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Reversible Quantum SHA-520 Circuits
Implements unitary quantum circuit for SHA-520 compression.
Used as oracle for Grover's algorithm.
"""
from typing import Optional, List, Dict, Any
import math
from qlambda.arrays import SHA520_DIGEST_BYTES, SHA520_IV_520, words_to_bits
class QuantumCircuit:
"""Minimal QuantumCircuit abstraction for reversible SHA-520.
This provides a device-independent representation that can be compiled
to various quantum platforms (Qiskit, ProjectQ, etc.).
"""
def __init__(self, num_qubits: int, name: str = "circuit"):
"""Initialize quantum circuit.
Parameters
----------
num_qubits : int
Number of qubits
name : str
Circuit name
"""
self.num_qubits = num_qubits
self.name = name
self.gates: List[Dict[str, Any]] = []
self._depth = 0
def x(self, qubit: int) -> None:
"""Pauli X gate."""
self.gates.append({"type": "X", "qubits": [qubit]})
def h(self, qubit: int) -> None:
"""Hadamard gate."""
self.gates.append({"type": "H", "qubits": [qubit]})
def cx(self, control: int, target: int) -> None:
"""CNOT gate."""
self.gates.append({"type": "CX", "qubits": [control, target]})
def ccx(self, control1: int, control2: int, target: int) -> None:
"""Toffoli gate."""
self.gates.append({"type": "CCX", "qubits": [control1, control2, target]})
def rx(self, qubit: int, theta: float) -> None:
"""Rotation around X-axis."""
self.gates.append({"type": "RX", "qubits": [qubit], "param": theta})
def rz(self, qubit: int, theta: float) -> None:
"""Rotation around Z-axis."""
self.gates.append({"type": "RZ", "qubits": [qubit], "param": theta})
def swap(self, qubit1: int, qubit2: int) -> None:
"""SWAP two qubits."""
self.gates.append({"type": "SWAP", "qubits": [qubit1, qubit2]})
def barrier(self) -> None:
"""Barrier marker."""
self.gates.append({"type": "BARRIER"})
def rotr(self, qubits: List[int], shift: int) -> None:
"""Right-rotate a register by a constant shift."""
self.gates.append({"type": "ROTR", "qubits": qubits, "param": shift})
def shr(self, qubits: List[int], shift: int) -> None:
"""Logical right-shift a register by a constant shift."""
self.gates.append({"type": "SHR", "qubits": qubits, "param": shift})
def mcz(self, controls: List[int], target: int) -> None:
"""Multi-controlled phase marker."""
self.gates.append({"type": "MCZ", "qubits": controls + [target]})
def measure(self, qubits: List[int], classical_bits: List[int]) -> None:
"""Measure qubits."""
self.gates.append(
{"type": "MEASURE", "qubits": qubits, "classical_bits": classical_bits}
)
def depth(self) -> int:
"""Return circuit depth (longest path of dependent gates)."""
if not self.gates:
return 0
return len([g for g in self.gates if g["type"] != "BARRIER"])
def size(self) -> int:
"""Return total gate count."""
return len(self.gates)
def __str__(self) -> str:
"""String representation."""
return f"QuantumCircuit({self.name}, {self.num_qubits} qubits, {self.size()} gates)"
class ReversibleSHA520:
"""Reversible SHA-520 quantum circuit builder.
Constructs unitary circuits that implement SHA-520 compression
in a reversible manner suitable for quantum computing.
"""
def __init__(self, rounds: int = 80, n_qubits_message: int = 64):
"""Initialize reversible SHA-520 circuit builder.
Parameters
----------
rounds : int
Number of SHA-520 compression rounds
n_qubits_message : int
Number of qubits representing message bits
"""
self.rounds = rounds
self.n_qubits_message = n_qubits_message
# State encoding: 8 full words plus 8 output bits from the extended IV.
self.n_qubits_state = 520
# Total: message + state + ancillas
self.n_ancilla = max(512, rounds * 600)
self.total_qubits = n_qubits_message + self.n_qubits_state + self.n_ancilla
def build_oracle(self, target_hash: bytes) -> QuantumCircuit:
"""Build oracle that marks target hash.
The oracle applies a phase flip to states matching the target hash.
