5.4. FHEOS Server (Computation)

The FHEOS (Fully Homomorphic Encryption Operating System) serves as the computational backbone of the CoFHE layer. By offloading heavy homomorphic comparisons (FHE.gt, FHE.select) from the L2 settlement chain to specialized off-chain coprocessors, the protocol achieves cryptographic finality without congesting block space or incurring prohibitive gas costs.

Version 2.0 formalizes FHEOS as a stateless, event-driven computation engine that receives encrypted ciphertext hashes, executes constant-time sorting and settlement logic, and returns mathematically verifiable results bound to EigenLayer AVS operator signatures. This architecture guarantees zero plaintext exposure, neutralizes timing side-channels, and scales horizontally independent of L2 throughput limits.

Core Design Principles

️ Technical Implementation

1. API & Endpoint Architecture

FHEOS exposes a secure, authenticated endpoint for batched ciphertext processing. The cofheDispatcher routes requests with strict timeout and retry logic.

// Conceptual FHEOS API Request Structure (cofheDispatcher → FHEOS)
const request = {
 endpoint: process.env.FHEOS_API_ENDPOINT, // e.g., https://fheos.fhenix.zone/v1/compare
 headers: { 
 'Authorization': `Bearer ${process.env.FHEOS_API_KEY}`,
 'Content-Type': 'application/json'
 },
 body: {
 batchId: uuidv4(),
 auctionIds: ['0x1a2...b3', '0x4c5...d6'], // Max 10
 ciphertextHashes: [
 { auctionId: '0x1a2...b3', hashes: ['0xabc...', '0xdef...', '0x123...'] }
],
 operation: 'vickrey_sort', // Constant-time encrypted comparison
 timeoutMs: 120_000 // Hard timeout before escalation
 }
};

2. Constant-Time Homomorphic Sorting Engine

The core computation relies on FHE.select to route encrypted values without decryption. This ensures that comparing 1 ETH vs 100 ETH consumes identical computational cycles.

// Pseudo-architecture: FHEOS Constant-Time Comparison Logic
function constantTimeVickreySort(encryptedBids: InEuint32[]): { winner: InEuint32, secondPrice: InEuint32 } {
 let highest = encryptedBids[0];
 let second = FHE.asEuint32(0);
 
 for (let i = 1; i < encryptedBids.length; i++) {
 const isGreater = FHE.gt(encryptedBids[i], highest);
 
 // FHE.select: Cryptographic multiplexer routes without decryption
 second = FHE.select(isGreater, highest, second);
 highest = FHE.select(isGreater, encryptedBids[i], highest);
 }
 
 return { winner: highest, secondPrice: second };
}

3. Batch Queue & Throughput Management

To prevent network congestion from overwhelming the coprocessor, FHEOS enforces strict batch limits and queue management:

• Max Batch Size: 10 auctions/block (configurable via config.ts)
• Queue Backend: Redis for distributed locking and request persistence
• Idempotency: Each batch carries a unique batchId to prevent duplicate processing during network retries
• Timeout Threshold: 120 seconds per batch. Exceeding this triggers a fallback log and escalates to the Dynamic Dead Man's Switch monitoring layer.

Data Flow: Dispatcher → FHEOS → AVS Binding

Performance & Security Specifications

️ Security & Reliability Guarantees

1. Timing Attack Neutralization: By enforcing FHE.select constant-time gates at the coprocessor level, execution clocks remain identical for high and low values. Attackers cannot infer bid ranges by measuring server response times or computational variance.
2. OOG & DoS Prevention: The strict 10 auctions/block batch cap ensures that sudden auction closures never overwhelm the coprocessor or trigger cascading L2 gas spikes.
3. Network Partition Tolerance: The Redis queue persists unprocessed batches. If FHEOS endpoints become unreachable, the dispatcher halts submission, logs the anomaly, and triggers the Dynamic Dead Man's Switch if the 120s threshold is breached.
4. Cryptographic Binding: FHEOS results are cryptographically signed by multiple nodes. The avsSubmitter service verifies the signature threshold before allowing on-chain resolution, preventing rogue coprocessor outputs from affecting state.

Audit Gate Compliance (P0)

Progression through Phase 3/4 is strictly blocked until all FHEOS-related P0 criteria are verified:

• [] Zero Plaintext Processing: FHEOS operates exclusively on bytes32 ciphertext hashes. No decryption, plaintext logging, or value exposure occurs during sorting.
• [] Constant-Time Enforcement: All comparative operations use FHE.select multiplexers. Timing variance < ±2ms across all input ranges (verified via side-channel audit).
• [] Batch Limit Compliance: Dispatcher never exceeds 10 auctions/block. Hard timeout of 120s enforced before escalation.
• [] Deterministic Output Verification: FHEOS results are cryptographically reproducible. AVS operators independently verify outputs before signing.
• [] Fault Tolerance Integration: Queue persistence and retry logic successfully handle simulated FHEOS downtime without data loss or state corruption.

Reference Architecture Files

Next Steps

• Proceed to 5.5. SlashedPot.sol (Compensations) to understand penalty routing, pro-rata distribution, and seller accountability mechanics.
• Review Security Model → Threat Matrix for side-channel, timing attack, and coprocessor spoofing mitigations.
• Explore Developer Quickstart → Integration Tests to run local FHEOS simulation suites and latency benchmarks.