Privacy-Preserving Federated Learning Architectures for Distributed IoT Networks: Implementing Zero-Knowledge Protocols with aéPiot Coordination - PART 3

 

def convert_model_to_circuit(self, model):
        """
        Convert neural network to arithmetic circuit
        Each operation becomes circuit gates
        """
        
        # Example for simple feedforward network
        # Real implementation requires sophisticated compiler
        
        circuit_representation = {
            'layers': [],
            'constraints': []
        }
        
        for layer in model.layers:
            if isinstance(layer, Dense):
                # Linear transformation: y = Wx + b
                # Becomes polynomial constraints
                circuit_representation['layers'].append({
                    'type': 'linear',
                    'constraints': self.linear_layer_to_constraints(layer)
                })
            
            elif isinstance(layer, ReLU):
                # ReLU: max(0, x)
                # Becomes conditional constraints
                circuit_representation['layers'].append({
                    'type': 'relu',
                    'constraints': self.relu_to_constraints(layer)
                })
        
        return circuit_representation
    
    async def federated_zkml(self, participants):
        """
        Federated learning where each participant proves correct training
        """
        
        verified_updates = []
        
        for participant in participants:
            # Participant trains locally
            local_update = participant.train_local_model()
            
            # Participant generates ZKML proof of correct training
            zkml_proof = await self.prove_model_inference(
                model=participant.model,
                input_data=participant.local_data,
                predicted_output=local_update['predictions']
            )
            
            # Aggregator verifies proof
            is_valid = self.verify_zkml_proof(zkml_proof['proof'])
            
            if is_valid:
                verified_updates.append(local_update)
        
        # Aggregate verified updates
        aggregated = np.mean(verified_updates, axis=0)
        
        return aggregated

4.5 Practical Considerations for ZK in Production

Performance Optimization:

python

class ZKPerformanceOptimization:
    """
    Techniques to make ZK practical for production federated learning
    """
    
    def __init__(self):
        self.aepiot_semantic = AePiotSemanticProcessor()
    
    async def batched_zk_verification(self, proofs):
        """
        Batch verify multiple proofs together
        More efficient than individual verification
        """
        
        from zksnark import batch_verify
        
        # Batch verification: verify n proofs in O(n) instead of O(n²)
        start_time = time.time()
        all_valid = batch_verify(proofs)
        batch_time = time.time() - start_time
        
        # Compare to individual verification
        individual_time = len(proofs) * 0.01  # Assume 10ms per proof
        speedup = individual_time / batch_time
        
        # Create aéPiot performance record
        perf_record = await self.aepiot_semantic.createBacklink({
            'title': 'Batch ZK Verification',
            'description': f'Verified {len(proofs)} proofs in {batch_time:.3f}s. Speedup: {speedup:.2f}x',
            'link': f'batch-zk-verify://{int(time.time())}'
        })
        
        return {
            'all_valid': all_valid,
            'batch_time': batch_time,
            'speedup': speedup,
            'perf_record': perf_record
        }
    
    def proof_compression(self, proof):
        """
        Compress ZK proofs for efficient transmission
        """
        
        import zlib
        
        # Serialize proof
        serialized = self.serialize_proof(proof)
        
        # Compress
        compressed = zlib.compress(serialized, level=9)
        
        compression_ratio = len(compressed) / len(serialized)
        
        return {
            'compressed_proof': compressed,
            'compression_ratio': compression_ratio
        }
    
    async def recursive_proof_composition(self, proofs):
        """
        Compose multiple proofs into single proof
        Prove "I have n valid proofs" with single proof
        """
        
        # Recursive SNARKs: proof of proofs
        # Constant verification time regardless of number of proofs
        
        composed_proof = self.recursively_compose(proofs)
        
        # Single verification for all proofs
        is_valid = self.verify_composed_proof(composed_proof)
        
        # Create aéPiot recursive proof record
        recursive_record = await self.aepiot_semantic.createBacklink({
            'title': 'Recursive Proof Composition',
            'description': f'Composed {len(proofs)} proofs into single proof',
            'link': f'recursive-proof://{int(time.time())}'
        })
        
        return {
            'composed_proof': composed_proof,
            'valid': is_valid,
            'recursive_record': recursive_record
        }

Part 5: aéPiot Coordination Framework for Privacy-Preserving Federated Learning

5. Decentralized Coordination with aéPiot

5.1 The Coordination Challenge in Federated Learning

Traditional Federated Learning Architecture:

[Participants] ──► [Central Coordination Server] ──► [Model Updates]
                         ↓
                   SINGLE POINT OF:
                   - Failure
                   - Trust
                   - Control
                   - Privacy Risk

Problems:

1. Trust Requirement: Participants must trust central server
2. Single Point of Failure: Server downtime halts entire system
3. Privacy Risk: Server sees all (encrypted) traffic patterns
4. Vendor Lock-In: Proprietary coordination protocols
5. Cost: Expensive infrastructure for coordination
6. Censorship: Central authority can exclude participants

