A post-quantum authenticated key exchange protocol (CRYSTALS-Kyber combined with a lattice-based digital signature) can be securely composed with a pulsar-timing-derived time-lock to authenticate ephemeral session key transmission during the T_target window, ensuring only pre-authorised parties can receive the session key even if the pulsar timing channel is observed by an adversary with a quantum computer.

A cryptographic protocol combining CRYSTALS-Kyber (NIST PQC KEM, security level 3, ~AES-192 equivalent) with a lattice-based digital signature (CRYSTALS-Dilithium3 or FALCON-512) can be securely composed with a pulsar-timing-array (PTA) derived time-lock mechanism such that: (1) ephemeral session keys are encrypted under a time-dependent commitment derived from pulsar timing residuals observable only within a target window T_target (±δt, where δt ≤ 10 seconds), (2) the composed protocol achieves IND-CCA2 security against quantum adversaries under the Module Learning With Errors (MLWE) hardness assumption, (3) an adversary possessing a cryptographically relevant quantum computer (CRQC) and full observation of the pulsar timing channel cannot recover the session key outside T_target with probability greater than 2^(-128), and (4) pre-authorised parties with valid Dilithium3 credentials can reliably decrypt the session key within T_target with success probability ≥ 0.999 under realistic pulsar timing noise conditions (RMS timing residual σ_t ≤ 100 ns for millisecond pulsars such as PSR J0437-4715).

PHASE 1 — Formal Security Analysis (Weeks 1–8): Construct a game-based security proof for the composed protocol in the Quantum Random Oracle Model (QROM). Verify that the time-lock commitment scheme based on PTA residuals satisfies hiding and binding properties. Use ProVerif or Tamarin Prover for automated protocol verification.

PHASE 2 — Simulation with Real PTA Data (Weeks 5–16): Implement the full protocol stack in Python/Rust using liboqs (Open Quantum Safe) for Kyber-768 and Dilithium3. Replay IPTA DR2 timing residuals to simulate the time-lock mechanism. Measure key recovery success rate across 10,000 simulated T_target windows.

PHASE 3 — Adversarial Simulation (Weeks 10–20): Simulate a quantum adversary attempting to break the time-lock using classical approximations of quantum attacks (BKZ-β lattice reduction, dual attacks). Measure distinguishing advantage as a function of adversary compute budget (up to 2^80 classical operations as proxy).

PHASE 4 — Performance Benchmarking (Weeks 16–24): Benchmark end-to-end protocol latency, key generation time, and communication overhead on commodity hardware (x86-64, ARM Cortex-A72). Target: total handshake < 500 ms on 1 Gbps link.

PHASE 5 — Red Team / Penetration Analysis (Weeks 20–28): Independent security team attempts protocol breaks via timing attacks, replay attacks, and ephemeris manipulation. Document all findings.

# Post-Quantum PTA Time-Lock Authenticated Key Exchange (PQ-PTA-AKE)
# Architecture Overview

## PROTOCOL PARAMETERS
KYBER_LEVEL = 768          # ML-KEM-768 (FIPS 203)
DILITHIUM_LEVEL = 3        # ML-DSA-65 (FIPS 204)
HASH = SHA3_256
T_TARGET_TOLERANCE = 10    # seconds
MIN_PULSAR_TIMING_RMS = 100e-9  # 100 nanoseconds

## DATA STRUCTURES
struct PulsarTimeLock:
    pulsar_id: str          # e.g., "J0437-4715"
    T_target: float         # Unix timestamp (UTC)
    delta_t: float          # window half-width in seconds
    ephemeris_hash: bytes   # SHA3-256 of TEMPO2 .par file
    commitment: bytes       # C = H(residual(T_target) || nonce)
    nonce: bytes            # 32-byte random nonce

struct SessionKeyPackage:
    kem_ciphertext: bytes   # Kyber-768 encapsulation
    signature: bytes        # Dilithium3 signature over (kem_ciphertext || time_lock)
    time_lock: PulsarTimeLock
    sender_pk: bytes        # Dilithium3 public key
    timestamp: float        # message creation time

## PROTOCOL PHASES

### PHASE 1: SETUP (offline, before T_target)
def Setup(security_param: int) -> (pk_A, sk_A, pk_B, sk_B):
    # Party A (sender) key generation
    (kem_pk_A, kem_sk_A) = Kyber768.KeyGen()
    (sig_pk_A, sig_sk_A) = Dilithium3.KeyGen()
    
    # Party B (receiver) key generation  
    (kem_pk_B, kem_sk_B) = Kyber768.KeyGen()
    (sig_pk_B, sig_sk_B) = Dilithium3.KeyGen()
    
    # Exchange public keys via authenticated channel (pre-protocol)
    return (kem_pk_A, sig_pk_A, kem_sk_B, sig_sk_B, ...)

### PHASE 2: TIME-LOCK COMMITMENT GENERATION
def GenerateTimeLock(pulsar_id: str, T_target: float, 
                     ephemeris: TEMPO2Ephemeris) -> PulsarTimeLock:
    # Predict pulsar timing residual at T_target
    predicted_residual = ephemeris.predict_residual(pulsar_id, T_target)
    # residual in nanoseconds, float64
    
    nonce = os.urandom(32)
    
