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Toy SHA-520 Variant for Testing and Development
Reduced-round, reduced-word-size SHA-520 for fast simulation
and verification of cryptanalysis techniques.
Parameters:
- 4 rounds (not 80)
- 32-bit words (not 64-bit)
- 4-word state (not 8)
- Result: 128-bit hashes (not 512-bit)
"""
import struct
from typing import List, Tuple, Dict, Any
import math
class ToySHA520:
"""Toy SHA-520 with reduced parameters for fast simulation.
Maintains SHA structure but reduces complexity for proof-of-concept
attacks (Grover, collision search, etc.).
Parameters
----------
rounds : int
Number of compression rounds (typically 4)
word_size : int
Bits per word (typically 32)
n_words : int
Number of state words (typically 4)
"""
# Toy constants (first 4 round constants, mod 2^32)
K_toy = [
0x67452301,
0xefcdab89,
0x98badcfe,
0x10325476,
]
# Toy IV
IV_toy = [0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a]
def __init__(self, rounds: int = 4) -> None:
"""Initialize Toy SHA-520.
Parameters
----------
rounds : int
Number of rounds
"""
self.rounds = rounds
self.word_size = 32
self.n_words = 4
self.digest_size = (self.n_words * self.word_size) // 8 # bytes
self.block_size = 64 # bytes
self._h = list(self.IV_toy)
self._buffer = b''
self._counter = 0
@staticmethod
def _rotr(x: int, n: int) -> int:
"""Right rotate 32-bit word."""
mask = (1 << 32) - 1
return ((x >> n) | (x << (32 - n))) & mask
@staticmethod
def _sigma0(x: int) -> int:
"""Lower sigma 0 function."""
return ToySHA520._rotr(x, 1) ^ ToySHA520._rotr(x, 5) ^ (x >> 7)
@staticmethod
def _sigma1(x: int) -> int:
"""Lower sigma 1 function."""
return ToySHA520._rotr(x, 11) ^ ToySHA520._rotr(x, 20) ^ (x >> 14)
@staticmethod
def _Sigma0(x: int) -> int:
"""Upper Sigma 0 function."""
return ToySHA520._rotr(x, 2) ^ ToySHA520._rotr(x, 6) ^ ToySHA520._rotr(x, 15)
@staticmethod
def _Sigma1(x: int) -> int:
"""Upper Sigma 1 function."""
return ToySHA520._rotr(x, 7) ^ ToySHA520._rotr(x, 12) ^ ToySHA520._rotr(x, 22)
@staticmethod
def _Ch(x: int, y: int, z: int) -> int:
"""Choice function."""
return (x & y) ^ (~x & z)
@staticmethod
def _Maj(x: int, y: int, z: int) -> int:
"""Majority function."""
return (x & y) ^ (x & z) ^ (y & z)
def _compress(self, block: bytes) -> None:
"""Compress a 64-byte block.
Parameters
----------
block : bytes
64-byte message block
"""
# Parse into 16 32-bit words (64 bytes = 16 * 4 bytes)
w = list(struct.unpack('>16I', block[:64]))
# Expand to 8 + rounds words
for i in range(8, min(8 + self.rounds, 16)):
s0 = self._sigma0(w[i - 7])
s1 = self._sigma1(w[i - 2])
w.append((w[i - 8] + s0 + w[i - 5] + s1) & 0xffffffff)
# Initialize working variables
a, b, c, d = self._h
# Compression function
for i in range(self.rounds):
K_idx = i % len(self.K_toy)
w_idx = i % len(w)
S1 = self._Sigma1(a)
ch = self._Ch(a, b, c)
temp1 = (d + S1 + ch + self.K_toy[K_idx] + w[w_idx]) & 0xffffffff
S0 = self._Sigma0(a)
maj = self._Maj(a, b, c)
temp2 = (S0 + maj) & 0xffffffff
d = c
c = b
b = a
a = (temp1 + temp2) & 0xffffffff
# Update hash state
self._h[0] = (self._h[0] + a) & 0xffffffff
self._h[1] = (self._h[1] + b) & 0xffffffff
self._h[2] = (self._h[2] + c) & 0xffffffff
self._h[3] = (self._h[3] + d) & 0xffffffff
def update(self, data: bytes) -> None:
"""Update hash with data.