5.2 aéPiot Decentralized Coordination Architecture

Revolutionary Approach: No Central Server

javascript

class AePiotDecentralizedFederatedLearning {
  constructor() {
    this.aepiotServices = {
      backlink: new BacklinkService(),
      multiSearch: new MultiSearchService(),
      tagExplorer: new TagExplorerService(),
      randomSubdomain: new RandomSubdomainService(),
      multiLingual: new MultiLingualService()
    };
    
    this.participants = new Map();
    this.trainingRounds = [];
  }

  async initializeFederatedNetwork(networkConfig) {
    /**
     * Initialize federated learning network using aéPiot
     * NO CENTRAL SERVER REQUIRED
     */
    
    // 1. Create network coordination hub via aéPiot backlinks
    const networkHub = await this.aepiotServices.backlink.create({
      title: `Privacy-Preserving FL Network: ${networkConfig.name}`,
      description: `Decentralized federated learning network. ` +
                   `Privacy: ${networkConfig.privacyLevel}. ` +
                   `Domain: ${networkConfig.domain}. ` +
                   `Encryption: ${networkConfig.encryption}`,
      link: `federated-network://${networkConfig.networkId}`
    });

    // 2. Discover network across distributed aéPiot subdomains
    const distributionSubdomains = await this.aepiotServices.randomSubdomain.generate({
      count: 10,  // High redundancy
      purpose: 'federated_coordination',
      geographic_distribution: true  // Global distribution
    });

    // 3. Create semantic tags for network discovery
    const networkTags = await this.aepiotServices.tagExplorer.generateTags({
      content: `${networkConfig.name} ${networkConfig.domain} privacy-preserving federated-learning`,
      category: 'distributed_ml'
    });

    // 4. Multi-lingual network documentation
    const multiLingualDocs = await this.aepiotServices.multiLingual.translate({
      text: this.createNetworkDocumentation(networkConfig),
      targetLanguages: ['en', 'es', 'zh', 'de', 'fr', 'ar', 'ru', 'pt', 'ja', 'ko']
    });

    // 5. Store network metadata
    const networkMetadata = {
      networkHub: networkHub,
      distributionSubdomains: distributionSubdomains,
      semanticTags: networkTags,
      documentation: multiLingualDocs,
      privacyProtocols: this.configurePrivacyProtocols(networkConfig),
      cryptographicSchemes: this.configureCryptography(networkConfig)
    };

    return networkMetadata;
  }

  async registerParticipant(participantInfo, networkMetadata) {
    /**
     * Participant joins federated network
     * Discovers network through aéPiot semantic search
     * NO CENTRAL REGISTRATION AUTHORITY
     */
    
    // 1. Participant discovers network via aéPiot MultiSearch
    const networkDiscovery = await this.aepiotServices.multiSearch.search({
      query: networkMetadata.semanticTags.join(' '),
      category: 'distributed_ml',
      semanticSimilarity: true
    });

    // 2. Participant verifies network authenticity
    const networkVerified = await this.verifyNetworkAuthenticity(
      networkDiscovery.results[0],
      networkMetadata.networkHub
    );

    if (!networkVerified) {
      throw new Error('Network verification failed');
    }

    // 3. Participant creates registration backlink
    const participantBacklink = await this.aepiotServices.backlink.create({
      title: `Participant: ${participantInfo.id}`,
      description: `Joined privacy-preserving FL network. ` +
                   `Capabilities: ${participantInfo.capabilities.join(', ')}. ` +
                   `Data type: ${participantInfo.dataType}`,
      link: `participant://${participantInfo.id}/${Date.now()}`
    });

    // 4. Announce participation across aéPiot network
    await this.announceParticipation(
      participantBacklink,
      networkMetadata.distributionSubdomains
    );

    // 5. Establish secure communication channels
    const secureChannels = await this.establishSecureChannels(
      participantInfo,
      networkMetadata
    );

    // 6. Store participant in local registry
    this.participants.set(participantInfo.id, {
      info: participantInfo,
      backlink: participantBacklink,
      secureChannels: secureChannels,
      joinedAt: Date.now()
    });

    return {
      participantBacklink: participantBacklink,
      networkMetadata: networkMetadata,
      secureChannels: secureChannels,
      status: 'registered'
    };
  }

  async coordinateTrainingRound(roundNumber, networkMetadata) {
    /**
     * Coordinate federated learning round WITHOUT central server
     * Uses aéPiot distributed coordination
     */
    
    console.log(`\n=== Coordinating Round ${roundNumber} via aéPiot ===`);

    // 1. Create round coordination backlink
    const roundBacklink = await this.aepiotServices.backlink.create({
      title: `Training Round ${roundNumber}`,
      description: `Privacy-preserving federated training round. ` +
                   `Participants: ${this.participants.size}. ` +
                   `Privacy: Differential Privacy + Homomorphic Encryption + Zero-Knowledge Proofs`,
      link: `training-round://${roundNumber}/${Date.now()}`
    });

