model; the simulator can therefore safely extract the discrete log when a nonce is reused. We will update the EU-CMA proof to reference this interface explicitly.","revision_made":"yes","referee_comment":"[Security Proof] Security Proof section: The EU-CMA reduction treats the one-time-use invariant as an external assumption on TPM hardware state (seed + monotonic counter) but does not explicitly model the full host-TPM command interface. Sequences such as counter reset, counter read without attestation, or attestation bypass are not analyzed; any such sequence would allow a host to force reuse of a previously committed nonce scalar, breaking the discrete-log extraction in the simulator."},{"response":"The threshold construction lets each signer independently derive and attest its own commitments using its local TPM, so the one-time-use invariant remains per-signer. In the revision we will supply a full game sequence for the (t,n) setting that reduces directly to the single-signer EU-CMA game. The simulator will handle t-out-of-n corruption by forwarding queries to the single-signer challenger for honest signers while simulating corrupted signers' commitments; coordinator interactions are already modeled as untrusted in the single-signer case and carry over unchanged. A detailed simulator description will be included.","revision_made":"yes","referee_comment":"[Threshold Extension] Threshold Extension: The extension to (t,n)-threshold signatures is stated but the security argument is only sketched by reduction to the single-signer case. No separate game sequence or simulator is provided for the threshold setting, leaving open whether the one-time-use invariant and coordinator interactions compose correctly under t-out-of-n corruption."}],"tokens_in":1449,"tokens_out":512,"duration_ms":29212,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that this paper solves the storage problem for precomputing nonces in Schnorr multi-signatures when the signer is a TPM with only a few KB of NVRAM. Instead of keeping a pile of commitments, each TPM holds a single seed and generates an unlimited sequence of them deterministically using a PRF and a counter. Commitments go to the coordinator ahead of time, scalars stay inside the TPM, and attestation ties everything to hardware state. They also add asynchronous refill so one signer can extend its pool without waiting for others, plus an extension to threshold signatures and some analysis of coordinator trust and crash recovery.","headline":"upTPM shows how to get unbounded nonce preprocessing for Schnorr multisigs on TPMs from one 32-byte seed with deterministic derivation and hardware attestation, which is new and practical, but the proof's handling of all TPM-host interactions is the part that needs checking.","tokens_in":2403,"tokens_out":224,"would_cite":false,"duration_ms":14312,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/RealityFromDistinction.lean","rs_theorem":"reality_from_one_distinction","paper_passage":"Each TPM stores a single 32-byte secret seed from which an unlimited sequence of nonce commitments is deterministically derived... one-time-use invariant enforced by TPM hardware state."},{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"We prove EU-CMA security in the random oracle model under the discrete logarithm assumption and Pseudo Random Function (PRF) security"}],"headline":"Cryptographic TPM multi-signature protocol with bounded-storage preprocessing; no overlap with RS distinction-forcing or J-cost machinery","alignment":"orthogonal","rationale":"Paper centers on EU-CMA security reduction for Schnorr multisignatures using PRF-derived nonces, monotonic NV counters, and TPM attestation. Central machinery (seed+PRF derivation, nexti/geni counters, one-time-use invariant) is standard crypto engineering with no J-cost, phi-ladder, 8-tick periodicity, or parameter-free constant derivation. Matches none of the RS forcing theorems.","tokens_in":52567,"confidence":"high","tokens_out":302,"duration_ms":12405,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A single 32-byte seed on each TPM generates unlimited nonce commitments for Schnorr multi-signatures while keeping all scalars inside the hardware.","keywords":["Schnorr multi-signatures","TPM preprocessing","unbounded nonce commitments","threshold signatures","EU-CMA security","discrete logarithm","hardware state enforcement"],"falsifier":"A concrete forgery in the EU-CMA game that succeeds after an adversary reuses a published commitment or extracts a nonce scalar from the TPM would falsify the security claim.","tokens_in":2708,"feed_emoji":"🔐","tokens_out":626,"duration_ms":25936,"temperature":0.7,"pith_summary":"The paper presents upTPM to overcome the storage limit that forces interactive nonce refill rounds in existing Schnorr multi-signature schemes when deployed on TPM 2.0 devices. Each signer stores only one secret seed instead of a growing list of precomputed commitments; an unlimited sequence of commitments is derived deterministically from the seed and sent to an untrusted coordinator ahead of time. Nonce scalars remain inside the TPM and are released only once, with hardware state enforcing the one-time-use rule. The construction adds TPM attestation for the commitments and extends to threshold signatures, with a security proof in the random oracle model.","feed_headline":"Single 32-byte seed removes storage limit on TPM Schnorr nonces","feed_subtitle":"Deterministic derivation lets each signer publish unlimited commitments ahead of time while scalars stay inside the hardware.","key_machinery":"Deterministic derivation of nonce commitments from a constant-size secret seed combined with TPM hardware state that enforces one-time use of each derived nonce.","core_discovery":"upTPM stores a single 32-byte secret seed on each TPM from which an unlimited sequence of nonce commitments is deterministically derived; commitments are published to the coordinator before use, nonce scalars never leave the TPM, and one-time-use is enforced by TPM hardware state, yielding EU-CMA security under the discrete logarithm assumption and PRF security.","pith_inferences":["The same seed-derivation pattern could be applied to other hardware security modules that offer protected state but limited storage.","Asynchronous refill removes a practical bottleneck for multi-party signing protocols that must operate across unreliable networks.","Hardware attestation of commitments creates a stronger binding between the published value and the protected seed than software-only methods provide."],"forward_implications":["Any signer can unilaterally extend its own commitment pool without an interactive round with other signers.","The scheme supports (t,n)-threshold signatures while preserving constant storage and unbounded preprocessing.","Coordinator trust is limited to storing and forwarding commitments because the underlying scalars stay protected inside each TPM.","Crash recovery and performance remain practical even with intermittent device connectivity."],"fun_headline_variants":["32-byte seed for unbounded TPM Schnorr nonces","Single seed derives unlimited Schnorr nonces on TPM","No storage bound for TPM Schnorr nonce prep","TPM Schnorr nonces from one 32-byte seed"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The TPM hardware must correctly maintain state to block nonce reuse and the derivation function must act as a secure PRF.","fun_headline_variants_meta":{"raw":{"variants":["32-byte seed for unbounded TPM Schnorr nonces","Single seed derives unlimited Schnorr nonces on TPM","No storage bound for TPM Schnorr nonce prep","TPM Schnorr nonces from one 32-byte seed"]},"model":"grok-4.3","cost_usd":0.006513,"raw_usage":{"total_tokens":2977,"prompt_tokens":690,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":65128000,"prompt_tokens_details":{"text_tokens":690,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2226,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":690,"tokens_out":61,"duration_ms":18144,"temperature":1.0,"reasoning_tokens":2226,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-16T05:26:03.488297+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A concrete forgery in the EU-CMA game that succeeds after an adversary reuses a published commitment or extracts a nonce scalar from the TPM would falsify the security claim.","supporting_citations":[],"review_version":1}