Randomizable ECC encryption

random_ecc.py

#!/usr/bin/env sage -python

from sage.all import *
import random

def generate_blind(n):
    r = 0
    rinv = 0
    while True:
        r = random.randint(1, n - 1)
        try:
            rinv = inverse_mod(r, n)
            break
        except:
            pass
    return r, rinv

# Curve25519 domain parameters for the group
curve = EllipticCurve(GF(2**255-19), [0,486662,0,1,0])
base = curve.gen(0)
n = base.order()
gen_random = lambda : random.randint(1, n - 1)

# Server generates a random key pair (k, kP)
k = gen_random()
pk = base * k

# Client generates random input to be encrypted (= sP)
token = base * gen_random()

# Client randomly blinds the input to be encrypted (= rsP)
r, rinv = generate_blind(n)
token = token * r

# Encrypt the token (= krsP)
sig = token * k

# Unblind the token and the encrypted value
token = token * rinv
sig = sig * rinv

# Assert that the unblinded message and ciphertext pair is valid
assert sig == (token * k)

# ... time passes

# Re-blind the token and encryption again
rp, rpinv = generate_blind(n)
tokenp = token * rp
sigp = sig * rp

# Assert that it's still a valid message, encryption tuple...
assert sigp == (tokenp * k)

# .. and that it's unique
assert token != tokenp