from typing import *

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
class Ge25519:
    '''
    EC point on ED25519
    '''
    def __init__(x: Optional[Union[Ge25519, bytes]] = None):
        '''
        Constructor
        '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
class Sc25519:
    '''
    EC scalar on SC25519
    '''
    def __init__(x: Optional[Union[Sc25519, bytes, int]] = None):
        '''
        Constructor
        '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
class Hasher:
    '''
    XMR hasher
    '''
    def __init__(x: Optional[bytes] = None):
        '''
        Constructor
        '''
   def update(buffer: bytes):
        '''
        Update hasher
        '''
   def digest() -> bytes:
        '''
        Computes digest
        '''
   def copy() -> Hasher:
        '''
        Creates copy of the hasher, preserving the state
        '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def init256_modm(dst: Optional[Sc25519], val: Union[int, bytes, Sc25519]) -> Sc25519:
    '''
    Initializes Sc25519 scalar
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def check256_modm(val: Sc25519):
    '''
    Throws exception if scalar is invalid
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def iszero256_modm(val: Sc25519) -> bool:
    '''
    Returns False if the scalar is zero
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def eq256_modm(a: Sc25519, b: Sc25519) -> int:
    '''
    Compares scalars, returns 1 on the same value
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def get256_modm(a: Sc25519) -> int:
    '''
    Extracts 64bit integer from the scalar. Raises exception if scalar is bigger than 2^64
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def add256_modm(r: Optional[Sc25519], a: Sc25519, b: Sc25519) -> Sc25519:
    '''
    Scalar addition
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def sub256_modm(r: Optional[Sc25519], a: Sc25519, b: Sc25519) -> Sc25519:
    '''
    Scalar subtraction
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def mul256_modm(r: Optional[Sc25519], a: Sc25519, b: Sc25519) -> Sc25519:
    '''
    Scalar multiplication
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def mulsub256_modm(r: Optional[Sc25519], a: Sc25519, b: Sc25519, c: Sc25519) -> Sc25519:
    '''
    c - a*b
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def muladd256_modm(r: Optional[Sc25519], a: Sc25519, b: Sc25519, c: Sc25519) -> Sc25519:
    '''
    c + a*b
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def inv256_modm(r: Optional[Sc25519], a: Sc25519) -> Sc25519:
    '''
    Scalar modular inversion
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def pack256_modm(r: Optional[bytes], a: Sc25519, offset: Optional[int] = 0) -> bytes:
    '''
    Scalar compression
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def unpack256_modm(r: Optional[Sc25519], a: bytes, offset: int = 0) -> Sc25519:
    '''
    Scalar decompression
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def unpack256_modm_noreduce(r: Optional[Sc25519], a: bytes, offset: int = 0) -> Sc25519:
    '''
    Scalar decompression, raw, without modular reduction
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_set_neutral(r: Optional[Ge25519]) -> Ge25519:
    '''
    Sets neutral point
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_set_xmr_h(r: Optional[Ge25519]) -> Ge25519:
    '''
    Sets H point
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_check(r: Ge25519):
    '''
    Checks point, throws if not on curve
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_eq(a: Ge25519, b: Ge25519) -> bool:
    '''
    Compares EC points
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_add(r: Optional[Ge25519], a: Ge25519, b: Ge25519) -> Ge25519:
    '''
    Adds EC points
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_sub(r: Optional[Ge25519], a: Ge25519, b: Ge25519) -> Ge25519:
    '''
    Subtracts EC points
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_double(r: Optional[Ge25519], p: Ge25519) -> Ge25519:
    '''
    EC point doubling
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_mul8(r: Optional[Ge25519], p: Ge25519) -> Ge25519:
    '''
    EC point * 8
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_double_scalarmult_vartime(r: Optional[Ge25519], p1: Ge25519, s1: Sc25519, s2: Sc25519) -> Ge25519:
    '''
    s1 * G + s2 * p1
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_double_scalarmult_vartime2(r: Optional[Ge25519], p1: Ge25519, s1: Sc25519, p2: Ge25519, s2: Sc25519) -> Ge25519:
    '''
    s1 * p1 + s2 * p2
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_scalarmult_base(r: Optional[Ge25519], s: Union[Sc25519, int]) -> Ge25519:
    '''
    s * G
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_scalarmult(r: Optional[Ge25519], p: Ge25519, s: Union[Sc25519, int]) -> Ge25519:
    '''
    s * p
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_pack(r: bytes, p: Ge25519, offset: int = 0) -> bytes:
    '''
    Point compression
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ge25519_unpack_vartime(r: Optional[Ge25519], buff: bytes, offset: int = 0) -> Ge25519:
    '''
    Point decompression
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def base58_addr_encode_check(tag: int, buff: bytes) -> bytes:
    '''
    Monero block base 58 encoding
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def base58_addr_decode_check(buff: bytes) -> Tuple[bytes, int]:
    '''
    Monero block base 58 decoding, returning (decoded, tag) or raising on error.
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_random_scalar(r: Optional[Sc25519] = None) -> Sc25519:
    '''
    Generates a random scalar
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_fast_hash(r: Optional[bytes], buff: bytes) -> bytes:
    '''
    XMR fast hash
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_hash_to_ec(r: Optional[Ge25519], buff: bytes) -> Ge25519:
    '''
    XMR hashing to EC point
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_hash_to_scalar(r: Optional[Sc25519], buff: bytes) -> Sc25519:
    '''
    XMR hashing to EC scalar
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_derivation_to_scalar(r: Optional[Sc25519], p: Ge25519, output_index: int) -> Sc25519:
    '''
    H_s(derivation || varint(output_index))
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_generate_key_derivation(r: Optional[Ge25519], A: Ge25519, b: Sc25519) -> Ge25519:
    '''
    8*(key2*key1)
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_derive_private_key(r: Optional[Sc25519], deriv: Ge25519, idx: int, base: Sc25519) -> Sc25519:
    '''
    base + H_s(derivation || varint(output_index))
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_derive_public_key(r: Optional[Ge25519], deriv: Ge25519, idx: int, base: Ge25519) -> Ge25519:
    '''
    H_s(derivation || varint(output_index))G + base
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_add_keys2(r: Optional[Ge25519], a: Sc25519, b: Sc25519, B: Ge25519) -> Ge25519:
    '''
    aG + bB, G is basepoint
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_add_keys2_vartime(r: Optional[Ge25519], a: Sc25519, b: Sc25519, B: Ge25519) -> Ge25519:
    '''
    aG + bB, G is basepoint
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_add_keys3(r: Optional[Ge25519], a: Sc25519, A: Ge25519, b: Sc25519, B: Ge25519) -> Ge25519:
    '''
    aA + bB
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_add_keys3_vartime(r: Optional[Ge25519], a: Sc25519, A: Ge25519, b: Sc25519, B: Ge25519) -> Ge25519:
    '''
    aA + bB
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_get_subaddress_secret_key(r: Optional[Sc25519], major: int, minor: int, m: Sc25519) -> Sc25519:
    '''
    Hs(SubAddr || a || index_major || index_minor)
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def xmr_gen_c(r: Optional[Ge25519], a: Sc25519, amount: int) -> Ge25519:
    '''
    aG + amount * H
    '''

# extmod/modtrezorcrypto/modtrezorcrypto-monero.h
def ct_equals(a: bytes, b: bytes) -> bool:
    '''
    Constant time buffer comparison
    '''