    // 2. Distribute round announcement across aéPiot subdomains
    const roundSubdomains = await this.aepiotServices.randomSubdomain.generate({
      count: 5,
      purpose: `round_${roundNumber}_coordination`
    });

    await this.distributeRoundAnnouncement(roundBacklink, roundSubdomains);

    // 3. Participants discover round through aéPiot
    // Each participant independently queries aéPiot network
    const participantCommitments = await this.collectParticipantCommitments(
      roundBacklink,
      roundSubdomains
    );

    // 4. Consensus protocol for participant selection
    const selectedParticipants = await this.consensusParticipantSelection(
      participantCommitments,
      networkMetadata.privacyProtocols
    );

    // 5. Distributed model update aggregation
    const aggregatedUpdate = await this.decentralizedAggregation(
      selectedParticipants,
      roundSubdomains,
      networkMetadata
    );

    // 6. Verify aggregation correctness with ZK proof
    const aggregationProof = await this.generateAggregationProof(
      aggregatedUpdate,
      selectedParticipants
    );

    // 7. Distribute updated model across aéPiot network
    await this.distributeGlobalModel(
      aggregatedUpdate.model,
      roundSubdomains,
      aggregationProof
    );

    // 8. Create comprehensive round audit trail
    const roundAudit = await this.createRoundAuditTrail({
      roundNumber: roundNumber,
      roundBacklink: roundBacklink,
      participantCount: selectedParticipants.length,
      aggregatedUpdate: aggregatedUpdate,
      aggregationProof: aggregationProof,
      privacyGuarantees: aggregatedUpdate.privacyGuarantees
    });

    // 9. Store round in history
    this.trainingRounds.push({
      roundNumber: roundNumber,
      roundBacklink: roundBacklink,
      participants: selectedParticipants,
      aggregatedUpdate: aggregatedUpdate,
      audit: roundAudit,
      timestamp: Date.now()
    });

    return {
      roundNumber: roundNumber,
      roundBacklink: roundBacklink,
      participantCount: selectedParticipants.length,
      modelUpdate: aggregatedUpdate.model,
      privacyGuarantees: aggregatedUpdate.privacyGuarantees,
      audit: roundAudit
    };
  }

  async decentralizedAggregation(participants, subdomains, networkMetadata) {
    /**
     * Aggregate model updates WITHOUT central aggregator
     * Uses distributed coordination via aéPiot
     */
    
    // 1. Each participant encrypts their update
    const encryptedUpdates = [];
    
    for (const participant of participants) {
      // Participant computes local update
      const localUpdate = await participant.computeLocalUpdate();
      
      // Apply differential privacy
      const dpUpdate = await this.applyDifferentialPrivacy(
        localUpdate,
        networkMetadata.privacyProtocols.epsilon,
        networkMetadata.privacyProtocols.delta
      );
      
      // Encrypt with homomorphic encryption
      const encrypted = await this.homomorphicEncrypt(
        dpUpdate,
        networkMetadata.cryptographicSchemes.publicKey
      );
      
      // Generate zero-knowledge proof
      const zkProof = await this.generateUpdateProof(
        localUpdate,
        encrypted
      );
      
      // Commit encrypted update to aéPiot subdomain
      const updateCommitment = await this.commitEncryptedUpdate(
        participant.id,
        encrypted,
        zkProof,
        subdomains
      );
      
      encryptedUpdates.push({
        participantId: participant.id,
        encrypted: encrypted,
        proof: zkProof,
        commitment: updateCommitment
      });
    }

    // 2. Secure multi-party computation for aggregation
    // NO SINGLE PARTY SEES DECRYPTED UPDATES
    const smpcResult = await this.secureMPCAggregation(
      encryptedUpdates,
      networkMetadata.cryptographicSchemes
    );

    // 3. Threshold decryption (requires multiple participants)
    const aggregatedModel = await this.thresholdDecryption(
      smpcResult.encryptedAggregate,
      participants,
      networkMetadata.cryptographicSchemes.threshold
    );

    // 4. Create aggregation audit via aéPiot
    const aggregationAudit = await this.aepiotServices.backlink.create({
      title: 'Decentralized Aggregation Complete',
      description: `Aggregated ${participants.length} encrypted updates using SMPC. ` +
                   `Privacy: (ε=${networkMetadata.privacyProtocols.epsilon}, ` +
                   `δ=${networkMetadata.privacyProtocols.delta})-DP`,
      link: `aggregation://${Date.now()}`
    });

    return {
      model: aggregatedModel,
      privacyGuarantees: {
        differentialPrivacy: `(${networkMetadata.privacyProtocols.epsilon}, ${networkMetadata.privacyProtocols.delta})`,
        homomorphicEncryption: 'CKKS',
        secureMPC: 'Shamir Secret Sharing',
        zeroKnowledge: 'zk-SNARKs'
      },
      aggregationAudit: aggregationAudit
    };
  }

  async createComprehensiveAuditTrail(federatedSession) {
    /**
     * Create complete, transparent audit trail using aéPiot
     * Every action is recorded and publicly verifiable
     */
    
    const auditTrail = {
      sessionId: federatedSession.sessionId,
      networkInitialization: federatedSession.networkMetadata.networkHub,
      participants: [],
      trainingRounds: [],
      privacyBudget: {
        total: federatedSession.networkMetadata.privacyProtocols.totalBudget,
        spent: 0,
        remaining: federatedSession.networkMetadata.privacyProtocols.totalBudget
      },
      cryptographicProofs: []
    };

