from os import urandom
from hashlib import sha512

def rsa_generate_keys():
    return [
        65537,
        58967658369561163583995664151705537612631456941226585145001736155445085885436956133402962616775555500479429922140321605063456075222335023020218578571558003435174909963319619244821157746252197885628802071763470174413201522569356053296685834595362968800778468737693074613267684084217204017873750446802044584084498581219849973790017343888256411013653688556278788070745635045095995056877259642839730825907965544973672656542601570609068817838234644958846427643088478240335082249677864789882511592486797239674160452077169411971273434857626735582274817190984442183721945999865859466422472845277588368259261760233826535480137
    ], [
        32639742054323523661031580828650534544392003478949839063736255562124081596351847364013089886417596950354636310108218358259943735367279937975211699593540109138569129405212055903155962561652878992005591100527818545966603574053221236696683939389678915058929150433015761702105657992264877747720954135956649973789334911071168428227464085150820871588160770978551544646965210798269197906675922224772713666123225990305644372957419486169245295190574189157389340237417783311258488777336686103120891002317113842264416737708675921812070527474901946450952078789439410581693777829144977217172397092723130874770379072485175449578961,
        58967658369561163583995664151705537612631456941226585145001736155445085885436956133402962616775555500479429922140321605063456075222335023020218578571558003435174909963319619244821157746252197885628802071763470174413201522569356053296685834595362968800778468737693074613267684084217204017873750446802044584084498581219849973790017343888256411013653688556278788070745635045095995056877259642839730825907965544973672656542601570609068817838234644958846427643088478240335082249677864789882511592486797239674160452077169411971273434857626735582274817190984442183721945999865859466422472845277588368259261760233826535480137
    ]

def bxor(x, y): 
    return bytes(i ^ j for i, j in zip(x, y))

def rsa_encrypt(plaintext, public_key):
    # iv[64] -> h1[64] -> h2[64] -> h3[64]
    iv = urandom(64)
    h1 = sha512(iv).digest()
    h2 = sha512(h1).digest()
    h3 = sha512(h2).digest()
    
    # x[192] := pt[192] ^ (h1|h2|h3)[192]
    pt = int.to_bytes(plaintext, 192, 'big')
    x192 = bxor(pt, h1 + h2 + h3)
    
    # x[64] := iv[64] ^ x[192->64]
    h4 = sha512(x192).digest()
    x64 = bxor(iv, h4)

    # x[256] := x[192]|x[64]
    x256 = int.from_bytes(x192 + x64, 'big')

    # rsa
    return pow(x256, *public_key)

def rsa_decrypt(ciphertext, secret_key):
    # rsa
    x256 = pow(ciphertext, *secret_key)
    
    # x[192]|x[64] := x[256]
    x256 = int.to_bytes(x256, 256, 'big')
    x192, x64 = x256[:192], x256[192:]
    
    # iv[64] := x[64] ^ x[192->64]
    h4 = sha512(x192).digest()
    iv = bxor(x64, h4)

    # iv[64] -> h1[64] -> h2[64] -> h3[64]
    h1 = sha512(iv).digest()
    h2 = sha512(h1).digest()
    h3 = sha512(h2).digest()
    
    # pt[192] := x[192] ^ (h1|h2|h3)[192]
    pt = bxor(x192, h1 + h2 + h3)
    
    # plaintext
    return int.from_bytes(pt, 'big')

public_key, secret_key = rsa_generate_keys()