Quantum Computing in Distributed Systems: Preparing for the Quantum Future

┌─────────────────────────────────────────────────────────┐
│                                                         │
│               Classical Computing                       │
│                                                         │
│  ┌─────────────┐         ┌─────────────┐                │
│  │             │         │             │                │
│  │    Bit 0    │         │    Bit 1    │                │
│  │             │         │             │                │
│  └─────────────┘         └─────────────┘                │
│                                                         │
│  • Deterministic operations                             │
│  • Binary states (0 or 1)                               │
│  • Sequential processing                                │
│                                                         │
└─────────────────────────────────────────────────────────┘

┌─────────────────────────────────────────────────────────┐
│                                                         │
│                Quantum Computing                        │
│                                                         │
│  ┌─────────────────────────────────────────┐            │
│  │                                         │            │
│  │       Qubit (Superposition of           │            │
│  │        multiple states)                 │            │
│  │                                         │            │
│  └─────────────────────────────────────────┘            │
│                                                         │
│  • Probabilistic measurements                           │
│  • Superposition of states                              │
│  • Parallel processing through superposition            │
│  • Entanglement between qubits                          │
│                                                         │
└─────────────────────────────────────────────────────────┘

# Python with Qiskit for quantum load balancing optimization
from qiskit import Aer, execute
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization.problems import QuadraticProgram
import numpy as np

def create_load_balancing_problem(servers, tasks, server_capacities, task_requirements):
    """Create a load balancing problem as a quadratic program."""
    # Initialize quadratic program
    problem = QuadraticProgram(name="Load Balancing")
    
    # Define binary variables: x[i,j] = 1 if task j is assigned to server i
    for i in range(servers):
        for j in range(tasks):
            problem.binary_var(name=f'x_{i}_{j}')
    
    # Objective: Minimize the maximum load on any server
    # We use a quadratic formulation to balance the load
    linear = {}
    quadratic = {}
    
    # Penalize uneven distribution
    for i in range(servers):
        for j in range(tasks):
            for k in range(j+1, tasks):
                quadratic[(f'x_{i}_{j}', f'x_{i}_{k}')] = 2 * task_requirements[j] * task_requirements[k]
    
    problem.minimize(quadratic=quadratic)
    
    # Constraint: Each task must be assigned to exactly one server
    for j in range(tasks):
        task_constraint = {}
        for i in range(servers):
            task_constraint[f'x_{i}_{j}'] = 1
        problem.linear_constraint(linear=task_constraint, sense='==', rhs=1, name=f'task_{j}_assignment')
    
    return problem

def solve_with_qaoa(problem, p=1):
    """Solve the load balancing problem using QAOA."""
    # Set up the quantum instance
    backend = Aer.get_backend('statevector_simulator')
    quantum_instance = QuantumInstance(backend)
    
    # Create QAOA solver
    optimizer = COBYLA(maxiter=100)
    qaoa = QAOA(optimizer=optimizer, reps=p, quantum_instance=quantum_instance)
    
    # Create minimum eigen optimizer
    solver = MinimumEigenOptimizer(qaoa)
    
    # Solve the problem
    result = solver.solve(problem)
    return result

// Go implementation of TLS with post-quantum cryptography
package main

import (
	"crypto/tls"
	"fmt"
	"net/http"
	
	"github.com/open-quantum-safe/liboqs-go/oqs"
)

func main() {
	// Initialize post-quantum key exchange and signature algorithms
	kemAlg := "Kyber512"
	sigAlg := "Dilithium2"
	
	// Set up TLS configuration with post-quantum algorithms
	tlsConfig := &tls.Config{
		MinVersion: tls.VersionTLS13,
		CipherSuites: []uint16{
			tls.TLS_CHACHA20_POLY1305_SHA256,
			tls.TLS_AES_256_GCM_SHA384,
		},
		// Custom post-quantum cipher suites would be defined here
	}
	
