secp256k1

# Curve parameters
P: int  # Field modulus: 2^256 - 2^32 - 977
N: int  # Curve order: 115792089237316195423570985008687907852837564279074904382605163141518161494337
A: int  # Curve coefficient a: 0
B: int  # Curve coefficient b: 7
G: Tuple[int, int]  # Generator point coordinates

def privtopub(privkey: bytes) -> Tuple[int, int]:
    """
    Convert a private key to its corresponding public key point.
    
    Args:
        privkey (bytes): 32-byte private key
        
    Returns:
        Tuple[int, int]: Public key as (x, y) coordinates
    """

def ecdsa_raw_sign(msghash: bytes, priv: bytes) -> Tuple[int, int, int]:
    """
    Sign a message hash using ECDSA.
    
    Args:
        msghash (bytes): 32-byte hash of the message to sign
        priv (bytes): 32-byte private key
        
    Returns:
        Tuple[int, int, int]: (v, r, s) signature components where:
            - v: recovery parameter (27 or 28)
            - r: signature r component
            - s: signature s component
    """

def ecdsa_raw_recover(msghash: bytes, vrs: Tuple[int, int, int]) -> Tuple[int, int]:
    """
    Recover the public key from an ECDSA signature.
    
    Args:
        msghash (bytes): 32-byte hash of the original message
        vrs (Tuple[int, int, int]): (v, r, s) signature components
        
    Returns:
        Tuple[int, int]: Recovered public key as (x, y) coordinates
    """

def multiply(a: Tuple[int, int], n: int) -> Tuple[int, int]:
    """
    Multiply a point by a scalar (point * scalar).
    
    Args:
        a (Tuple[int, int]): Point as (x, y) coordinates
        n (int): Scalar multiplier
        
    Returns:
        Tuple[int, int]: Resulting point coordinates
    """

def add(a: Tuple[int, int], b: Tuple[int, int]) -> Tuple[int, int]:
    """
    Add two elliptic curve points.
    
    Args:
        a (Tuple[int, int]): First point as (x, y) coordinates
        b (Tuple[int, int]): Second point as (x, y) coordinates
        
    Returns:
        Tuple[int, int]: Sum of the two points
    """

def to_jacobian(p: Tuple[int, int]) -> Tuple[int, int, int]:
    """Convert point from affine to Jacobian coordinates."""

def from_jacobian(p: Tuple[int, int, int]) -> Tuple[int, int]:
    """Convert point from Jacobian to affine coordinates."""

def jacobian_double(p: Tuple[int, int, int]) -> Tuple[int, int, int]:
    """Double a point in Jacobian coordinates."""

def jacobian_add(p: Tuple[int, int, int], q: Tuple[int, int, int]) -> Tuple[int, int, int]:
    """Add two points in Jacobian coordinates."""

def jacobian_multiply(a: Tuple[int, int, int], n: int) -> Tuple[int, int, int]:
    """Multiply a point by scalar in Jacobian coordinates."""

def inv(a: int, n: int) -> int:
    """Modular inverse using extended Euclidean algorithm."""

def bytes_to_int(x: bytes) -> int:
    """Convert bytes to integer."""

def deterministic_generate_k(msghash: bytes, priv: bytes) -> int:
    """Generate deterministic k value for ECDSA signing (RFC 6979)."""

from py_ecc.secp256k1 import privtopub, ecdsa_raw_sign, ecdsa_raw_recover
import os
import hashlib

# Generate a random private key
private_key = os.urandom(32)
print(f"Private key: {private_key.hex()}")

# Derive public key
public_key = privtopub(private_key)
print(f"Public key: ({public_key[0]}, {public_key[1]})")

# Sign a message
message = b"Hello, secp256k1!"
message_hash = hashlib.sha256(message).digest()
v, r, s = ecdsa_raw_sign(message_hash, private_key)
print(f"Signature: v={v}, r={r}, s={s}")

# Recover public key from signature
recovered_pubkey = ecdsa_raw_recover(message_hash, (v, r, s))
assert recovered_pubkey == public_key
print("Signature verification successful!")

from py_ecc.secp256k1 import G, multiply, add

# Generate some points
point1 = multiply(G, 123)  # 123 * G
point2 = multiply(G, 456)  # 456 * G

# Add points
sum_point = add(point1, point2)

# This should equal (123 + 456) * G
expected = multiply(G, 123 + 456)
assert sum_point == expected
print("Point arithmetic verified!")

from py_ecc.secp256k1 import privtopub
import hashlib

def pubkey_to_address(pubkey):
    """Convert secp256k1 public key to Bitcoin address format."""
    # Compress public key
    x, y = pubkey
    if y % 2 == 0:
        compressed = b'\x02' + x.to_bytes(32, 'big')
    else:
        compressed = b'\x03' + x.to_bytes(32, 'big')
    
    # Hash with SHA256 then RIPEMD160
    sha256_hash = hashlib.sha256(compressed).digest()
    ripemd160 = hashlib.new('ripemd160', sha256_hash).digest()
    
    return ripemd160

# Example usage
private_key = b'\x01' * 32  # Don't use this in production!
public_key = privtopub(private_key)
address_hash = pubkey_to_address(public_key)
print(f"Address hash: {address_hash.hex()}")

from py_ecc.secp256k1 import ecdsa_raw_sign, ecdsa_raw_recover
import hashlib

def verify_signature(message_hash, signature, expected_pubkey):
    """Manually verify an ECDSA signature."""
    try:
        recovered_pubkey = ecdsa_raw_recover(message_hash, signature)
        return recovered_pubkey == expected_pubkey
    except:
        return False

# Example
private_key = b'\x12' * 32
public_key = privtopub(private_key)
message = b"Test message"
message_hash = hashlib.sha256(message).digest()

# Sign
signature = ecdsa_raw_sign(message_hash, private_key)

# Verify
is_valid = verify_signature(message_hash, signature, public_key)
print(f"Signature valid: {is_valid}")

from typing import Tuple

# Point representations
PlainPoint2D = Tuple[int, int]  # Affine coordinates (x, y)
PlainPoint3D = Tuple[int, int, int]  # Jacobian coordinates (x, y, z)

from py_ecc.secp256k1 import privtopub, ecdsa_raw_recover

try:
    # Validate private key range
    if not (1 <= int.from_bytes(private_key, 'big') < N):
        raise ValueError("Private key out of range")
    
    public_key = privtopub(private_key)
    recovered = ecdsa_raw_recover(message_hash, signature)
except ValueError as e:
    print(f"Invalid input: {e}")
except Exception as e:
    print(f"Cryptographic error: {e}")