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Classical Cryptanalysis Baselines for SHA-520
Implements preimage, collision, and timing benchmarks.
Used to establish classical lower bounds for quantum advantage.
"""
import os
import time
import random
from typing import Callable, Dict, Any, Tuple, Optional
from collections import defaultdict
import hashlib
def brute_force_preimage(
target: bytes,
hash_fn: Callable[[bytes], bytes],
max_trials: int = 1000000,
timeout_sec: Optional[float] = None,
) -> Tuple[Optional[bytes], int, float]:
"""Brute force preimage search.
Parameters
----------
target : bytes
Target hash value
hash_fn : Callable
Hash function that takes bytes and returns bytes
max_trials : int
Maximum number of hash computations to attempt
timeout_sec : float, optional
Timeout in seconds
Returns
-------
tuple
(preimage, trials_used, elapsed_time)
preimage is None if not found
"""
start_time = time.time()
trials = 0
try:
for trials in range(max_trials):
if timeout_sec and (time.time() - start_time) > timeout_sec:
break
# Generate random message
message = os.urandom(random.randint(1, 128))
digest = hash_fn(message)
if digest == target:
return message, trials, time.time() - start_time
trials += 1
return None, trials, time.time() - start_time
except KeyboardInterrupt:
return None, trials, time.time() - start_time
def birthday_collision(
hash_fn: Callable[[bytes], bytes],
max_trials: int = 1000000,
timeout_sec: Optional[float] = None,
) -> Tuple[Optional[Tuple[bytes, bytes]], int, float]:
"""Birthday attack collision search.
Uses hash table to detect collision with O(sqrt(N)) expected time.
Parameters
----------
hash_fn : Callable
Hash function
max_trials : int
Maximum number of trials
timeout_sec : float, optional
Timeout in seconds
Returns
-------
tuple
((m1, m2), trials, elapsed_time) or (None, trials, elapsed_time)
"""
start_time = time.time()
hash_table: Dict[bytes, bytes] = {}
trials = 0
try:
for trials in range(max_trials):
if timeout_sec and (time.time() - start_time) > timeout_sec:
break
message = os.urandom(random.randint(1, 128))
digest = hash_fn(message)
if digest in hash_table:
return (hash_table[digest], message), trials, time.time() - start_time
hash_table[digest] = message
trials += 1
return None, trials, time.time() - start_time
except KeyboardInterrupt:
return None, trials, time.time() - start_time
def measure_classical_complexity(
rounds: int,
target_bits: int,
) -> Dict[str, Any]:
"""Estimate classical complexity for SHA-520 variants.
Parameters
----------
rounds : int
Number of hash rounds
target_bits : int
Output bits being targeted
Returns
-------
dict
Complexity metrics:
- preimage_trials: Expected trials for preimage
- collision_trials: Expected trials for collision (birthday bound)
- preimage_time_sec: Estimated time on reference hardware
- collision_time_sec: Estimated time for collision
"""
# Classical preimage: 2^n operations
preimage_trials = 2 ** target_bits
# Birthday collision: 2^(n/2) operations
collision_trials = 2 ** (target_bits // 2)
# Approximate timing on modern CPU (~10^9 ops/sec)
ops_per_sec = 1e9
preimage_time = preimage_trials / ops_per_sec
collision_time = collision_trials / ops_per_sec
# Adjust for round count (more rounds = slower)
round_factor = max(1.0, rounds / 80.0)
preimage_time *= round_factor
collision_time *= round_factor
return {
"target_bits": target_bits,
"rounds": rounds,
"preimage_trials": int(preimage_trials),
"collision_trials": int(collision_trials),
"preimage_time_sec": preimage_time,
"collision_time_sec": collision_time,
"preimage_time_years": preimage_time / (365.25 * 24 * 3600),
"collision_time_years": collision_time / (365.25 * 24 * 3600),
}
def timing_benchmark(
hash_fn: Callable[[bytes], bytes],
message_size: int = 128,
iterations: int = 10000,
) -> Dict[str, Any]:
"""Benchmark hash function performance.
Parameters
----------
hash_fn : Callable
Hash function to benchmark
message_size : int
Size of test messages in bytes
iterations : int
Number of iterations
Returns
-------
dict
Timing statistics
"""
test_message = os.urandom(message_size)
# Warm up
for _ in range(100):
hash_fn(test_message)
# Measure
start = time.time()
for _ in range(iterations):
hash_fn(test_message)
elapsed = time.time() - start
per_call = elapsed / iterations
throughput = message_size * iterations / elapsed # bytes/sec
return {
"total_time_sec": elapsed,
"iterations": iterations,
"time_per_call_us": per_call * 1e6,
"throughput_mbps": throughput / (1024 * 1024),
"message_size_bytes": message_size,
}
def estimate_grover_advantage(
classical_trials: int,
grover_circuits: int,
circuit_depth: int,
gate_time_us: float = 100.0,
) -> Dict[str, Any]:
"""Estimate Grover algorithm advantage over classical.