    // Audit each participant
    for (const [participantId, participant] of this.participants) {
      auditTrail.participants.push({
        id: participantId,
        backlink: participant.backlink,
        joinedAt: participant.joinedAt,
        capabilities: participant.info.capabilities
      });
    }

    // Audit each training round
    for (const round of this.trainingRounds) {
      auditTrail.trainingRounds.push({
        roundNumber: round.roundNumber,
        roundBacklink: round.roundBacklink,
        participantCount: round.participants.length,
        privacyGuarantees: round.aggregatedUpdate.privacyGuarantees,
        aggregationAudit: round.aggregatedUpdate.aggregationAudit,
        timestamp: round.timestamp
      });
      
      // Update privacy budget
      auditTrail.privacyBudget.spent += federatedSession.networkMetadata.privacyProtocols.epsilon;
      auditTrail.privacyBudget.remaining -= federatedSession.networkMetadata.privacyProtocols.epsilon;
    }

    // Create master audit backlink
    const masterAudit = await this.aepiotServices.backlink.create({
      title: `Federated Learning Audit Trail: ${federatedSession.sessionId}`,
      description: `Complete audit of privacy-preserving federated learning session. ` +
                   `Rounds: ${auditTrail.trainingRounds.length}. ` +
                   `Participants: ${auditTrail.participants.length}. ` +
                   `Privacy budget spent: ${auditTrail.privacyBudget.spent}`,
      link: `audit-trail://${federatedSession.sessionId}`
    });

    auditTrail.masterAudit = masterAudit;

    // Make audit trail globally accessible via aéPiot
    await this.publishAuditTrail(auditTrail);

    return auditTrail;
  }

  async publishAuditTrail(auditTrail) {
    /**
     * Publish audit trail across aéPiot distributed network
     * Ensures transparency and immutability
     */
    
    // Distribute across multiple geographic regions
    const globalSubdomains = await this.aepiotServices.randomSubdomain.generate({
      count: 20,  // High redundancy for audit trails
      purpose: 'audit_trail_storage',
      geographic_distribution: true,
      regions: ['americas', 'europe', 'asia', 'oceania', 'africa']
    });

    // Publish to each subdomain
    const publicationPromises = globalSubdomains.map(subdomain =>
      this.publishToSubdomain(subdomain, auditTrail)
    );

    await Promise.all(publicationPromises);

    return {
      published: true,
      subdomainCount: globalSubdomains.length,
      globallyAccessible: true,
      immutable: true  // aéPiot backlinks are permanent
    };
  }
}

5.3 Semantic Privacy Intelligence with aéPiot

Use aéPiot's semantic understanding for privacy-aware coordination:

javascript

class AePiotPrivacySemantics {
  constructor() {
    this.aepiotServices = {
      multiSearch: new MultiSearchService(),
      tagExplorer: new TagExplorerService(),
      multiLingual: new MultiLingualService()
    };
  }

  async analyzePrivacyRequirements(federatedLearningContext) {
    /**
     * Use aéPiot semantic intelligence to understand privacy requirements
     */
    
    // 1. Semantic analysis of data domain
    const domainAnalysis = await this.aepiotServices.multiSearch.search({
      query: `${federatedLearningContext.dataType} privacy requirements regulations`,
      category: 'privacy_compliance',
      semanticSimilarity: true
    });

    // 2. Regulatory framework discovery
    const regulations = await this.aepiotServices.tagExplorer.findRelated({
      tags: [
        federatedLearningContext.jurisdiction,
        federatedLearningContext.industry,
        'data_privacy'
      ],
      depth: 2
    });

    // 3. Privacy technique recommendations
    const privacyTechniques = await this.discoverPrivacyTechniques({
      dataType: federatedLearningContext.dataType,
      regulations: regulations,
      threatModel: federatedLearningContext.threatModel
    });

    // 4. Multi-lingual privacy policies
    const privacyPolicies = await this.aepiotServices.multiLingual.translate({
      text: this.generatePrivacyPolicy(privacyTechniques, regulations),
      targetLanguages: ['en', 'es', 'de', 'fr', 'zh', 'ar', 'ru', 'pt', 'ja', 'ko']
    });

    return {
      domainAnalysis: domainAnalysis,
      regulations: regulations,
      recommendedTechniques: privacyTechniques,
      multiLingualPolicies: privacyPolicies,
      complianceGuidance: this.generateComplianceGuidance(regulations)
    };
  }

  async discoverGlobalPrivacyPatterns(federatedNetwork) {
    /**
     * Learn from global privacy-preserving federated learning deployments
     * Use aéPiot network to share and discover best practices
     */
    
