TL;DR:
Hereafter, I present DSM (Decentralized State Machine), a cryptographic system model that enforces double-spend impossibility and device unclonability without global consensus or centralized trust. Security derives from atomic bilateral commitments, hardware-bound identities (DBRW), and cryptographic tripwire proofs. Formal definitions, a complete symbol index, system architecture, and game-based security theorems are provided, demonstrating double-spend resistance and physical unclonability in both online and offline settings.
Notation and Symbol Index
| Symbol | Definition |
|---|---|
| H | Collision-resistant hash function |
| \lambda | Security parameter (bits) |
| D_i | Device i |
| \mathcal{D} | Set of all devices |
| \mathcal{R} | Set of all bilateral relationships |
| S_n | State at transition n |
| C_{i,j} | Hash chain for relationship (D_i, D_j) |
| r_i | SMT root of device D_i |
| R_n | Fresh entropy for state n |
| \text{SMT}_n | Sparse Merkle Tree root at state n |
| \sigma_i | Signature by device D_i |
| G | Genesis state |
| b_i | MPC entropy contribution from participant i |
| \text{DBRW} | Dual-Binding Random Walk binding function |
| K_n | Hardware+environment binding at step n |
Preliminaries and System Model
Cryptographic Primitives
- H: \{0,1\}^* \rightarrow \{0,1\}^\lambda, collision-resistant hash function, requiring \Omega(2^{\lambda/2}) operations for collision.
- HMAC with unforgeability under chosen-message attack.
- Sparse Merkle Trees (SMT) with O(\log n) membership and position binding proofs.
System Architecture
DSM Network:
- Devices: \mathcal{D} = \{D_1, ..., D_n\}, each maintaining independent local state.
- Bilateral relationships: \mathcal{R} = \{(D_i, D_j): i \neq j\}, each with its own hash chain.
- No global state: Only pairwise state synchronization.
State Structure:
Each D_i maintains:
- Genesis state S_0^i (via MPC ceremony)
- Relationship chains \{C_{i,j}\}
- SMT root r_i binding all relationship heads
Threat Model
- Adversary is PPT, can corrupt devices and extract all state/keys, control network scheduling/partition, and attempt physical cloning.
- Cannot break cryptographic assumptions, cannot forge hardware characteristics, cannot violate device physical uniqueness.
Security Goals
- Double-spend resistance: No device can create two conflicting valid states.
- Clone detection: Cloned states on new hardware cannot produce valid transitions.
- Causal finality: All state transitions are immediately final.
- Offline security: All properties hold without network connectivity.
Balance Model in DSM
Balances do not exist as global records across devices or any central ledger. Each device only tracks the state of relationships it has directly participated in.
Tokens are like physical cash: transfer requires bilateral, atomic state updates.
- Lost devices lose tokens permanently.
- No other device can reconstruct or duplicate balances except via valid, linked state transitions.
Transaction Modes and State Synchronization
Bilateral Mode (Offline Transactions)
A bilateral transaction between D_i and D_j requires:
- Co-presence of both devices.
- Mutual signing:T_{bilateral} = \{\text{op}, \sigma_i, \sigma_j, S_i^{new}, S_j^{new}\}
- Immediate finality.
- Atomic state update on both chains.
Bilateral transactions are the ground truth, immune to network manipulation.
Unilateral Mode (Online, via Storage Nodes)
If D_j is offline, D_i posts a state transition to decentralized storage:
- Inbox:\text{Inbox}_j = H(\text{Genesis}_j \,\|\, \text{DeviceID}_j)
- Asynchronous delivery:\text{Post}_{i \to j} = \{S_i^{new}, \text{op}, \sigma_i, \text{SMT}_i, \text{timestamp}\}
- Synchronization: D_j retrieves and validates transactions upon reconnection.
State Precedence Invariant:
If D_i posts unilateral transitions for D_j, then before any new bilateral transaction:
This blocks double-spend windows: bilateral updates are forbidden until pending unilateral posts are synced (on a per relationship basis). Relationships without pending online updates can proceed with bilateral (offline) transactions unaffected.
Genesis, Bootstrap, and Device Identity
Blind MPC Genesis Protocol
Participants: Small randomized group consisting of:
- Storage nodes \{S_1, S_2, ..., S_k\} (economically incentivized to participate)
- User device D_{new} (requesting genesis)
- Group size: Typically n = 5-7 nodes, requiring t = 3-4 honest participants
Protocol Steps
-
Storage Node Contributions: Each storage node S_i provides:
b_i = H(\text{local\_random}_i \,\|\, \text{timestamp}_i \,\|\, \text{node\_id}_i) -
Device Contribution: User device provides:
b_{device} = H(\text{user\_seed} \,\|\, \text{DBRW}(\text{device})) -
MPC Genesis Computation: Randomized group computes:
G = H(b_1 \,\|\, b_2 \,\|\, ... \,\|\, b_t \,\|\, b_{device})where t-of-n threshold ensures unbiasable output with t honest storage nodes.
-
Device-Specific Hardware Binding: Final device identity:
G_{device} = H(G_{master} \,\|\, \text{DBRW}(\text{device}))
Economic Incentive Model
Storage Node Rewards: Participation in genesis ceremonies is part of storage nodes’ reward mechanism, ensuring:
- Reliable availability for new device onboarding
- Economic motivation for honest participation
- Distributed capacity across the network
- No bootstrap coordination bottleneck
Security Properties
Each device derives a unique sub-genesis:
Isolation Guarantee: Compromise of one device does not affect others due to hardware-specific binding in the genesis derivation.