Parameters
----------
data : bytes
Data to hash
"""
if isinstance(data, str):
data = data.encode()
self._buffer += data
self._counter += len(data)
# Process complete blocks
while len(self._buffer) >= self.block_size:
self._compress(self._buffer[:self.block_size])
self._buffer = self._buffer[self.block_size:]
def finalize(self) -> bytes:
"""Finalize hash.
Returns
-------
bytes
16-byte (128-bit) digest
"""
# Copy state
h = list(self._h)
buffer = self._buffer
counter = self._counter
# Padding
mdi = counter % self.block_size
length = counter * 8
if mdi < 56:
padlen = 56 - mdi
else:
padlen = self.block_size + 56 - mdi
padding = b'\x80' + (b'\x00' * (padlen - 1))
buffer += padding
buffer += struct.pack('>Q', length)
# Temporary state
temp_h = h
# Process remaining blocks
for i in range(0, len(buffer), self.block_size):
block = buffer[i:i + self.block_size]
if len(block) == self.block_size:
# Inline compress with temp state
w = list(struct.unpack('>16I', block[:64]))
for j in range(8, 8 + self.rounds):
s0 = self._sigma0(w[j - 7])
s1 = self._sigma1(w[j - 2])
w.append((w[j - 8] + s0 + w[j - 5] + s1) & 0xffffffff)
a, b, c, d = temp_h
for j in range(self.rounds):
K_idx = j % len(self.K_toy)
w_idx = j % len(w)
S1 = self._Sigma1(a)
ch = self._Ch(a, b, c)
temp1 = (d + S1 + ch + self.K_toy[K_idx] + w[w_idx]) & 0xffffffff
S0 = self._Sigma0(a)
maj = self._Maj(a, b, c)
temp2 = (S0 + maj) & 0xffffffff
d = c
c = b
b = a
a = (temp1 + temp2) & 0xffffffff
temp_h[0] = (temp_h[0] + a) & 0xffffffff
temp_h[1] = (temp_h[1] + b) & 0xffffffff
temp_h[2] = (temp_h[2] + c) & 0xffffffff
temp_h[3] = (temp_h[3] + d) & 0xffffffff
return struct.pack('>4I', *temp_h)
def digest(self, data: bytes = b'') -> bytes:
"""Compute digest.
Parameters
----------
data : bytes
Data to hash
Returns
-------
bytes
128-bit hash
"""
h = ToySHA520(self.rounds)
if data:
h.update(data)
else:
h._h = list(self._h)
h._buffer = self._buffer
h._counter = self._counter
return h.finalize()
def hexdigest(self, data: bytes = b'') -> str:
"""Hex digest."""
return self.digest(data).hex()
def build_toy_grover_circuit(
toy: ToySHA520,
target_hash: bytes,
iterations: int = 10,
) -> Dict[str, Any]:
"""Build Grover circuit description for Toy SHA-520.
This is a symbolic representation (not executable circuit code).
