def generate_keys():
"""
Supplicant Mode - Key Generation
"""
# Select an elliptic curve [it is defined in ecc.py]
ec = ecc.ECcurve()
# a = r <- {0, ..., Q − 1} [Alice calculates the private key.]
print "* Generating an a random number. (Private Key)"
a = Crypto.Util.number.getRandomRange(0, (q - 1))
# v = −a.G(modP) [Alice calculates the public key v (a point in the elliptic curve).]
# v = (-a*ec_G) % p
# atenção à coordenada y! G = (xi, xf)
print "* Generating an elliptic curve point. (Public Key)"
pbp = ecc.ECPoint(ec.xi, ec.yi)
pbp = pbp.multiplyPointByScalar(a)
pbp = pbp.simmetric()
print "--- BEGIN PRIVATE KEY ---"
print a
print "--- BEGIN PUBLIC KEY ---"
print "v(x,-) = " + str(pbp.x)
print "v(-,y) = " + str(pbp.y)
return [a, pbp.x, pbp.y]
def generate_keys():
"""
Supplicant Mode - Key Generation
"""
# Select an elliptic curve [it is defined in ecc.py]
ec = ecc.ECcurve()
# a = r <- {0, ..., Q － 1} [Alice calculates the private key.]
print("* Generating an a random number. (Private Key)")
a = Crypto.Util.number.getRandomRange(0, (q - 1))
a = 1742413906660797398263574261320583321084828220183690165741
# v = －a.G(modP) [Alice calculates the public key v (a point in the elliptic curve).]
# v = (-a*ec_G) % p
# atencao a coordenada y! G = (xi, xf)
print("* Generating an elliptic curve point. (Public Key)")
pbp = ecc.ECPoint(ec.xi, ec.yi)
pbp = pbp.multiplyPointByScalar(a)
pbp = pbp.simmetric()
print("--- BEGIN PRIVATE KEY ---")
print(a)
print("--- BEGIN PUBLIC KEY ---")
print("v(x,-) = ", pbp.x)
print("v(-,y) = ", pbp.y)
return [a, pbp.x, pbp.y]
def sign(message, private_key):
ec = ecc.ECcurve()
r = Crypto.Util.number.getRandomRange(0, (q - 1))
x = ecc.ECPoint(ec.xi, ec.yi)
x = x.multiplyPointByScalar(r)
# generates e
# e = Crypto.Util.number.getRandomRange(0, 2**80)
e = int.from_bytes(sha224(message).digest(), 'big') % dataSize
""" calculate Y """
y = _hex2int(private_key) * e + r
return _ele2hex(x) + _int2hex(y, b=34)
def verify(message, x_y, public_key):
px, py = _hex2ele(public_key)
v = ecc.ECPoint(px, py)
e = int.from_bytes(sha224(message).digest(), 'big') % dataSize
print(hex(e))
v = v.multiplyPointByScalar(e)
# calculate z
ec = ecc.ECcurve()
z = ecc.ECPoint(ec.xi, ec.yi)
z = z.multiplyPointByScalar(_hex2int(x_y[byte * 4:]))
z = z.sum(v)
# verify z e x
xx, xy = _hex2ele(x_y[:byte * 4])
if z.x == xx and z.y == xy:
return True
else:
return False
def supplicant(a):
"""
Alice / Supplicant / Client Mode
"""
#host = 'localhost'
#port = 8888
#dataSize = 1024
print "* Opening socket"
print "* - host: " + str(host)
print "* - port: " + str(port)
aChannel = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
aChannel.connect((host, port))
print "\n* Connected to Bob (Authenticator)."
#Generate a number R to use in [ x=r.G(modP) ] to calculate a point on the elliptic curve
print "* Generating a r random number."
ec = ecc.ECcurve()
r = Crypto.Util.number.getRandomRange(0, (q - 1))
print "* Number r generated."
print "\tr = " + str(r)
print "* Getting point X on the elliptic curve."
x = ecc.ECPoint(ec.xi, ec.yi)
x = x.multiplyPointByScalar(r)
# enviar V
#print "\nVx: " + hex(x.x)
#print "Vy: " + hex(x.y)
#aChannel.send(str(x.x))
#aChannel.send(str(x.y))
# send x
# print "\n<- sending X."
print "\tXx: " + hex(x.x)
print "\tXy: " + hex(x.y)
aChannel.send(str(x.x))
aChannel.send(str(x.y))
print "\n<- X sent."
