from typing import List

def mask_r(r: int) -> int:
    r_bytes = r.to_bytes(16, "little")

    r_masked = bytearray(r_bytes)
    r_masked[3] &= 15;
    r_masked[7] &= 15;
    r_masked[11] &= 15;
    r_masked[15] &= 15;
    r_masked[4] &= 252;
    r_masked[8] &= 252;
    r_masked[12] &= 252;


    r_masked = int.from_bytes(r_masked, "little")

    return r_masked


def poly1305(message: bytes, r: int, s: int):
    r = mask_r(r)
    p = 2**130-5
    acc = 0

    blocks = [int.from_bytes(message[i:i+16], "little") for i in range(0, len(message), 16)]

    for block in blocks:
        byte_length = (block.bit_length() + 7) // 8
        
        block += 1 << (8*byte_length)

        acc = ((acc+block)*r) % p

    acc += s

    return acc & (2**128-1)

def parallel_poly1305(message: bytes, r: int, s: int, lanes: int):
    r = mask_r(r)
    p = 2**130-5
    
    acc = [0]*lanes

    blocks = [int.from_bytes(message[i:i+16], "little") for i in range(0, len(message), 16)]

    lane_blocks = [blocks[i:i+lanes] for i in range(0, len(blocks), lanes)]

    for i, lane_block in enumerate(lane_blocks):
        for j, lane in enumerate(lane_block):
            idx = i*lanes + j
            power = min(lanes, len(blocks) - idx)

            byte_length = (lane.bit_length() + 7) // 8
            lane += 1 << (8*byte_length)

            acc[j] = ((acc[j] + lane)*(r**power)) % p

    combined_acc = sum(acc) % p
    combined_acc += s

    return combined_acc & (2**128-1)


def test_regular():
    r = 0xa806d542fe52447f336d555778bed685
    s = 0x1bf54941aff6bf4afdb20dfb8a800301
    
    golden_result = 0xa927010caf8b2bc2c6365130c11d06a8

    msg = b"Cryptographic Forum Research Group"

    result = poly1305(msg, r, s)

    print(f"{golden_result:x}")
    print(f"{result:x}")

def test_parallel():
    r = 0xa806d542fe52447f336d555778bed685
    s = 0x1bf54941aff6bf4afdb20dfb8a800301
    
    golden_result = 0xa927010caf8b2bc2c6365130c11d06a8

    msg = b"Cryptographic Forum Research Group"

    result = parallel_poly1305(msg, r, s, 8)
    
    print(f"{golden_result:x}")
    print(f"{result:x}")


def test_on_long_string():
    r = 0xa806d542fe52447f336d555778bed685
    s = 0x1bf54941aff6bf4afdb20dfb8a800301

    msg = b"Very long message with lots of words that is very long and requires a lot of cycles to complete because of how long it is"

    regular_result = poly1305(msg, r, s)
    parallel_result = parallel_poly1305(msg, r, s, 8)

    print(f"{regular_result:x}")
    print(f"{parallel_result:x}")


def main():
    test_regular()
    test_parallel()
    test_on_long_string()

if __name__ == "__main__":
    main()