Encrypted Settlement

Offline execution in KnoxNet minimizes observability at the moment of value transfer, but global settlement remains necessary to enforce correctness, supply safety, and accountability. Conventional blockchain systems perform settlement by processing plaintext transaction data, exposing transaction flows, balances, and accounting structure to validators and observers.

KnoxNet adopts a different approach. Settlement is enforced over encrypted data, allowing the Layer 1 ledger to verify global constraints without learning sensitive transaction details.

8.1 Settlement Without Plaintext Disclosure

During reconciliation, the KnoxNet Layer 1 ledger must verify a limited set of global properties, including:

• Conservation of $KNX$ value

• Adherence to issuance and escrow limits

• Consistency of settlement deltas across submissions

Importantly, enforcing these properties does not require access to individual transaction histories, sender–receiver relationships, or plaintext amounts. KnoxNet therefore avoids processing settlement data in plaintext.

Instead, reconciliation submissions encode settlement-relevant information in encrypted form. The ledger verifies constraints directly over encrypted values, ensuring correctness without revealing underlying financial data.

8.2 Homomorphic Encryption Model

KnoxNet uses homomorphic encryption (HE) to enable computation over encrypted settlement data. Under this model, values such as balances, aggregates, and deltas are encrypted using the ledger's homomorphic public key pkHEpk_{HE}pkHE.

Homomorphic encryption allows specific operations such as addition and subtraction to be performed directly on ciphertexts. The result of these operations, when decrypted, matches the result that would have been obtained had the operations been performed on plaintext values.

This property allows the ledger to verify arithmetic constraints without decrypting individual values.

8.3 Enforced Settlement Constraints

Using homomorphic encryption, the KnoxNet Layer 1 ledger enforces the following settlement constraints:

Value Conservation

The sum of encrypted inputs across reconciliation submissions must equal the sum of encrypted outputs, modulo authorized issuance and burns.

Issuance and Escrow Limits

Encrypted settlement updates are verified to ensure that the total circulating $KNX$ does not exceed the sum of authorized issuance and escrowed value.

Settlement Delta Consistency

Encrypted deltas applied to ledger state must be internally consistent and correspond to valid consumption of offline notes.

These checks are performed without revealing individual transaction amounts or account balances.

8.4 Interaction with Fraud Proofs

Encrypted settlement constraints complement, rather than replace, deterministic fraud proofs.

Fraud proofs rely on structural contradictions such as reuse of the same offline note identifier and do not depend on encrypted arithmetic. When a fraud proof is triggered, penalties are applied independently of encrypted settlement checks.

This separation ensures that:

• Arithmetic correctness is enforced through encrypted computation

• Logical correctness is enforced through deterministic contradiction detection

Together, these mechanisms provide comprehensive enforcement without requiring transparent settlement.

8.5 Decryption and Trust Distribution

Decryption of settlement-related ciphertexts is not required for routine verification. In cases where decryption is necessary such as auditing or controlled disclosure decryption capability may be distributed across a validator committee using threshold decryption.

This design avoids concentration of decryption authority and reduces trust assumptions. No single validator is able to unilaterally decrypt settlement data.

8.6 Privacy Properties of Encrypted Settlement

Encrypted settlement ensures that the privacy gains achieved during offline execution are not undone during reconciliation. Specifically, the settlement process does not reveal:

• Individual transaction amounts

• Participant balances

• Detailed transaction graphs

• Temporal patterns of execution

Only the minimal information required to enforce global correctness becomes observable.

By combining offline execution with encrypted settlement, KnoxNet addresses privacy leakage at both the execution layer and the settlement layer.

8.7 Design Tradeoffs

Encrypted settlement introduces computational overhead compared to plaintext verification. KnoxNet accepts this cost deliberately, as settlement occurs asynchronously and can be amortized across batches of offline activity.

This tradeoff reflects a broader design philosophy: settlement efficiency is secondary to reducing observability at privacy-critical boundaries. Encrypted settlement is therefore treated as a core system component rather than an optional optimization.