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x25519.py
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x25519.py
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# https://asecuritysite.com/encryption/python_25519ecdh
P = 2 ** 255 - 19
A24 = 121665
def bytes_to_int(bytes):
result = 0
for b in bytes:
result = result * 256 + int(b)
return result
def int_to_bytes(value, length):
result = []
for i in range(0, length):
result.append(value >> (i * 8) & 0xff)
return result
def cswap(swap, x_2, x_3):
dummy = swap * ((x_2 - x_3) % P)
x_2 = x_2 - dummy
x_2 %= P
x_3 = x_3 + dummy
x_3 %= P
return (x_2, x_3)
# Based on https://tools.ietf.org/html/rfc7748
def X25519(k, u):
x_1 = u
x_2 = 1
z_2 = 0
x_3 = u
z_3 = 1
swap = 0
for t in reversed(range(255)):
k_t = (k >> t) & 1
swap ^= k_t
x_2, x_3 = cswap(swap, x_2, x_3)
z_2, z_3 = cswap(swap, z_2, z_3)
swap = k_t
A = x_2 + z_2
A %= P
AA = A * A
AA %= P
B = x_2 - z_2
B %= P
BB = B * B
BB %= P
E = AA - BB
E %= P
C = x_3 + z_3
C %= P
D = x_3 - z_3
D %= P
DA = D * A
DA %= P
CB = C * B
CB %= P
x_3 = ((DA + CB) % P)**2
x_3 %= P
z_3 = x_1 * (((DA - CB) % P)**2) % P
z_3 %= P
x_2 = AA * BB
x_2 %= P
z_2 = E * ((AA + (A24 * E) % P) % P)
z_2 %= P
x_2, x_3 = cswap(swap, x_2, x_3)
z_2, z_3 = cswap(swap, z_2, z_3)
return (x_2 * pow(z_2, P - 2, P)) % P
def decodeScalar25519(k):
k_list = [(b) for b in k]
k_list[0] &= 248
k_list[31] &= 127
k_list[31] |= 64
return decodeLittleEndian(k_list)
def decodeLittleEndian(b):
return sum([b[i] << 8*i for i in range( 32 )])
def unpack2(s):
if len(s) != 32:
raise ValueError('Invalid Curve25519 scalar (len=%d)' % len(s))
t = sum((ord(s[i]) if type(s[i]) == str else s[i]) << (8 * i) for i in range(31))
t += (((ord(s[31]) if type(s[31]) == str else s[31]) & 0x7f) << 248)
return t
def pack(n):
return ''.join([chr((n >> (8 * i)) & 255) for i in range(32)])
def clamp(n):
n &= ~7
n &= ~(128 << 8 * 31)
n |= 64 << 8 * 31
return n
# Return nP
def multscalar(n, p):
n = clamp(decodeScalar25519(n))
p = unpack2(p)
return pack(X25519(n, p))
# Start at x=9. Find point n times x-point
def base_point_mult(n):
n = clamp(decodeScalar25519(n))
return pack(X25519(n, 9))