import socket
import hashlib
import random

def powMod (n ,power ,mod):
    res=1
    while power>0:
        if (power&1):
            res = (res * n) % mod
        n = (n * n) % mod
        power>>=1
    return res

def gcd(a, b):
    while b:
        a, b = b, a%b
    return a

def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = egcd(b % a, a)
        return g, x - (b // a) * y, y

def modinv(a, m):
    g, x, y = egcd(a, m)
    if g != 1:
        raise Exception ('modular inverse does not exist')
    else :
        return x % m


def number2hashnum(number):
    tNumber = number
    hashObj = hashlib.sha256()
    byteNumber = bytearray()
    while tNumber > 0:
        byteNumber.append(tNumber & 0xFF)
        tNumber >>= 8
    byteNumber.reverse()
    hashObj.update(byteNumber)
    hash = hashObj.digest()
    hashArray = bytearray(hash)
    hashNumber = 0
    hashArray.reverse()
    length = len(hashArray)
    i = 0
    while i<length :
        hashNumber += hashArray[i] << (i * 8)
        i += 1
    return hashNumber

def parseMessageTo2Ints(message):
    message = message.decode()
    message = message.split(' ')
    return int(message[0]), int(message[1])

def createVote(answer):
    R = ((random.getrandbits(128)) << 20) | answer #R'
    h = number2hashnum(R)
    return R, h

def blindSignPrepare(N, h, D):
    X = random.getrandbits(512)
    while (gcd(X,N) != 1 or X < 3):
        X = random.getrandbits(512)
    h_ = (powMod(X, D, N) * h) % N
    return h_, X

def secretManupulations(S_, X, N):
    Xinv = modinv(X, N)
    return (S_ * Xinv % N)

connSock = socket.socket()
print("Введите адрес сервера:")
IP_ADDRESS = input()
connSock.connect((IP_ADDRESS,9090))
message = connSock.recv(2048)
N, D = parseMessageTo2Ints(message)

message = connSock.recv(2048)

print("Введите номер для голосования")
R, h = createVote(int(input()))
h_, X = blindSignPrepare(N,h,D)

connSock.send(str(h_).encode())
message = connSock.recv(2048)

signedHash = secretManupulations(int(message.decode()),X,N)
connSock.close()
connSock = socket.socket()
connSock.connect((IP_ADDRESS,9091))

connSock.send((str(R)+' '+str(signedHash)).encode())