Source of Truth: Storage and Mandatory Online Genesis/Anchor Verification
In DSM, the decentralized storage network is the sole source of truth for every Genesis and recovery (invalidation) anchor.
No device, peer, or user may initialize an identity, onboard a contact, or recover an account by referencing only a local cache, offline backup, or peer-provided data.
It is mandatory that every device retrieves the canonical Genesis or recovery marker directly from decentralized storage during initialization or recovery.
This guarantees that all cryptographic lineage for an identity is globally unique, tamper-evident, and immune to forgery or local replay attacks.
Why is this mandatory?
- Local or peer-based Genesis/recovery references are untrustworthy, since they can be forked, stale, or maliciously fabricated.
- Only by fetching from storage can a device verify that the anchor it uses is the globally accepted and recognized state.
- This enforcement prevents any attack where a user is tricked into onboarding with a forged Genesis, or where an adversary attempts to recover or fork an identity offline.
- All subsequent protocol operations including adding contacts are secure only if they originate from a canonical anchor proven by direct storage retrieval.
Recovery and Forward-Only Invalidation
DSM recovery is strictly forward-only and cryptographically auditable.
When a device is lost, compromised, or intentionally invalidated, the recovery process operates as follows:
- Anchor publication:
The device (or recovery agent) publishes an invalidation marker to decentralized storage, committing to the last valid state S_k:I(S_k) = H(S_k \,\|\, \text{recovery\_tag}) - New state creation:
The next valid state is anchored to the invalidation marker with fresh entropy:S_{new} = H(I(S_k) \,\|\, R_{new}) - Protocol rule:
All future transitions for this identity must chain to S_{new}; any attempt to continue from the pre-recovery branch is automatically rejected by honest peers and storage nodes. - Irreversibility and auditability:
Once published, I(S_k) permanently severs the link to any compromised or lost state, ensuring the new chain is both cryptographically and publicly anchored. The recovery event and all subsequent transitions are transparently auditable by any party.
This guarantees that recovery and invalidation are both globally visible and mathematically irreversible, enforced by the decentralized storage network as the ultimate arbiter of identity lineage.
Why Honest Devices Cannot Be Fooled by Cached or Offline State
In DSM, offline operation is fully supported devices are not required to publish every state transition online in real time.
However, the validity of any branch is determined by its cryptographic lineage to the canonical anchor in decentralized storage (Genesis or recovery marker), not by local SMT roots or cached state alone.
1. Cache/Offline State Is Never Sufficient for Global Validity
- Devices can cache and operate on local state for offline bilateral operations.
- But: Whenever a device or counterparty needs to onboard, recover, or verify the legitimacy of a chain (such as when adding a contact, restoring a device, or rejoining the network), it must verify the root anchor by querying decentralized storage.
- If a device’s local SMT root, cache, or chain tip is not chained from the current storage anchor, it becomes instantly and mathematically invalid.
- No amount of local history or bilateral agreements can override a mismatch with the global anchor.
2. Detection on Sync or Critical Protocol Actions
- If two devices operate entirely offline after a recovery marker is published, they might temporarily “believe” their state is valid.
- The first time any of them, or any counterparty they interact with, syncs with storage (or initiates a protocol event requiring anchor verification), any transition or chain not rooted in the up-to-date anchor is:
- Automatically and cryptographically rejected,
- Mathematically proven to be an invalid fork.
3. No “Silent Fork” Attack Is Possible
- DSM does not require publishing every transition online.
- But: At any point where global consistency is required (onboarding, adding contacts, recovery, state resync), all honest devices enforce that their current branch must be a descendant of the storage anchor.
- Devices that continue on an invalid or pre-recovery fork will find their transitions rejected the moment any verification against storage is required.
4. Local SMT Roots Are Trustless Only with Canonical Anchor
- Updating the SMT root locally has no effect unless it is chained from the canonical anchor in storage.
- This is why storage anchors are mandatory for identity initiation, recovery, and any action requiring trust outside the purely local context.
In summary:
DSM’s design ensures that offline, cached, or bilateral-only state is always subordinate to the canonical anchor in storage.
All global protocol actions enforce this—guaranteeing finality, anti-forking, and recovery without requiring constant online publication, but always with mathematically provable convergence to the network’s single source of truth.
Formal Security Theorems
Theorem 1: Atomic Interlock Tripwire (Double-Spend Impossibility)
Each state:
Adversary attempts to produce two valid next states (S_{n+1}, S'_{n+1}) for the same S_n, both accepted by honest peers.
- If \text{SMT}_A = \text{SMT}_B, only operation or entropy differs; SMT commits to same balances, double-spend impossible.
- If \text{SMT}_A \neq \text{SMT}_B, SMT inclusion proofs for peers are inconsistent and immediately detected; device is rejected (“tripwire”).
- Any successful double-spend reduces to a hash collision, violating $H$’s collision resistance.
Q.E.D.
Theorem 2: DBRW Unclonable Identity
where
Clone can only succeed if K'_{n+1} = K_{n+1}, but K_n binds to hardware and environment. Any deviation yields K'_{n+1} \neq K_{n+1}, so honest peers reject the transition. Even with all past keys, future K values remain unpredictable due to forward walk and entropy evolution.
Q.E.D.
Corollary: Causal Finality
No double-spend or clone is possible. All state transitions are causally final and device identities are unique and non-replayable. Only cryptographically provable history is valid; there is no way to undo or fork history, online or offline.
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. thanks so much for your insights!
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