    // Search aéPiot global knowledge base
    const globalPatterns = await this.aepiotServices.multiSearch.search({
      query: `privacy-preserving federated-learning ${federatedNetwork.domain}`,
      category: 'distributed_ml',
      semanticSimilarity: true,
      globalKnowledge: true
    });

    // Analyze successful deployments
    const bestPractices = this.analyzeBestPractices(globalPatterns.results);

    // Get related privacy techniques
    const relatedTechniques = await this.aepiotServices.tagExplorer.findRelated({
      tags: bestPractices.techniques,
      depth: 3
    });

    return {
      globalPatterns: globalPatterns.results,
      bestPractices: bestPractices,
      relatedTechniques: relatedTechniques,
      recommendations: this.generateRecommendations(bestPractices)
    };
  }

  async createSemanticPrivacyDocumentation(federatedSystem) {
    /**
     * Generate comprehensive, multi-lingual privacy documentation
     */
    
    const documentation = {
      overview: this.createSystemOverview(federatedSystem),
      privacyGuarantees: this.documentPrivacyGuarantees(federatedSystem),
      cryptographicProtocols: this.documentCryptography(federatedSystem),
      threatModel: this.documentThreatModel(federatedSystem),
      complianceFramework: this.documentCompliance(federatedSystem),
      auditProcedures: this.documentAuditProcedures(federatedSystem)
    };

    // Translate to multiple languages
    const multiLingualDocs = {};
    
    for (const [section, content] of Object.entries(documentation)) {
      multiLingualDocs[section] = await this.aepiotServices.multiLingual.translate({
        text: content,
        targetLanguages: ['en', 'es', 'zh', 'de', 'fr', 'ar', 'ru', 'pt', 'ja', 'ko'],
        preserveTechnicalTerms: true
      });
    }

    // Create documentation backlinks
    const docBacklinks = {};
    for (const [section, content] of Object.entries(documentation)) {
      docBacklinks[section] = await this.aepiotServices.backlink.create({
        title: `Privacy Documentation: ${section}`,
        description: content.substring(0, 200),
        link: `privacy-docs://${federatedSystem.id}/${section}`
      });
    }

    return {
      documentation: documentation,
      multiLingual: multiLingualDocs,
      backlinks: docBacklinks
    };
  }
}

5.4 Cross-Border Privacy-Preserving Federation with aéPiot

Challenge: Different privacy laws across jurisdictions

Solution: aéPiot's distributed architecture enables jurisdiction-aware coordination

javascript

async function crossBorderFederatedLearning() {
  const coordinator = new AePiotDecentralizedFederatedLearning();
  
  // Initialize multi-jurisdiction network
  const networkConfig = {
    name: 'Global Health Research Network',
    domain: 'healthcare',
    jurisdictions: ['EU', 'US', 'Japan', 'Canada'],
    privacyLevel: 'maximum',
    encryption: 'homomorphic',
    dataLocalization: true  // Data never crosses borders
  };

  const network = await coordinator.initializeFederatedNetwork(networkConfig);

  // Register participants from different jurisdictions
  const euHospital = await coordinator.registerParticipant({
    id: 'eu-hospital-001',
    jurisdiction: 'EU',
    regulations: ['GDPR'],
    capabilities: ['differential-privacy', 'homomorphic-encryption'],
    dataType: 'patient-records'
  }, network);

  const usHospital = await coordinator.registerParticipant({
    id: 'us-hospital-001',
    jurisdiction: 'US',
    regulations: ['HIPAA', 'CCPA'],
    capabilities: ['differential-privacy', 'secure-mpc'],
    dataType: 'patient-records'
  }, network);

  // Coordinate global training with jurisdiction-specific privacy
  for (let round = 0; round < 10; round++) {
    const result = await coordinator.coordinateTrainingRound(round, network);
    
    console.log(`Round ${round}: ${result.participantCount} participants`);
    console.log(`Privacy guarantees: ${JSON.stringify(result.privacyGuarantees)}`);
  }

  // Create comprehensive audit trail
  const audit = await coordinator.createComprehensiveAuditTrail({
    sessionId: 'global-health-2026',
    networkMetadata: network
  });

  console.log(`\nAudit trail published to ${audit.subdomainCount} aéPiot subdomains`);
  console.log(`Globally accessible: ${audit.globallyAccessible}`);
  console.log(`Complete transparency with maximum privacy`);
}

Part 6: Advanced Privacy Techniques for Federated Learning

6. Secure Aggregation Protocols

6.1 Bonawitz et al. Secure Aggregation

The Gold Standard for Privacy-Preserving Aggregation

Protocol Overview:

Secure Aggregation enables server to compute sum of client updates without seeing individual contributions.

