Quantum Computing Attack Threat Analysis

Version: 1.0
Last Updated: 2025-01-02
Security Classification: PUBLIC

Overview

Quantum computing poses an existential threat to many classical cryptographic algorithms. This document analyzes specific quantum attack algorithms, their impact on current cryptography, and timeline estimates for practical threats.

Quantum Attack Algorithms

Shor’s Algorithm

Purpose: Factor integers and compute discrete logarithms in polynomial time

Quantum Resource Requirements:

def shor_resources(bit_size):
    """Estimate quantum resources for Shor's algorithm"""
    # Logical qubits needed
    logical_qubits = 2 * bit_size + 3
    
    # Gate count estimate
    gate_count = bit_size ** 3
    
    # With error correction overhead (1000:1 ratio)
    physical_qubits = logical_qubits * 1000
    
    return {
        'logical_qubits': logical_qubits,
        'physical_qubits': physical_qubits,
        'gate_count': gate_count,
        'coherence_time_needed': 'hours'
    }

# RSA-2048 requirements
rsa_2048 = shor_resources(2048)
# Result: ~4,099 logical qubits, ~4 million physical qubits

Grover’s Algorithm

Purpose: Search unsorted databases with quadratic speedup

Security Level Adjustments:

def grover_adjusted_security(classical_bits):
    """Calculate post-quantum security level"""
    # Grover provides quadratic speedup
    quantum_bits = classical_bits / 2
    
    # Collision resistance for hash functions
    collision_classical = classical_bits / 2
    collision_quantum = classical_bits / 3
    
    return {
        'key_search': quantum_bits,
        'collision_resistance': collision_quantum,
        'recommended_key_size': max(256, classical_bits * 2)
    }

Quantum Period Finding

Purpose: Solve hidden subgroup problems

Applications:

Breaking discrete log cryptosystems
Attacking certain lattice problems
Solving hidden shift problems

Simon’s Algorithm

Purpose: Find hidden period with exponential speedup

Vulnerable Algorithms:

Certain block cipher constructions
Some authenticated encryption modes
Specific MAC constructions

Quantum Threat Timeline

Current State (2025)

quantum_state_2025 = {
    'best_quantum_computer': {
        'logical_qubits': 10-20,
        'physical_qubits': 1000+,
        'coherence_time': 'milliseconds',
        'error_rate': 0.1-1%
    },
    'cryptographic_impact': 'None',
    'research_focus': 'Error correction'
}

Projected Timeline

Quantum-Resistant Algorithms

NIST PQC Standards

pqc_algorithms = {
    'kem': {
        'ML-KEM': 'Lattice-based, FIPS 203',
        'security_levels': [128, 192, 256]
    },
    'signatures': {
        'ML-DSA': 'Lattice-based, FIPS 204',
        'SLH-DSA': 'Hash-based, FIPS 205',
        'Falcon': 'NTRU lattice, Round 3'
    },
    'quantum_resistance': 'Proven under standard assumptions'
}

Hybrid Quantum-Classical Attacks

Quantum-Enhanced Classical Attacks

class HybridAttacks:
    """Attacks combining quantum and classical computing"""
    
    def quantum_sieve(self, lattice_problem):
        """Use quantum computer for sieving step"""
        # Quantum speedup: polynomial
        # Still exponential overall
        quantum_advantage = 2 ** (0.265 * n)  # vs 2 ** (0.292 * n)
        return quantum_advantage
    
    def variational_quantum_attacks(self):
        """NISQ-era attacks using VQE/QAOA"""
        return {
            'current_capability': 'Limited to small problems',
            'potential': 'May improve classical optimization',
            'threat_level': 'Research only'
        }

Quantum Attack Mitigation

Immediate Actions

Inventory: Identify quantum-vulnerable systems
Prioritize: Focus on long-term secrets
Hybrid: Implement classical+PQC combinations

Migration Strategy

def migration_priority(system):
    """Determine migration urgency"""
    
    scores = {
        'data_sensitivity': 0,  # 0-10
        'data_lifetime': 0,     # years
        'system_criticality': 0, # 0-10
        'migration_complexity': 0 # 0-10
    }
    
    # Long-lived sensitive data
    if system['data_lifetime'] > 10:
        scores['data_sensitivity'] += 5
    
    # Critical infrastructure
    if system['type'] in ['pki', 'root_ca', 'key_management']:
        scores['system_criticality'] = 10
    
    # Calculate priority
    priority = (scores['data_sensitivity'] * scores['data_lifetime'] + 
                scores['system_criticality'] * 10) / scores['migration_complexity']
    
    return priority

Quantum-Safe Security Levels

Bit Security Equivalence

| Classical | Post-Quantum | NIST Level | Example Algorithm | |———–|————–|————|——————-| | 128-bit | 128-bit | Level 1 | ML-KEM-512, AES-128 | | 192-bit | 192-bit | Level 3 | ML-KEM-768, AES-192 | | 256-bit | 256-bit | Level 5 | ML-KEM-1024, AES-256 |

Store-Now-Decrypt-Later (SNDL)

Risk Assessment

def sndl_risk(data_classification, protection_years):
    """Assess SNDL attack risk"""
    
    # Probability of quantum computer by year
    quantum_probability = {
        2030: 0.05,
        2035: 0.25,
        2040: 0.60,
        2045: 0.85,
        2050: 0.95
    }
    
    # Calculate exposure risk
    exposure_end = 2025 + protection_years
    risk = 0
    
    for year, prob in quantum_probability.items():
        if year <= exposure_end:
            risk = max(risk, prob)
    
    return {
        'risk_level': risk,
        'recommendation': 'Immediate PQC' if risk > 0.3 else 'Planned migration'
    }