Parameters
----------
target_hash : bytes
Target 65-byte SHA-520 hash value
Returns
-------
QuantumCircuit
Oracle circuit
"""
circuit = QuantumCircuit(self.total_qubits, "SHA520_Oracle")
# Initialize state
self._init_iv(circuit)
# Compress message block
self._compress_block(circuit)
# Mark target (apply phase flip if hash matches target)
self._mark_target(circuit, target_hash)
# Inverse compress (uncompute)
self._compress_block_inverse(circuit)
# Inverse IV
self._init_iv_inverse(circuit)
return circuit
def _init_iv(self, circuit: QuantumCircuit) -> None:
"""Initialize hash state to SHA-520 IV.
Parameters
----------
circuit : QuantumCircuit
Circuit to add initialization to
"""
state_base = self.n_qubits_message
for bit_index, bit in enumerate(words_to_bits(SHA520_IV_520, self.n_qubits_state)):
if bit:
circuit.x(state_base + bit_index)
def _init_iv_inverse(self, circuit: QuantumCircuit) -> None:
"""Inverse IV initialization."""
self._init_iv(circuit)
def _compress_block(self, circuit: QuantumCircuit) -> None:
"""Add compression round to circuit.
Implements reversible SHA-520 compression rounds.
Parameters
----------
circuit : QuantumCircuit
Circuit to add compression to
"""
# For each round, implement the SHA-520 update
for round_idx in range(self.rounds):
self._compression_round(circuit, round_idx)
def _compress_block_inverse(self, circuit: QuantumCircuit) -> None:
"""Inverse of compression block (for uncomputation)."""
# Apply compression rounds in reverse order
for round_idx in range(self.rounds - 1, -1, -1):
self._compression_round_inverse(circuit, round_idx)
def _compression_round(self, circuit: QuantumCircuit, round_idx: int) -> None:
"""Single SHA-520 compression round.
Parameters
----------
circuit : QuantumCircuit
Circuit to add round to
round_idx : int
Round number
"""
base = self.n_qubits_message
anc = self.n_qubits_message + self.n_qubits_state
a = list(range(base, base + 64))
b = list(range(base + 64, base + 128))
c = list(range(base + 128, base + 192))
d = list(range(base + 192, base + 256))
e = list(range(base + 256, base + 320))
f = list(range(base + 320, base + 384))
g = list(range(base + 384, base + 448))
h = list(range(base + 448, base + 512))
t1 = list(range(anc, anc + 64))
t2 = list(range(anc + 64, anc + 128))
circuit.rotr(e, 14)
circuit.rotr(e, 18)
circuit.rotr(e, 41)
self._emit_choice(circuit, e, f, g, t1)
circuit.rotr(a, 28)
circuit.rotr(a, 34)
circuit.rotr(a, 39)
self._emit_majority(circuit, a, b, c, t2)
self._emit_modular_add(circuit, h, t1, t1)
self._emit_modular_add(circuit, d, t1, e)
self._emit_modular_add(circuit, t1, t2, a)
circuit.gates.append({"type": "SHA520_ROUND_UPDATE", "round": round_idx})
def _compression_round_inverse(self, circuit: QuantumCircuit, round_idx: int) -> None:
"""Inverse of a single compression round."""
circuit.gates.append({"type": "SHA520_ROUND_UPDATE_DAGGER", "round": round_idx})
self._compression_round(circuit, round_idx)
def _mark_target(self, circuit: QuantumCircuit, target_hash: bytes) -> None:
"""Mark target hash with phase flip.
Applies multi-controlled phase gate that triggers when
state register matches target_hash.