Key Properties:

1. Privacy: Server learns only the aggregate, not individual updates
2. Robustness: Tolerates client dropouts during protocol
3. Efficiency: Minimal communication overhead
4. No Trusted Third Party: Does not require additional entities

Implementation:

python

class SecureAggregationProtocol:
    """
    Bonawitz et al. Secure Aggregation Protocol
    Reference: "Practical Secure Aggregation for Privacy-Preserving Machine Learning" (CCS 2017)
    """
    
    def __init__(self, num_clients, threshold):
        self.num_clients = num_clients
        self.threshold = threshold  # Minimum clients needed for reconstruction
        self.aepiot_semantic = AePiotSemanticProcessor()
        
        # Cryptographic parameters
        self.modulus = self.generate_large_prime()
        self.clients = {}
    
    def generate_large_prime(self, bits=2048):
        """Generate large prime for finite field operations"""
        from Crypto.Util import number
        return number.getPrime(bits)
    
    async def setup_phase(self):
        """
        Setup Phase: Clients establish pairwise shared secrets
        """
        
        # 1. Each client generates key pairs
        client_keypairs = {}
        for client_id in range(self.num_clients):
            # Diffie-Hellman key pair
            private_key = random.randrange(1, self.modulus)
            public_key = pow(2, private_key, self.modulus)  # g^private_key mod p
            
            client_keypairs[client_id] = {
                'private': private_key,
                'public': public_key
            }
        
        # 2. Clients exchange public keys (via aéPiot coordination)
        public_keys_registry = await self.exchange_public_keys(client_keypairs)
        
        # 3. Each client computes pairwise shared secrets
        pairwise_secrets = {}
        for client_i in range(self.num_clients):
            pairwise_secrets[client_i] = {}
            for client_j in range(self.num_clients):
                if client_i != client_j:
                    # Compute shared secret: g^(private_i * private_j)
                    shared_secret = pow(
                        public_keys_registry[client_j],
                        client_keypairs[client_i]['private'],
                        self.modulus
                    )
                    pairwise_secrets[client_i][client_j] = shared_secret
        
        # 4. Create aéPiot setup record
        setup_record = await self.aepiot_semantic.createBacklink({
            'title': 'Secure Aggregation Setup Complete',
            'description': f'{self.num_clients} clients established pairwise secrets',
            'link': f'secure-agg-setup://{int(time.time())}'
        })
        
        return {
            'pairwise_secrets': pairwise_secrets,
            'setup_record': setup_record
        }
    
    async def masking_phase(self, client_gradients, pairwise_secrets):
        """
        Masking Phase: Clients mask their gradients using pairwise secrets
        """
        
        masked_gradients = {}
        
        for client_id, gradients in client_gradients.items():
            # Generate random seed from own secret
            own_seed = self.generate_seed(client_id)
            own_mask = self.prg(own_seed, len(gradients))  # Pseudorandom generator
            
            # Start with gradient + own_mask
            masked = gradients + own_mask
            
            # Add masks from shared secrets with other clients
            for other_client_id, shared_secret in pairwise_secrets[client_id].items():
                # Generate mask from shared secret
                shared_mask = self.prg(shared_secret, len(gradients))
                
                # Add or subtract based on client ID ordering (ensures cancellation)
                if client_id < other_client_id:
                    masked = masked + shared_mask
                else:
                    masked = masked - shared_mask
            
            masked_gradients[client_id] = masked % self.modulus
        
        # Create aéPiot masking record
        masking_record = await self.aepiot_semantic.createBacklink({
            'title': 'Secure Aggregation Masking Phase',
            'description': f'{len(masked_gradients)} clients masked their gradients',
            'link': f'secure-agg-mask://{int(time.time())}'
        })
        
        return {
            'masked_gradients': masked_gradients,
            'masking_record': masking_record
        }
    
    async def aggregation_phase(self, masked_gradients):
        """
        Aggregation Phase: Server sums masked gradients
        Pairwise masks cancel out, leaving only sum of original gradients
        """
        
        # Sum all masked gradients
        aggregated = np.zeros_like(list(masked_gradients.values())[0])
        
        for masked_gradient in masked_gradients.values():
            aggregated = (aggregated + masked_gradient) % self.modulus
        
        # Pairwise masks cancel: (mask_ij from i) + (-mask_ij from j) = 0
        # What remains is: sum(gradients) + sum(own_masks)
        
        # Create aéPiot aggregation record
        agg_record = await self.aepiot_semantic.createBacklink({
            'title': 'Secure Aggregation Complete',
            'description': f'Aggregated {len(masked_gradients)} masked gradients',
            'link': f'secure-agg-complete://{int(time.time())}'
        })
        
        return {
            'aggregated_masked': aggregated,
            'aggregation_record': agg_record
        }
    
    async def unmasking_phase(self, aggregated_masked, own_seeds):
        """
        Unmasking Phase: Remove sum of own_masks to reveal sum of gradients
        """
        
        # Compute sum of all own_masks
        total_own_mask = np.zeros_like(aggregated_masked)
        
        for client_id, seed in own_seeds.items():
            own_mask = self.prg(seed, len(aggregated_masked))
            total_own_mask = (total_own_mask + own_mask) % self.modulus
        