# receive e
#print "\n-> Receiving e."
e = aChannel.recv(dataSize)
e = int(e)
print "\n-> e received."
print "\te: " + hex(e)
if e < 2**80:
print "* e is valid."
else:
print "* e is not valid."
return
# Alice verifies that the value [e] is in the appropriate interval
# calculate Y
#print "\n* Calculating y."
y = a * e + r
print "\n* y was calculed."
print "\ty: " + hex(y)
# send y
# print "\n<- sending y."
aChannel.send(str(y))
print "\n<- y sent."
aChannel.close()
print "* Connection closed.\n"
def authenticator(v):
"""
Bob / Authenticator / Server Mode
"""
#host = ''
#port = 8888
nClients = 5
#dataSize = 1024
s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.bind((host, port))
s.listen(nClients)
bChannel, address = s.accept()
print "* Alice is connected."
# receive v
#vx = bChannel.recv(dataSize)
#vy = bChannel.recv(dataSize)
#v = ecc.ECPoint(int(vx), int(vy))
#print "\n-> V received with the following values: "
#print "\tVx: " + hex(v.x)
#print "\tVy: " + hex(v.y)
# receives x
xx = bChannel.recv(dataSize)
xy = bChannel.recv(dataSize)
x = ecc.ECPoint(int(xx), int(xy))
print "\n-> x received with the following values: "
print "\txx: " + hex(x.x)
print "\txy: " + hex(x.y)
# generates e
e = Crypto.Util.number.getRandomRange(0, 2**80)
print "\n* e generated.\n\t e: " + hex(e)
# send e
bChannel.send(str(e))
print "\n<- e sent."
# receive y
y = bChannel.recv(dataSize)
y = int(y)
print "\n-> y received with the following value: "
print "\ty: " + hex(y)
# calculate z
ec = ecc.ECcurve()
z = ecc.ECPoint(ec.xi, ec.yi)
z = z.multiplyPointByScalar(y)
v = v.multiplyPointByScalar(e)
z = z.sum(v)
# verify z e x
print "\n\n* Final Result: \n"
if z.x == x.x and z.y == x.y:
print "\t\tSuccess!"
else:
print "\t\tFail!"
print "\n"
bChannel.close()
print "* Connection closed\n"
usage = '''
Usage: ./schnorr [OPTION]... [ARGS]...
Authenticates someone using Schnorr Protocol over Elliptic Curves
Shows this message if none of options is used.
Mandatory arguments to long options are mandatory for short options too.
-gk,\t--generate-keys\tGenerates a Key Pair.
-a,\t--authenticator\tUses a Public Key to authenticate a client.
-s,\t--supplicant\tUses the Private Key to authenticate itself to a server.\n
'''
host = 'localhost'
port = 6666
dataSize = 2048
p = ecc.ECcurve().p
q = ecc.ECcurve().q
# --generate_keys
def generate_keys():
"""
Supplicant Mode - Key Generation
"""
# Select an elliptic curve [it is defined in ecc.py]
ec = ecc.ECcurve()
# a = r <- {0, ..., Q − 1} [Alice calculates the private key.]
print "* Generating an a random number. (Private Key)"
a = Crypto.Util.number.getRandomRange(0, (q - 1))
def get_public_key(private_key):
ec = ecc.ECcurve()
pbp = ecc.ECPoint(ec.xi, ec.yi)
pbp = pbp.multiplyPointByScalar(_hex2int(private_key))
pbp = pbp.simmetric()
return _ele2hex(pbp)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import sys
import ecc
import Crypto.Util.number
from binascii import hexlify, unhexlify
from hashlib import sha224
p = ecc.ECcurve().p
q = ecc.ECcurve().q
byte = ecc.ECcurve().fieldSize // 8
dataSize = 2**80
# --INT to bytes HEX
def _int2hex(i, b=byte):
return hexlify(i.to_bytes(b, 'big')).decode('utf8')
# --bytes HEX to INT
def _hex2int(i):
return int.from_bytes(unhexlify(i.encode('utf8')), 'big')
# --2element to hex
def _ele2hex(e):
return _int2hex(e.x) + _int2hex(e.y)
# --hex to 2element