	// Create HTTP server with post-quantum TLS
	server := &http.Server{
		Addr:      ":8443",
		TLSConfig: tlsConfig,
		Handler:   createHandler(),
	}
	
	fmt.Printf("Starting server with post-quantum algorithms: KEM=%s, Signature=%s\n", kemAlg, sigAlg)
	err = server.ListenAndServeTLS("", "")
	if err != nil {
		panic(fmt.Sprintf("Server failed: %v", err))
	}
}

# Python simulation of QKD integration with classical communication
import numpy as np
from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.backends import default_backend

class QKDSimulator:
    def __init__(self, key_length=256):
        self.key_length = key_length
    
    def generate_bb84_key(self, error_rate=0.0, eavesdropping=False):
        """Simulate BB84 QKD protocol."""
        # Alice generates random bits and random bases
        alice_bits = np.random.randint(0, 2, self.key_length)
        alice_bases = np.random.randint(0, 2, self.key_length)  # 0: rectilinear, 1: diagonal
        
        # Bob generates random bases
        bob_bases = np.random.randint(0, 2, self.key_length)
        
        # Simulate quantum transmission
        bob_bits = np.copy(alice_bits)
        
        # Simulate errors and eavesdropping
        if eavesdropping:
            # Eve measures with random bases
            eve_bases = np.random.randint(0, 2, self.key_length)
            
            # Eve's measurement affects the qubits
            for i in range(self.key_length):
                if eve_bases[i] != alice_bases[i]:
                    # Eve measured in wrong basis, changing the state
                    bob_bits[i] = np.random.randint(0, 2)
        
        # Basis reconciliation: keep only bits where Alice and Bob used the same basis
        matching_bases = alice_bases == bob_bases
        alice_sifted = alice_bits[matching_bases]
        bob_sifted = bob_bits[matching_bases]
        
        # Convert bit arrays to bytes
        alice_key_bytes = self._bits_to_bytes(alice_sifted)
        bob_key_bytes = self._bits_to_bytes(bob_sifted)
        
        return {
            'alice_key': alice_key_bytes,
            'bob_key': bob_key_bytes,
            'key_length_bits': len(alice_sifted),
            'secure': True  # Simplified for this example
        }

# Kubernetes configuration for hybrid quantum-classical architecture
apiVersion: v1
kind: Service
metadata:
  name: quantum-service
  labels:
    app: quantum-service
spec:
  selector:
    app: quantum-service
  ports:
  - port: 8080
    targetPort: 8080
  type: ClusterIP
---
apiVersion: apps/v1
kind: Deployment
metadata:
  name: quantum-service
spec:
  replicas: 1
  selector:
    matchLabels:
      app: quantum-service
  template:
    metadata:
      labels:
        app: quantum-service
    spec:
      containers:
      - name: quantum-service
        image: quantum-service:1.0
        ports:
        - containerPort: 8080
        env:
        - name: QUANTUM_PROVIDER
          value: "aws-braket"
        - name: QUANTUM_DEVICE_ARN
          value: "arn:aws:braket:::device/quantum-simulator/amazon/sv1"

# Flask API for quantum service
from flask import Flask, request, jsonify
import boto3
from braket.aws import AwsDevice
from braket.circuits import Circuit
import numpy as np

app = Flask(__name__)

@app.route('/api/quantum/optimization', methods=['POST'])
def quantum_optimization():
    # Parse request data
    data = request.json
    problem_type = data.get('problem_type', 'max-cut')
    problem_data = data.get('problem_data', {})
    
    # Select quantum device
    device_arn = os.environ.get('QUANTUM_DEVICE_ARN')
    device = AwsDevice(device_arn)
    
    # Create quantum circuit based on problem type
    if problem_type == 'max-cut':
        circuit = create_max_cut_circuit(problem_data)
    elif problem_type == 'tsp':
        circuit = create_tsp_circuit(problem_data)
    else:
        return jsonify({'error': 'Unsupported problem type'}), 400
    
    # Run quantum task
    task = device.run(circuit, shots=1000)
    result = task.result()
    
    # Process and return results
    processed_result = process_quantum_result(result, problem_type, problem_data)
    
    return jsonify({
        'task_id': task.id,
        'result': processed_result,
        'execution_time': result.task_metadata.runtime,
        'quantum_device': device_arn
    })