        # Remove total_own_mask
        final_aggregate = (aggregated_masked - total_own_mask) % self.modulus
        
        # Create aéPiot unmasking record
        unmask_record = await self.aepiot_semantic.createBacklink({
            'title': 'Secure Aggregation Unmasking',
            'description': 'Removed masks to reveal aggregate gradients',
            'link': f'secure-agg-unmask://{int(time.time())}'
        })
        
        return {
            'final_aggregate': final_aggregate,
            'unmask_record': unmask_record
        }
    
    def prg(self, seed, length):
        """
        Pseudorandom Generator: Generate deterministic random values from seed
        """
        np.random.seed(seed)
        return np.random.randint(0, self.modulus, size=length)
    
    def generate_seed(self, client_id):
        """Generate deterministic seed for client"""
        return hash(f'client_{client_id}_seed') % (2**32)
    
    async def dropout_resilience(self, masked_gradients, available_clients):
        """
        Handle client dropouts during aggregation
        Uses secret sharing to reconstruct missing masks
        """
        
        dropped_clients = set(masked_gradients.keys()) - set(available_clients)
        
        if len(dropped_clients) > 0:
            print(f"Handling {len(dropped_clients)} dropped clients")
            
            # Reconstruct masks for dropped clients using secret sharing
            # (Simplified - real implementation uses Shamir secret sharing)
            
            # Create aéPiot dropout record
            dropout_record = await self.aepiot_semantic.createBacklink({
                'title': 'Secure Aggregation Dropout Recovery',
                'description': f'Recovered from {len(dropped_clients)} client dropouts',
                'link': f'secure-agg-dropout://{int(time.time())}'
            })
            
            return dropout_record
        
        return None

6.2 Advanced Differential Privacy Techniques

Rényi Differential Privacy (RDP)

Tighter privacy accounting than standard DP:

python

class RenyiDifferentialPrivacy:
    """
    Rényi Differential Privacy - Improved privacy accounting
    """
    
    def __init__(self, alpha=10):
        self.alpha = alpha  # Rényi parameter
        self.aepiot_semantic = AePiotSemanticProcessor()
    
    def compute_rdp_epsilon(self, noise_scale, sensitivity, steps):
        """
        Compute RDP privacy cost
        More accurate than standard DP composition
        """
        
        # RDP epsilon for Gaussian mechanism
        rdp_epsilon = (steps * sensitivity**2) / (2 * noise_scale**2 * (self.alpha - 1))
        
        return rdp_epsilon
    
    def convert_rdp_to_dp(self, rdp_epsilon, delta):
        """
        Convert RDP to standard (ε, δ)-DP
        """
        
        epsilon = rdp_epsilon + (np.log(1/delta)) / (self.alpha - 1)
        
        return epsilon
    
    async def rdp_gaussian_mechanism(self, gradients, sensitivity, target_epsilon, delta):
        """
        Apply Gaussian noise with RDP accounting
        """
        
        # Compute noise scale for target epsilon
        noise_scale = self.compute_noise_scale_rdp(
            sensitivity=sensitivity,
            epsilon=target_epsilon,
            delta=delta,
            steps=1
        )
        
        # Add Gaussian noise
        noise = np.random.normal(0, noise_scale, gradients.shape)
        noisy_gradients = gradients + noise
        
        # Compute actual privacy cost
        rdp_epsilon = self.compute_rdp_epsilon(noise_scale, sensitivity, steps=1)
        dp_epsilon = self.convert_rdp_to_dp(rdp_epsilon, delta)
        
        # Create aéPiot RDP record
        rdp_record = await self.aepiot_semantic.createBacklink({
            'title': 'Rényi Differential Privacy Applied',
            'description': f'RDP ε={rdp_epsilon:.4f}, converted to DP ε={dp_epsilon:.4f}, δ={delta}',
            'link': f'rdp://{int(time.time())}'
        })
        
        return {
            'noisy_gradients': noisy_gradients,
            'rdp_epsilon': rdp_epsilon,
            'dp_epsilon': dp_epsilon,
            'delta': delta,
            'rdp_record': rdp_record
        }
    
    def compute_noise_scale_rdp(self, sensitivity, epsilon, delta, steps):
        """Compute noise scale to achieve target epsilon with RDP"""
        
        # Numerical solution (simplified)
        noise_scale = sensitivity * np.sqrt(steps / (2 * epsilon * (self.alpha - 1)))
        
        return noise_scale

Adaptive Differential Privacy

Adjust privacy budget based on data importance:

python

class AdaptiveDifferentialPrivacy:
    """
    Adaptive DP: Allocate privacy budget based on iteration importance
    """
    
    def __init__(self, total_budget=10.0, num_iterations=100):
        self.total_budget = total_budget
        self.num_iterations = num_iterations
        self.aepiot_semantic = AePiotSemanticProcessor()
        
        # Privacy budget allocation
        self.budget_allocation = self.compute_adaptive_allocation()
    
    def compute_adaptive_allocation(self):
        """
        Allocate more privacy budget to early iterations
        Early iterations more important for convergence
        """
        
        # Exponential decay allocation
        allocations = []
        decay_rate = 0.1
        
        for i in range(self.num_iterations):
            # More budget for early iterations
            weight = np.exp(-decay_rate * i)
            allocations.append(weight)
        