Parameters
----------
classical_trials : int
Classical trials needed
grover_circuits : int
Number of Grover iterations
circuit_depth : int
Depth of each Grover iteration circuit
gate_time_us : float
Average gate time in microseconds
Returns
-------
dict
Speedup factors and absolute times
"""
classical_time = classical_trials * 1e-3 # Assume 1ms per classical hash
grover_time = grover_circuits * circuit_depth * gate_time_us * 1e-6
speedup = classical_time / max(grover_time, 1e-9)
return {
"classical_time_sec": classical_time,
"grover_time_sec": grover_time,
"speedup_factor": speedup,
"grover_iterations": grover_circuits,
"circuit_depth": circuit_depth,
}
def collision_resistance_margin(
hash_output_bits: int,
security_bits: int = 128,
) -> Dict[str, Any]:
"""Analyze collision resistance margin.
Parameters
----------
hash_output_bits : int
Output size in bits
security_bits : int
Target security level in bits
Returns
-------
dict
Security margin analysis
"""
# Birthday bound: 2^(n/2) for collision resistance
collision_security = hash_output_bits // 2
# Preimage resistance: 2^n
preimage_security = hash_output_bits
margin_collision = collision_security - security_bits
margin_preimage = preimage_security - security_bits
return {
"output_bits": hash_output_bits,
"target_security_bits": security_bits,
"collision_security_bits": collision_security,
"preimage_security_bits": preimage_security,
"collision_margin_bits": max(0, margin_collision),
"preimage_margin_bits": max(0, margin_preimage),
"collision_margin_satisfied": collision_security >= security_bits,
"preimage_margin_satisfied": preimage_security >= security_bits,
}
def estimate_required_qubits(
target_bits: int,
grover_factor: float = 0.25,
) -> Dict[str, Any]:
"""Estimate qubits needed for quantum attack.
Parameters
----------
target_bits : int
Bits of the hash to target
grover_factor : float
Factor of target space requiring qubits (0-1)
Returns
-------
dict
Qubit requirements and feasibility
"""
# Grover needs sqrt(N) amplitude amplification steps
# Reversible circuit needs log2(N) qubits for search space
search_space = 2 ** target_bits
grover_iterations = int((3.14159 / 4) * (search_space ** 0.5))
# Qubits for search space (input)
data_qubits = target_bits
# Ancilla qubits for reversible compression (typically 2-3x data)
ancilla_qubits = data_qubits * 3
# Total logical qubits
total_logical = data_qubits + ancilla_qubits
# Physical qubits with surface code error correction (~1000:1)
physical_per_logical = 1000
total_physical = total_logical * physical_per_logical
feasible_128bit_machine = total_physical < 1e7
return {
"target_bits": target_bits,
"search_space": search_space,
"grover_iterations": grover_iterations,
"data_qubits": data_qubits,
"ancilla_qubits": ancilla_qubits,
"total_logical_qubits": total_logical,
"total_physical_qubits": int(total_physical),
"feasible_on_128bit_machine": feasible_128bit_machine,
}
if __name__ == "__main__":
print("Classical Cryptanalysis Baselines")
print("=" * 50)
# Complexity analysis
for rounds in [4, 8, 16, 80]:
for bits in [32, 64]:
metrics = measure_classical_complexity(rounds, bits)
print(f"\nSHA-520-{rounds}, targeting {bits} bits:")
print(f" Preimage trials: {metrics['preimage_trials']:.2e}")
print(f" Collision trials: {metrics['collision_trials']:.2e}")
print(f" Preimage time (years): {metrics['preimage_time_years']:.2e}")
# Collision resistance
print("\n" + "=" * 50)
print("Collision Resistance Analysis (SHA-520 = 512 bits)")
margins = collision_resistance_margin(512, security_bits=128)
print(f"Collision security: {margins['collision_security_bits']} bits")
print(f"Margin above 128-bit: {margins['collision_margin_bits']} bits")
# Qubit requirements
print("\n" + "=" * 50)
print("Quantum Attack Requirements")
for bits in [32, 64, 128]:
reqs = estimate_required_qubits(bits)
print(f"\nTargeting {bits} bits:")
print(f" Logical qubits: {reqs['total_logical_qubits']}")
print(f" Physical qubits (w/ error correction): {reqs['total_physical_qubits']}")
print(f" Feasible on 128-qubit machine: {reqs['feasible_on_128bit_machine']}")
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