Parameters
----------
toy : ToySHA520
Toy hash instance
target_hash : bytes
Target 16-byte hash
iterations : int
Number of Grover iterations
Returns
-------
dict
Circuit specification with gates and resources
"""
# For toy with 4 rounds and 32-bit words, hash input can be small
# Assume 32-bit search space (reasonable for toy)
n_qubits = 32
# Oracle requires:
# - Reversible compression rounds
# - Comparison with target hash
# - Phase flip
# Estimate: 4 rounds * ~50 gates per round + ~100 for comparison
oracle_gates = 4 * 50 + 100
oracle_depth = 50
# Diffusion: ~4*n + 50
diffusion_gates = 4 * n_qubits + 50
diffusion_depth = 30
# Total
total_gates = iterations * (oracle_gates + diffusion_gates) + n_qubits
total_depth = iterations * (oracle_depth + diffusion_depth) + n_qubits
# Circuit description
circuit_spec = {
"algorithm": "Grover",
"hash_variant": "Toy-SHA-520",
"target_bits": n_qubits,
"search_space": 2 ** n_qubits,
"target_hash": target_hash.hex(),
"grover_iterations": iterations,
"n_qubits": n_qubits,
"oracle_gates": oracle_gates,
"oracle_depth": oracle_depth,
"diffusion_gates": diffusion_gates,
"diffusion_depth": diffusion_depth,
"total_gates": total_gates,
"total_depth": total_depth,
"operations": [
"Initialize superposition (H on all qubits)",
f"Repeat {iterations} times:",
" - Apply SHA-520 oracle (mark target hash)",
" - Apply Grover diffusion operator",
"Measure qubits",
],
}
return circuit_spec
def estimate_toy_grover_speedup(target_bits: int = 32) -> Dict[str, Any]:
"""Estimate speedup of Grover over classical for toy SHA-520.
Parameters
----------
target_bits : int
Bits in search space
Returns
-------
dict
Speedup metrics
"""
search_space = 2 ** target_bits
# Classical: 2^n evaluations
classical_evals = search_space
classical_time_sec = classical_evals * 1e-6 # 1 μs per eval
# Grover iterations
grover_iters = int((math.pi / 4.0) * math.sqrt(search_space))
# Circuit execution (gate time ~100 ns)
gates_per_iter = 400 # Rough estimate
gate_time_sec = 100e-9
grover_time_sec = grover_iters * gates_per_iter * gate_time_sec
speedup = classical_time_sec / max(grover_time_sec, 1e-9)
return {
"target_bits": target_bits,
"search_space": search_space,
"classical_evaluations": classical_evals,
"classical_time_sec": classical_time_sec,
"grover_iterations": grover_iters,
"gates_per_iteration": gates_per_iter,
"gate_time_sec": gate_time_sec,
"grover_time_sec": grover_time_sec,
"speedup_factor": speedup,
}
if __name__ == "__main__":
print("Toy SHA-520 for Cryptanalysis Testing")
print("=" * 60)
# Test Toy SHA-520
toy = ToySHA520(rounds=4)
print(f"Toy SHA-520-{toy.rounds}")
print(f" Word size: {toy.word_size} bits")
print(f" State words: {toy.n_words}")
print(f" Digest size: {toy.digest_size} bytes ({toy.digest_size * 8} bits)")
# Test vectors
print("\nTest vectors:")
test_cases = [b'', b'abc', b'hello world', b'a' * 100]
for msg in test_cases:
digest = toy.digest(msg)
msg_display = msg.decode() if len(msg) < 20 else f"{msg[:20].decode()}..."
print(f" {msg_display:30s} -> {digest.hex()}")
# Grover circuit
print("\n" + "=" * 60)
print("Grover Circuit for Toy SHA-520")
target = b'\x00' * 16
circuit_spec = build_toy_grover_circuit(toy, target, iterations=10)
print(f"\nCircuit specification:")
for key, value in circuit_spec.items():
if key != "operations":
print(f" {key}: {value}")
print(f"\nOperations:")
for op in circuit_spec["operations"]:
print(f" {op}")
# Speedup analysis
print("\n" + "=" * 60)
print("Grover vs Classical Speedup")
for bits in [16, 24, 32]:
speedup = estimate_toy_grover_speedup(bits)
print(
f"\n{bits}-bit search:"
f"\n Classical time: {speedup['classical_time_sec']:.2e} sec"
f"\n Grover time: {speedup['grover_time_sec']:.2e} sec"
f"\n Speedup: {speedup['speedup_factor']:.2e}x"
)
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