"""
Shor-inspired algorithms for quantum-resistant key generation.

This module provides algorithms inspired by Shor's quantum factoring approach,
used to generate quantum-resistant keys and hashes.
"""

import numpy as np
import math
from typing import Tuple, List, Optional

def continued_fraction_expansion(x: float, limit: int = 100) -> List[int]:
    """
    Compute the continued fraction expansion of a number.
    
    Args:
        x: The number to expand
        limit: Maximum number of iterations
        
    Returns:
        List of coefficients in the continued fraction expansion
    """
    result = []
    for _ in range(limit):
        a = math.floor(x)
        result.append(a)
        frac = x - a
        if abs(frac) < 1e-10:
            break
        x = 1 / frac
    return result


def convergents(expansion: List[int]) -> List[Tuple[int, int]]:
    """
    Compute the convergents from a continued fraction expansion.
    
    Args:
        expansion: List of coefficients in continued fraction expansion
        
    Returns:
        List of convergents as (numerator, denominator) tuples
    """
    p = [1, expansion[0]]
    q = [0, 1]
    
    result = [(p[1], q[1])]
    
    for i in range(1, len(expansion)):
        p.append(expansion[i] * p[i] + p[i-1])
        q.append(expansion[i] * q[i] + q[i-1])
        result.append((p[i+1], q[i+1]))
    
    return result


def period_finding_classical(a: int, N: int, max_iterations: int = 1000) -> Optional[int]:
    """
    Classical simulation of Shor's period finding algorithm.
    
    Args:
        a: Base for modular exponentiation
        N: Modulus
        max_iterations: Maximum number of iterations
        
    Returns:
        Period r such that a^r ≡ 1 (mod N), or None if not found
    """
    # Ensure a and N are coprime
    if math.gcd(a, N) != 1:
        return None
    
    # Compute modular exponentiation sequence
    values = [1]
    for i in range(1, max_iterations):
        next_val = (values[-1] * a) % N
        if next_val == 1:
            return i
        values.append(next_val)
    
    return None


def quantum_inspired_factorization(N: int, attempts: int = 10) -> Tuple[int, int]:
    """
    Factor a number using a quantum-inspired algorithm.
    
    This is a classical simulation inspired by Shor's algorithm.
    
    Args:
        N: Number to factorize
        attempts: Number of attempts to try
        
    Returns:
        Tuple of factors (p, q) such that p*q = N
    """
    if N % 2 == 0:
        return 2, N // 2
    
    for _ in range(attempts):
        # Choose random base
        a = np.random.randint(2, N)
        
        # Ensure a and N are coprime
        g = math.gcd(a, N)
        if g > 1:
            return g, N // g
        
        # Find period
        r = period_finding_classical(a, N)
        if r is None or r % 2 != 0:
            continue
        
        # Try to find a factor
        x = pow(a, r // 2, N)
        if x == N - 1:
            continue
            
        factor = math.gcd(x + 1, N)
        if factor > 1 and factor < N:
            return factor, N // factor
    
    # Fallback to a simpler approach
    for i in range(2, int(math.sqrt(N)) + 1):
        if N % i == 0:
            return i, N // i
    
    return 1, N


def shor_inspired_key_generation(bit_length: int = 256) -> Tuple[int, int]:
    """
    Generate key material using Shor-inspired algorithms.
    
    Args:
        bit_length: Length of the key in bits
        
    Returns:
        Tuple of (p, q) which can be used for key generation
    """
    # Generate a random number of appropriate size
    # Use Python's built-in random for larger bit lengths
    if bit_length > 62:  # numpy.random.randint has limited range for int64
        import random
        N = random.randrange(2**(bit_length-1), 2**bit_length)
    else:
        N = np.random.randint(2**(bit_length-1), 2**bit_length)
    
    # Ensure N is odd
    if N % 2 == 0:
        N += 1
    
    # Find a quantum-resistant prime-like number by applying 
    # Shor-inspired perturbations to the value
    a = np.random.randint(2, min(N, 2**31-1))  # Ensure a is within numpy's range
    r = period_finding_classical(a, N, max_iterations=100) or np.random.randint(2, 100)
    
    # Apply quantum-inspired transformations
    p = (N + r) // 2
    q = (N - r) // 2
    
    # Ensure p and q are positive and their product is close to N
    p = max(1, p)
    q = max(1, q)
    
    return p, q


def shor_hash(data: bytes, digest_size: int = 32) -> bytes:
    """
    Generate a hash using Shor-inspired transformations.
    
    Args:
        data: Input data to hash
        digest_size: Size of the output hash in bytes
    
    Returns:
        Hashed output as bytes
    """
    # Convert input to numeric array
    data_array = np.frombuffer(data, dtype=np.uint8)
    
    # Initialize result array
    result = bytearray(digest_size)
    
    # Process input in chunks
    chunk_size = max(8, len(data_array) // 4)
    chunks = [data_array[i:i+chunk_size] for i in range(0, len(data_array), chunk_size)]
    
    # Initialize seed value
    seed = 0x123456789abcdef  # Initial seed value
    
    for chunk in chunks:
        # Convert chunk to a large integer
        chunk_val = int.from_bytes(chunk, byteorder='big')
        
        # Apply Shor-inspired transformation (period finding and modular arithmetic)
        a = (seed ^ chunk_val) % (2**64 - 1) + 1
        N = (seed + chunk_val) % (2**64 - 1) + 1
        
        # Find a period-like value
        r = period_finding_classical(a % N, N, max_iterations=10) or 1
        
        # Apply quantum-inspired transformation
        seed = (seed + a * r) % (2**64)
        
        # Update result using the new seed
        for i in range(min(8, digest_size)):
            idx = i % digest_size
            result[idx] ^= (seed >> (8 * (i % 8))) & 0xFF
    
    # Final diffusion pass
    for i in range(digest_size):
        idx1 = (i + 1) % digest_size
        idx2 = (i + 7) % digest_size
        result[i] = (result[i] + result[idx1] * result[idx2]) % 256
    
    return bytes(result) 