import numpy as np
import torch
from typing import List, Tuple, Optional
from dataclasses import dataclass

@dataclass
class DimensionalMarker:
    """Represents a security marker in high-dimensional space"""
    coordinates: np.ndarray
    signature: bytes
    timestamp: float
    verification_level: int

class NurvSecure:
    def __init__(self, base_dimensions: int = 3, extra_dimensions: int = 5):
        self.base_dims = base_dimensions
        self.extra_dims = extra_dimensions
        self.total_dims = base_dimensions + extra_dimensions
        
        # Initialize the dimensional transformation matrices
        self.transform_matrices = self._initialize_transforms()
        
    def _initialize_transforms(self) -> List[torch.Tensor]:
        """Initialize transformation matrices for each extra dimension"""
        transforms = []
        for i in range(self.extra_dims):
            # Create a random orthogonal matrix for dimension transformation
            random_matrix = torch.randn(self.total_dims, self.total_dims)
            q, r = torch.linalg.qr(random_matrix)
            transforms.append(q)
        return transforms
    
    def project_to_higher_dimensions(self, data: np.ndarray) -> List[torch.Tensor]:
        """Project base dimensional data into higher dimensions"""
        base_tensor = torch.tensor(data, dtype=torch.float32)
        projections = []
        
        current_projection = base_tensor
        for transform in self.transform_matrices:
            # Apply transformation to get to next dimension
            next_projection = torch.matmul(current_projection, transform)
            projections.append(next_projection)
            current_projection = next_projection
            
        return projections
    
    def create_security_marker(self, data: np.ndarray, signature: bytes) -> DimensionalMarker:
        """Create a security marker in high-dimensional space"""
        import time
        
        # Project data into higher dimensions
        projections = self.project_to_higher_dimensions(data)
        
        # Use the highest dimensional projection for the marker
        final_projection = projections[-1].detach().numpy()
        
        return DimensionalMarker(
            coordinates=final_projection,
            signature=signature,
            timestamp=time.time(),
            verification_level=self.extra_dims
        )
    
    def verify_marker(self, marker: DimensionalMarker, tolerance: float = 1e-6) -> bool:
        """Verify a security marker's authenticity"""
        # Project the marker's coordinates through our transformation
        verification_projections = self.project_to_higher_dimensions(marker.coordinates)
        
        # Check if the final projection matches within tolerance
        original_projection = torch.tensor(marker.coordinates)
        final_verification = verification_projections[-1]
        
        return torch.allclose(original_projection, final_verification, atol=tolerance)

# Example usage
if __name__ == "__main__":
    # Initialize NurvSecure with 3 base dimensions and 5 extra dimensions
    security_system = NurvSecure(base_dimensions=3, extra_dimensions=5)
    
    # Create some test data (e.g., a 3D point)
    test_data = np.array([1.0, 2.0, 3.0])
    test_signature = b"test_signature"
    
    # Create a security marker
    marker = security_system.create_security_marker(test_data, test_signature)
    print(f"Created marker in {security_system.total_dims}-dimensional space")
    
    # Verify the marker
    is_valid = security_system.verify_marker(marker)
    print(f"Marker verification: {'Success' if is_valid else 'Failed'}")