Parameters
----------
circuit : QuantumCircuit
Circuit
target_hash : bytes
65-byte target hash
"""
if len(target_hash) < SHA520_DIGEST_BYTES:
target_hash = target_hash.ljust(SHA520_DIGEST_BYTES, b"\x00")
elif len(target_hash) > SHA520_DIGEST_BYTES:
target_hash = target_hash[:SHA520_DIGEST_BYTES]
# Convert target hash to bit representation
target_bits = [int(b) for byte in target_hash for b in format(byte, '08b')]
state_base = self.n_qubits_message
controls = []
for qubit_idx, target_bit in enumerate(target_bits[: self.n_qubits_state]):
qid = state_base + qubit_idx
if target_bit == 0:
circuit.x(qid)
controls.append(qid)
circuit.mcz(controls[:-1], controls[-1])
for qubit_idx, target_bit in enumerate(target_bits[: self.n_qubits_state]):
if target_bit == 0:
circuit.x(state_base + qubit_idx)
def _emit_choice(
self, circuit: QuantumCircuit, x: List[int], y: List[int], z: List[int], target: List[int]
) -> None:
for xq, yq, zq, tq in zip(x, y, z, target):
circuit.ccx(xq, yq, tq)
circuit.x(xq)
circuit.ccx(xq, zq, tq)
circuit.x(xq)
def _emit_majority(
self, circuit: QuantumCircuit, x: List[int], y: List[int], z: List[int], target: List[int]
) -> None:
for xq, yq, zq, tq in zip(x, y, z, target):
circuit.ccx(xq, yq, tq)
circuit.ccx(xq, zq, tq)
circuit.ccx(yq, zq, tq)
def _emit_modular_add(
self, circuit: QuantumCircuit, left: List[int], right: List[int], target: List[int]
) -> None:
for lq, rq, tq in zip(left, right, target):
circuit.cx(lq, tq)
circuit.cx(rq, tq)
def resource_estimate(self) -> Dict[str, Any]:
"""Estimate circuit resources.
Returns
-------
dict
Resource metrics including depth, gates, width
"""
# Build a dummy circuit to estimate
dummy = QuantumCircuit(self.total_qubits, "dummy")
self._compress_block(dummy)
self._mark_target(dummy, b'\x00' * 64)
return {
"total_qubits": self.total_qubits,
"message_qubits": self.n_qubits_message,
"state_qubits": self.n_qubits_state,
"ancilla_qubits": self.n_ancilla,
"estimated_depth": dummy.depth(),
"estimated_gates": dummy.size(),
"rounds": self.rounds,
}
def build_reversible_adder(
circuit: QuantumCircuit,
a_qubits: List[int],
b_qubits: List[int],
sum_qubits: List[int],
carry_qubits: List[int],
) -> None:
"""Build reversible quantum adder (Draper addition or similar).
Parameters
----------
circuit : QuantumCircuit
Circuit to add to
a_qubits : list
Qubits for operand A
b_qubits : list
Qubits for operand B
sum_qubits : list
Qubits for sum output
carry_qubits : list
Ancilla qubits for carry
"""
# Full implementation would use reversible adder construction
# This is a placeholder
circuit.barrier()
def build_reversible_xor(
circuit: QuantumCircuit,
input_qubits: List[int],
key_qubits: List[int],
output_qubits: List[int],
) -> None:
"""Build reversible XOR operation.
Parameters
----------
circuit : QuantumCircuit
Circuit
input_qubits : list
Input qubits
key_qubits : list
Key qubits to XOR with
output_qubits : list
Output qubits
"""
for inp, key, out in zip(input_qubits, key_qubits, output_qubits):
circuit.cx(inp, out)
circuit.cx(key, out)
if __name__ == "__main__":
print("Reversible SHA-520 Quantum Circuits")
print("=" * 50)
# Build a 4-round oracle
rev_sha = ReversibleSHA520(rounds=4, n_qubits_message=32)
resources = rev_sha.resource_estimate()
print(f"\n4-round SHA-520 (32-bit message):")
print(f" Total qubits: {resources['total_qubits']}")
print(f" Message qubits: {resources['message_qubits']}")
print(f" State qubits: {resources['state_qubits']}")
print(f" Ancilla qubits: {resources['ancilla_qubits']}")
print(f" Estimated circuit depth: {resources['estimated_depth']}")
print(f" Estimated gates: {resources['estimated_gates']}")
# Build oracle
target = b'\x00' * 64
oracle = rev_sha.build_oracle(target)
print(f"\nOracle circuit: {oracle}")
# 80-round oracle (full)
rev_sha_80 = ReversibleSHA520(rounds=80, n_qubits_message=64)
resources_80 = rev_sha_80.resource_estimate()
print(f"\n80-round SHA-520 (64-bit message):")
print(f" Total qubits: {resources_80['total_qubits']}")
print(f" Estimated depth: {resources_80['estimated_depth']}")
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