# Python script to inventory cryptographic algorithms
import os
import re
import json
import subprocess
from collections import defaultdict

def scan_repository(repo_path):
    """Scan a code repository for cryptographic usage."""
    crypto_patterns = {
        'RSA': r'RSA|rsa_encrypt|rsa_decrypt',
        'ECC': r'ECC|ECDSA|ECDH|elliptic.curve',
        'DSA': r'DSA|dsa_sign|dsa_verify',
        'DH': r'DiffieHellman|DH_KEY|dh_compute',
        'AES': r'AES|aes_encrypt|aes_decrypt',
        'SHA2': r'SHA-?2|SHA2|sha2',
        'SHA3': r'SHA-?3|SHA3|sha3',
        'Post-Quantum': r'Kyber|Dilithium|FALCON|SPHINCS|NewHope|Frodo|SIKE'
    }
    
    results = defaultdict(list)
    
    # Get all files in repository
    for root, _, files in os.walk(repo_path):
        for file in files:
            # Skip binary files and certain directories
            if file.endswith(('.jpg', '.png', '.pdf', '.bin')) or '.git' in root:
                continue
            
            file_path = os.path.join(root, file)
            try:
                with open(file_path, 'r', encoding='utf-8', errors='ignore') as f:
                    content = f.read()
                    
                    # Check for crypto patterns
                    for algo, pattern in crypto_patterns.items():
                        matches = re.findall(pattern, content)
                        if matches:
                            rel_path = os.path.relpath(file_path, repo_path)
                            results[algo].append({
                                'file': rel_path,
                                'matches': len(matches)
                            })
            except Exception as e:
                print(f"Error processing {file_path}: {e}")
    
    # Classify algorithms by quantum vulnerability
    vulnerability_assessment = {
        'quantum_vulnerable': {
            'RSA': len(results['RSA']),
            'ECC': len(results['ECC']),
            'DSA': len(results['DSA']),
            'DH': len(results['DH'])
        },
        'quantum_resistant': {
            'AES': len(results['AES']),
            'SHA2': len(results['SHA2']),
            'SHA3': len(results['SHA3']),
            'Post-Quantum': len(results['Post-Quantum'])
        }
    }
    
    return {
        'detailed_results': dict(results),
        'vulnerability_assessment': vulnerability_assessment
    }

def check_tls_configuration(hostname, port=443):
    """Check TLS configuration for quantum readiness."""
    try:
        # Use OpenSSL to check TLS configuration
        output = subprocess.check_output(
            ['openssl', 's_client', '-connect', f'{hostname}:{port}', '-tls1_2'],
            stderr=subprocess.STDOUT,
            text=True
        )
        
        # Check for key exchange algorithms
        key_exchange = re.search(r'Server Temp Key: (.+)', output)
        if key_exchange:
            key_info = key_exchange.group(1)
            
            # Assess quantum vulnerability
            vulnerable = any(algo in key_info.lower() for algo in ['rsa', 'ecdh', 'dh'])
            
            return {
                'hostname': hostname,
                'port': port,
                'key_exchange': key_info,
                'quantum_vulnerable': vulnerable,
                'recommendation': 'Upgrade to post-quantum algorithms' if vulnerable else 'Configuration is quantum-resistant'
            }
        
        return {
            'hostname': hostname,
            'port': port,
            'error': 'Could not determine key exchange algorithm',
            'output': output[:500] + '...' if len(output) > 500 else output
        }
    
    except subprocess.CalledProcessError as e:
        return {
            'hostname': hostname,
            'port': port,
            'error': f'OpenSSL command failed: {e}',
            'output': e.output[:500] + '...' if len(e.output) > 500 else e.output
        }

# Example usage
if __name__ == "__main__":
    # Scan a repository
    repo_results = scan_repository('/path/to/your/repo')
    with open('crypto_inventory.json', 'w') as f:
        json.dump(repo_results, f, indent=2)
    