    # Commitment: binding to predicted residual value
    # Hiding: residual unpredictable to adversary before T_target
    commitment = SHA3_256(
        struct.pack('>d', predicted_residual) + nonce
    )
    
    return PulsarTimeLock(
        pulsar_id=pulsar_id,
        T_target=T_target,
        delta_t=T_TARGET_TOLERANCE,
        ephemeris_hash=SHA3_256(ephemeris.serialize()),
        commitment=commitment,
        nonce=nonce  # KEPT SECRET until T_target
    )

### PHASE 3: SESSION KEY ENCAPSULATION (at time T_send < T_target)
def Encapsulate(kem_pk_B: bytes, sig_sk_A: bytes, 
                time_lock: PulsarTimeLock) -> SessionKeyPackage:
    # KEM encapsulation: generates shared secret K and ciphertext C
    (kem_ciphertext, shared_secret_K) = Kyber768.Encap(kem_pk_B)
    
    # Derive session key: bind to time-lock commitment
    session_key = HKDF(
        ikm=shared_secret_K,
        salt=time_lock.commitment,
        info=b"PQ-PTA-AKE-v1",
        length=32
    )
    
    # Sign the package: authenticate sender, bind to time-lock
    message_to_sign = kem_ciphertext + time_lock.serialize()
    signature = Dilithium3.Sign(sig_sk_A, message_to_sign)
    
    return SessionKeyPackage(
        kem_ciphertext=kem_ciphertext,
        signature=signature,
        time_lock=time_lock,  # commitment included, nonce withheld
        sender_pk=Dilithium3.GetPublicKey(sig_sk_A),
        timestamp=time.time()
    )

### PHASE 4: TIME-LOCK OPENING (at time T_open, T_target - delta_t <= T_open <= T_target + delta_t)
def OpenTimeLock(time_lock: PulsarTimeLock, 
                 observed_residual: float) -> (bool, bytes):
    # Verify we are within T_target window
    current_time = get_gps_disciplined_time()  # GPS-disciplined clock
    if abs(current_time - time_lock.T_target) > time_lock.delta_t:
        return (False, None)  # Outside window
    
    # Reconstruct commitment from observed pulsar residual
    # Receiver observes actual residual from radio telescope / PTA network
    reconstructed_commitment = SHA3_256(
        struct.pack('>d', observed_residual) + time_lock.nonce
        # NOTE: nonce revealed by sender at T_target via authenticated channel
    )
    
    # Verify commitment matches
    if not constant_time_compare(reconstructed_commitment, time_lock.commitment):
        return (False, None)  # Timing mismatch or wrong residual
    
    return (True, reconstructed_commitment)

### PHASE 5: SESSION KEY DECAPSULATION
def Decapsulate(package: SessionKeyPackage, kem_sk_B: bytes,
                sig_pk_A: bytes, observed_residual: float) -> bytes:
    # Step 1: Verify signature (authentication)
    message_to_verify = package.kem_ciphertext + package.time_lock.serialize()
    if not Dilithium3.Verify(sig_pk_A, message_to_verify, package.signature):
        raise AuthenticationError("Invalid sender signature")
    
    # Step 2: Open time-lock (timing verification)
    (lock_valid, verified_commitment) = OpenTimeLock(
        package.time_lock, observed_residual
    )
    if not lock_valid:
        raise TimeLockError("Outside T_target window or commitment mismatch")
    
    # Step 3: KEM decapsulation
    shared_secret_K = Kyber768.Decap(kem_sk_B, package.kem_ciphertext)
    
    # Step 4: Derive session key (must match sender's derivation)
    session_key = HKDF(
        ikm=shared_secret_K,
        salt=verified_commitment,
        info=b"PQ-PTA-AKE-v1",
        length=32
    )
    
    return session_key  # 256-bit post-quantum session key

## SECURITY PROPERTIES (to be formally verified)
# 1. IND-CCA2: session_key indistinguishable from random under MLWE
# 2. Mutual Authentication: both parties authenticated via Dilithium3
# 3. Time-Lock Binding: session_key derivation requires verified_commitment
# 4. Forward Secrecy: ephemeral Kyber keys; compromise of long-term keys
#    does not reveal past session keys
# 5. Quantum Resistance: all hardness assumptions are MLWE-based

## VERIFICATION HARNESS
def run_validation(n_trials: int = 10000) -> dict:
    results = {'success': 0, 'timing_fail': 0, 'auth_fail': 0, 'other': 0}
    
    for trial in range(n_trials):
        # Sample realistic pulsar residual from IPTA DR2 distribution
        true_residual = sample_ipta_residual("J0437-4715")
        
        # Simulate T_target window (±10s)
        T_target = time.time() + 3600  # 1 hour ahead
        
        # Run full protocol
        try:
            time_lock = GenerateTimeLock("J0437-4715", T_target, ephemeris)
            package = Encapsulate(kem_pk_B, sig_sk_A, time_lock)
            
            # Simulate time passing to T_target
            # Inject realistic timing noise
            observed = true_residual + np.random.normal(0, 50e-9)  # 50ns noise
            
            session_key = Decapsulate(package, kem_sk_B, sig_pk_A, observed)
            results['success'] += 1
        except TimeLockError:
            results['timing_fail'] += 1
        except AuthenticationError:
            results['auth_fail'] += 1
        except Exception:
            results['other'] += 1
    
    results['success_rate'] = results['success'] / n_trials
    return results

# TARGET: results['success_rate'] >= 0.999