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171 lines
4.8 KiB
171 lines
4.8 KiB
# By Nicko van Someren, 2021. This code is released into the public domain.
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# Small modifications for use in Reticulum, and constant time key exchange
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# added by Mark Qvist in 2022.
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# WARNING! Only the X25519PrivateKey.exchange() method attempts to hide execution time.
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# In the context of Reticulum, this is sufficient, but it may not be in other systems. If
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# this code is to be used to provide cryptographic security in an environment where the
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# start and end times of the execution can be guessed, inferred or measured then it is
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# critical that steps are taken to hide the execution time, for instance by adding a
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# delay so that encrypted packets are not sent until a fixed time after the _start_ of
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# execution.
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import os
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import time
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P = 2 ** 255 - 19
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_A = 486662
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def _point_add(point_n, point_m, point_diff):
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"""Given the projection of two points and their difference, return their sum"""
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(xn, zn) = point_n
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(xm, zm) = point_m
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(x_diff, z_diff) = point_diff
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x = (z_diff << 2) * (xm * xn - zm * zn) ** 2
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z = (x_diff << 2) * (xm * zn - zm * xn) ** 2
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return x % P, z % P
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def _point_double(point_n):
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"""Double a point provided in projective coordinates"""
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(xn, zn) = point_n
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xn2 = xn ** 2
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zn2 = zn ** 2
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x = (xn2 - zn2) ** 2
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xzn = xn * zn
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z = 4 * xzn * (xn2 + _A * xzn + zn2)
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return x % P, z % P
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def _const_time_swap(a, b, swap):
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"""Swap two values in constant time"""
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index = int(swap) * 2
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temp = (a, b, b, a)
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return temp[index:index+2]
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def _raw_curve25519(base, n):
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"""Raise the point base to the power n"""
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zero = (1, 0)
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one = (base, 1)
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mP, m1P = zero, one
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for i in reversed(range(256)):
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bit = bool(n & (1 << i))
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mP, m1P = _const_time_swap(mP, m1P, bit)
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mP, m1P = _point_double(mP), _point_add(mP, m1P, one)
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mP, m1P = _const_time_swap(mP, m1P, bit)
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x, z = mP
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inv_z = pow(z, P - 2, P)
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return (x * inv_z) % P
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def _unpack_number(s):
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"""Unpack 32 bytes to a 256 bit value"""
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if len(s) != 32:
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raise ValueError('Curve25519 values must be 32 bytes')
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return int.from_bytes(s, "little")
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def _pack_number(n):
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"""Pack a value into 32 bytes"""
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return n.to_bytes(32, "little")
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def _fix_secret(n):
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"""Mask a value to be an acceptable exponent"""
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n &= ~7
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n &= ~(128 << 8 * 31)
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n |= 64 << 8 * 31
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return n
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def curve25519(base_point_raw, secret_raw):
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"""Raise the base point to a given power"""
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base_point = _unpack_number(base_point_raw)
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secret = _fix_secret(_unpack_number(secret_raw))
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return _pack_number(_raw_curve25519(base_point, secret))
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def curve25519_base(secret_raw):
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"""Raise the generator point to a given power"""
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secret = _fix_secret(_unpack_number(secret_raw))
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return _pack_number(_raw_curve25519(9, secret))
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class X25519PublicKey:
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def __init__(self, x):
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self.x = x
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@classmethod
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def from_public_bytes(cls, data):
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return cls(_unpack_number(data))
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def public_bytes(self):
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return _pack_number(self.x)
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class X25519PrivateKey:
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MIN_EXEC_TIME = 0.002
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MAX_EXEC_TIME = 0.5
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DELAY_WINDOW = 10
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T_CLEAR = None
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T_MAX = 0
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def __init__(self, a):
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self.a = a
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@classmethod
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def generate(cls):
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return cls.from_private_bytes(os.urandom(32))
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@classmethod
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def from_private_bytes(cls, data):
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return cls(_fix_secret(_unpack_number(data)))
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def private_bytes(self):
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return _pack_number(self.a)
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def public_key(self):
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return X25519PublicKey.from_public_bytes(_pack_number(_raw_curve25519(9, self.a)))
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def exchange(self, peer_public_key):
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if isinstance(peer_public_key, bytes):
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peer_public_key = X25519PublicKey.from_public_bytes(peer_public_key)
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start = time.time()
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shared = _pack_number(_raw_curve25519(peer_public_key.x, self.a))
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end = time.time()
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duration = end-start
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if X25519PrivateKey.T_CLEAR == None:
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X25519PrivateKey.T_CLEAR = end + X25519PrivateKey.DELAY_WINDOW
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if end > X25519PrivateKey.T_CLEAR:
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X25519PrivateKey.T_CLEAR = end + X25519PrivateKey.DELAY_WINDOW
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X25519PrivateKey.T_MAX = 0
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if duration < X25519PrivateKey.T_MAX or duration < X25519PrivateKey.MIN_EXEC_TIME:
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target = start+X25519PrivateKey.T_MAX
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if target > start+X25519PrivateKey.MAX_EXEC_TIME:
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target = start+X25519PrivateKey.MAX_EXEC_TIME
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if target < start+X25519PrivateKey.MIN_EXEC_TIME:
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target = start+X25519PrivateKey.MIN_EXEC_TIME
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try:
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time.sleep(target-time.time())
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except Exception as e:
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pass
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elif duration > X25519PrivateKey.T_MAX:
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X25519PrivateKey.T_MAX = duration
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return shared |