    # Check TLS configurations
    tls_results = []
    for hostname in ['example.com', 'api.example.com', 'secure.example.com']:
        tls_results.append(check_tls_configuration(hostname))
    
    with open('tls_assessment.json', 'w') as f:
        json.dump(tls_results, f, indent=2)

// Java implementation of hybrid classical/post-quantum cryptography
import org.bouncycastle.crypto.AsymmetricCipherKeyPair;
import org.bouncycastle.pqc.crypto.crystals.kyber.*;
import org.bouncycastle.pqc.crypto.crystals.dilithium.*;
import java.security.*;
import javax.crypto.Cipher;

public class HybridCryptography {
    
    public static class HybridKeyPair {
        private final KeyPair classicalKeyPair;
        private final AsymmetricCipherKeyPair quantumKeyPair;
        
        public HybridKeyPair(KeyPair classicalKeyPair, AsymmetricCipherKeyPair quantumKeyPair) {
            this.classicalKeyPair = classicalKeyPair;
            this.quantumKeyPair = quantumKeyPair;
        }
        
        public KeyPair getClassicalKeyPair() {
            return classicalKeyPair;
        }
        
        public AsymmetricCipherKeyPair getQuantumKeyPair() {
            return quantumKeyPair;
        }
    }
    
    public static HybridKeyPair generateHybridKeys() throws NoSuchAlgorithmException {
        // Generate classical RSA key pair
        KeyPairGenerator keyGen = KeyPairGenerator.getInstance("RSA");
        keyGen.initialize(2048);
        KeyPair classicalKeyPair = keyGen.generateKeyPair();
        
        // Generate post-quantum key pair (Kyber)
        KyberKeyPairGenerator kyberKeyGen = new KyberKeyPairGenerator();
        kyberKeyGen.init(new KyberKeyGenerationParameters(new SecureRandom(), KyberParameters.kyber768));
        AsymmetricCipherKeyPair quantumKeyPair = kyberKeyGen.generateKeyPair();
        
        return new HybridKeyPair(classicalKeyPair, quantumKeyPair);
    }
    
    public static byte[] hybridEncrypt(PublicKey classicalPubKey, KyberPublicKeyParameters quantumPubKey, byte[] data) 
            throws Exception {
        // Classical encryption (RSA)
        Cipher rsaCipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
        rsaCipher.init(Cipher.ENCRYPT_MODE, classicalPubKey);
        byte[] classicalCiphertext = rsaCipher.doFinal(data);
        
        // Post-quantum encryption (Kyber)
        KyberKEMGenerator kemGenerator = new KyberKEMGenerator(new SecureRandom());
        KyberKEMExtractor kemExtractor = new KyberKEMExtractor(quantumPubKey);
        
        // Generate encapsulation
        KyberEncapsulation encapsulation = kemGenerator.generateEncapsulated(quantumPubKey);
        byte[] encapsulatedKey = encapsulation.getEncapsulation();
        byte[] sharedSecret = encapsulation.getSecret();
        
        // Combine results
        byte[] result = new byte[classicalCiphertext.length + encapsulatedKey.length + 8];
        // Store lengths and concatenate data
        System.arraycopy(intToBytes(classicalCiphertext.length), 0, result, 0, 4);
        System.arraycopy(intToBytes(encapsulatedKey.length), 0, result, 4, 4);
        System.arraycopy(classicalCiphertext, 0, result, 8, classicalCiphertext.length);
        System.arraycopy(encapsulatedKey, 0, result, 8 + classicalCiphertext.length, encapsulatedKey.length);
        
        return result;
    }
    
    private static byte[] intToBytes(int value) {
        return new byte[] {
            (byte)(value >>> 24),
            (byte)(value >>> 16),
            (byte)(value >>> 8),
            (byte)value
        };
    }
    
    private static int bytesToInt(byte[] bytes, int offset) {
        return ((bytes[offset] & 0xFF) << 24) |
               ((bytes[offset + 1] & 0xFF) << 16) |
               ((bytes[offset + 2] & 0xFF) << 8) |
               (bytes[offset + 3] & 0xFF);
    }
}