soft3/mudra/audit/signature-optimality.md

Mudra: the Cyber choice

2026-09-12 · Architecture recommendation. The current design and proposed extension are distinguished below; concrete cryptographic profiles still need qualification.

Cyber keeps proof-based authority, confidential state and CSIDH stealth. The next step is private, verifiable wallet recovery through the node. This combines Neptune's useful idea of proving private ownership with Cyber's existing programmable execution and authenticated graph.

How the chosen scheme works

  1. Authorize with Hemera + Zheng. Hemera commits to the owner's secret; a Zheng proof shows that the owner satisfies the spending/policy rules for this exact action. The verifier checks the proof without learning the secret. The same proof can cover authorization and the state transition.
  2. Receive privately with Mudra. CSIDH/stealth lets sender and recipient derive a shared secret for an encrypted payment, even while the recipient is offline. Per-payment stealth uses a public ephemeral announcement. The spend secret stays independent: the sender also knows the shared secret. seal supplies a separate lattice KEM for recipient encryption where that interface is needed.
  3. Keep confidential state in BBG. Commitments hide owners and values; public nullifiers prevent reuse of spent notes. Authenticated state gives the node a root against which to prove balances and transitions. Exact public graph-aggregate changes still need disclosure control: an isolated contribution can be recovered by subtraction.
  4. Recover through private, verifiable queries. Today the BBG design asks recipients to scan announcements. The proposed extension lets a node find a wallet's incoming notes privately, then prove that it processed the full requested history. The client verifies the result and current spend state.

Why this fits Cyber: programmable authorization, private balances and provable queries share the existing execution/state stack. This architecture choice does not require adopting a new detached signature algorithm.

Why the other designs are not the whole answer

  • Quantus: attractive mobile recovery and proof aggregation, but public amounts and endpoint-visible wallet queries fall short of Cyber's privacy goal. Keep its interoperability and product lessons.
  • Neptune Cash: the closest model for private proof-based spending. Its ordinary wallet still downloads global stripped history; Cyber already has BBG/Inf for the state and query layer.
  • Neptune Privacy: compact CTIDH receiving addresses are directly relevant. Its indexed SDK recovery still exposes recipient interests, and the CSIDH-512 parameter choice needs a defensible quantum attack model.

Visual assessment

My engineering assessment for Cyber's requirements. These grades compare mechanisms and tradeoffs; they are not benchmark scores or security certificates.

🟢 3 — strong fit · 🟡 2 — material tradeoff · 🔴 1 — weak fit · ? — unestablished

XNT = Neptune Privacy; NPT = Neptune Cash. Cyber¹ = current specification; Cyber+² = proposed architecture target. The two Cyber columns assess designs, not delivered guarantees.

Criterion Quantus XNT NPT Cyber¹ Cyber+²
Hidden amounts 🔴 1 🟢 3 🟢 3 🟡 2 🟢 3
Recipient-selection privacy 🔴 1 🔴 1 🟡 2 🟡 2 🟢 3
Low client recovery work 🟢 3 🟢 3 🔴 1 🔴 1 🟡 2
Verified history coverage 🔴 1 🔴 1 🔴 1 🟡 2 🟢 3
Programmable authority 🟡 2 🟢 3 🟢 3 🟢 3 🟢 3
Low crypto review burden 🟡 2 🟡 2 🟡 2 🔴 1 🔴 1
Measured private-send speed ? ? ? ? ?

The grades have specific reasons:

  • Amounts: current Cyber commits private values, but BBG's exact public aggregate deltas can disclose isolated contributions. Its grade is therefore 2 until that release policy is resolved. The target 3 requires closing this channel; private recovery alone cannot do it.
  • Recovery: Quantus and XNT index a wallet's history on the server. NPT and current BBG scan global history on the client. The assessed UnifOMR path reduces downloaded payloads and client decryption, but retains a history-sized detection response and substantial server work; hence Cyber+ gets 2, not a free 3.
  • Query trust: NPT's common-history scan hides discovery interests, but witness requests leak information. Current Cyber has the Inf proof contract; the private-recovery composition is the extension. Coverage proves that the declared history was processed; detection errors and overflow need their own bounds. IP addresses, session timing and queried ranges remain observable.
  • Complexity: both Neptunes combine proofs with a custom KEM; XNT also offers CTIDH. Cyber adds its own Hemera and RLWE/polynomial-commitment state composition; the extension adds OMR's homomorphic encryption/PIR. The lower grade reflects that additional qualification burden, not predicted bug rates.
  • Speed: no matched full private-transfer benchmark supports a ranking.

Detailed mechanisms, versions and evidence remain available separately. No total score is used: strong recovery cannot compensate for disclosing amounts when amount privacy is a requirement.

UnifOMR: what the new paper changes

OMR means Oblivious Message Retrieval: retrieving your messages without the server learning which messages belong to you. For a wallet, the messages are encrypted payment notifications.

With UnifOMR, the sender adds an encrypted detection clue. A server processes those clues using recipient-supplied encrypted detection material. The recipient decodes a compact response and privately retrieves candidate payloads using PIR — Private Information Retrieval. This moves expensive discovery work off the wallet while protecting its selection. It retains server-side history processing and adds clue/key storage. Paper.

Cyber integration follow-up, 2026-09-12

OMR hides the selection; Inf/Zheng authenticate the computation. BBG commits the complete notification board. Inf defines the root/range and complete-query semantics. Zheng proves encrypted detection and the PIR answer against that board, without the server needing the recipient's decryption key. The wallet then verifies note inclusion and spend state against canonical roots.

This is the selected direction for a normal node capability or adjacent worker. Detection error, overflow, transcript privacy and data availability remain part of the contract. Cybergraph design, Inf coverage, node roadmap C2.1.

What still needs a decision

Choose the exact CSIDH profile and scan budget; select a standard ML-KEM profile or qualify the separate Goldilocks seal; instantiate the specified independent view/spend roles and action/policy binding. These qualify the chosen architecture. Parameter evidence.

The canonical recovery contract now fixes the privacy, delivery, coverage and lifecycle requirements. The next recovery-index proposal prioritizes neuron-prepared updates/checkpoints and private indexing, with compact OMR as a comparison baseline. Its goal is the highest client-work grade, including private lookup and spend preparation; the table's 2 still describes the earlier UnifOMR-shaped path. The full composition remains to be measured.

Concrete costs

The retained size and cost table separates signatures, receiving material, encrypted notifications and proofs. The UnifOMR measurements also account for server work, keys and per-message clues.

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