        # Normalize to total budget
        total_weight = sum(allocations)
        allocations = [a * self.total_budget / total_weight for a in allocations]
        
        return allocations
    
    async def adaptive_noise_addition(self, gradients, iteration):
        """
        Add noise based on adaptive budget allocation
        """
        
        # Get budget for this iteration
        epsilon_i = self.budget_allocation[iteration]
        
        # Compute noise scale
        sensitivity = 1.0  # Assuming gradients clipped to norm 1
        noise_scale = sensitivity / epsilon_i
        
        # Add Gaussian noise
        noise = np.random.normal(0, noise_scale, gradients.shape)
        noisy_gradients = gradients + noise
        
        # Track remaining budget
        remaining_budget = sum(self.budget_allocation[iteration+1:])
        
        # Create aéPiot adaptive DP record
        adaptive_record = await self.aepiot_semantic.createBacklink({
            'title': f'Adaptive DP - Iteration {iteration}',
            'description': f'ε={epsilon_i:.4f}, Remaining budget={remaining_budget:.4f}',
            'link': f'adaptive-dp://{iteration}/{int(time.time())}'
        })
        
        return {
            'noisy_gradients': noisy_gradients,
            'epsilon_used': epsilon_i,
            'remaining_budget': remaining_budget,
            'adaptive_record': adaptive_record
        }

6.3 Privacy Amplification through Sampling

Poisson Sampling Privacy Amplification:

python

class PrivacyAmplificationSampling:
    """
    Privacy amplification by sampling
    Selecting random subset of participants improves privacy
    """
    
    def __init__(self, sampling_rate=0.1):
        self.sampling_rate = sampling_rate
        self.aepiot_semantic = AePiotSemanticProcessor()
    
    def compute_amplified_privacy(self, base_epsilon, base_delta, sampling_rate):
        """
        Compute amplified privacy guarantee
        
        Theorem: If mechanism M is (ε, δ)-DP, then sampling q fraction
        and running M gives (ε', δ')-DP where:
        ε' ≈ q·ε (for small ε)
        δ' ≈ q·δ
        """
        
        amplified_epsilon = sampling_rate * base_epsilon
        amplified_delta = sampling_rate * base_delta
        
        # More precise formula (from privacy amplification theorem)
        if base_epsilon < 1:
            amplified_epsilon = np.log(1 + sampling_rate * (np.exp(base_epsilon) - 1))
        
        return amplified_epsilon, amplified_delta
    
    async def poisson_sampling_aggregation(self, all_participants, base_epsilon, base_delta):
        """
        Federated learning with Poisson sampling
        """
        
        # Sample participants (Poisson sampling)
        sampled_participants = []
        for participant in all_participants:
            if np.random.random() < self.sampling_rate:
                sampled_participants.append(participant)
        
        actual_sampling_rate = len(sampled_participants) / len(all_participants)
        
        # Compute amplified privacy
        amplified_epsilon, amplified_delta = self.compute_amplified_privacy(
            base_epsilon=base_epsilon,
            base_delta=base_delta,
            sampling_rate=actual_sampling_rate
        )
        
        # Aggregate sampled participants
        # Apply base DP mechanism to aggregation
        
        # Create aéPiot amplification record
        amplification_record = await self.aepiot_semantic.createBacklink({
            'title': 'Privacy Amplification by Sampling',
            'description': f'Sampled {len(sampled_participants)}/{len(all_participants)} participants. ' +
                          f'Amplified privacy: (ε={amplified_epsilon:.4f}, δ={amplified_delta:.8f})',
            'link': f'privacy-amplification://{int(time.time())}'
        })
        
        return {
            'sampled_participants': sampled_participants,
            'amplified_epsilon': amplified_epsilon,
            'amplified_delta': amplified_delta,
            'amplification_factor': base_epsilon / amplified_epsilon,
            'amplification_record': amplification_record
        }

6.4 Local Differential Privacy (LDP)

Strongest privacy model: Noise added before sending data

python

class LocalDifferentialPrivacy:
    """
    Local Differential Privacy: Each client adds noise locally
    Provides privacy even against malicious aggregator
    """
    
    def __init__(self, epsilon=1.0):
        self.epsilon = epsilon
        self.aepiot_semantic = AePiotSemanticProcessor()
    
    def randomized_response(self, true_value, epsilon):
        """
        Randomized Response mechanism for binary values
        Classic LDP technique
        """
        
        # Probability of reporting true value
        p = np.exp(epsilon) / (np.exp(epsilon) + 1)
        
        # Flip coin
        if np.random.random() < p:
            return true_value
        else:
            return 1 - true_value
    
    def laplace_mechanism_local(self, value, sensitivity, epsilon):
        """
        Local Laplace mechanism for numeric values
        """
        
        # Laplace noise scale
        scale = sensitivity / epsilon
        
        # Add Laplace noise
        noise = np.random.laplace(0, scale)
        noisy_value = value + noise
        
        return noisy_value
    
    async def local_gradient_perturbation(self, gradients, epsilon):
        """
        Each client perturbs their gradients locally with LDP
        """