def generate_private_key(security_level=SECURITY_LEVEL, s_size=S_SIZE, a=A, modulus=MODULUS): r = random_integer(64) target = random_integer(31) t = modular_subtraction(target, r, modulus) assert (t + r) % modulus == target s = random_integer(s_size) >> 4 r += t % s ae = t / s e = modular_subtraction(ae, a, modulus) print log(a, 2), log(s, 2), log(e, 2), log(r, 2) assert e > 0 assert ((s * (a + e)) + r) % modulus == target, (((s * (a + e)) + r) % modulus, target) #if e < 0 or modulus - (s * (a + e) return s, e, r
def generate_public_key(private_key, modulus=P): x_i, z_i, xz_i = private_key x = modular_inverse(x_i, modulus) z = modular_inverse(z_i, modulus) a = modular_subtraction(z, x, modulus) # z - x public_key = ((a * x) + (x * 2)) % modulus return public_key
def generate_public_key(private_key, modulus=P): x_i, z_i, xz_i = private_key x = modular_inverse(x_i, modulus) z = modular_inverse(z_i, modulus) a = modular_subtraction(z, x, modulus) # z - x public_key = ((a * x) + (x * 2)) % modulus return public_key
def decrypt(ciphertext, private_key, p=N, _hash=hash_function): private_key, pubk_i = private_key e = recover_key(ciphertext, private_key, p) pubk_ciphertext = modular_subtraction(ciphertext, e, p) _ciphertext = (pubk_ciphertext * pubk_i) % p key = _hash(e) return _ciphertext ^ key
def decrypt(ciphertext, private_key, p=N, _hash=hash_function): private_key, pubk_i = private_key e = recover_key(ciphertext, private_key, p) pubk_ciphertext = modular_subtraction(ciphertext, e, p) _ciphertext = (pubk_ciphertext * pubk_i) % p key = _hash(e) return _ciphertext ^ key
def generate_parameters(a_size=A_SIZE, b_size=B_SIZE, x_size=X_SIZE, p_size=P_SIZE): a = random_integer(a_size) b = random_integer(b_size) x = random_integer(x_size) p = big_prime(p_size) z = modular_inverse(modular_subtraction(1, a, p), p) return a, b, x, p, z
def generate_parameters(a_size=A_SIZE, b_size=B_SIZE, x_size=X_SIZE, p_size=P_SIZE): a = random_integer(a_size) b = random_integer(b_size) x = random_integer(x_size) p = big_prime(p_size) z = modular_inverse(modular_subtraction(1, a, p), p) return a, b, x, p, z
def generate_private_key(security_level=SECURITY_LEVEL, s_size=S_SIZE, a=A, modulus=MODULUS): r = random_integer(64) target = random_integer(31) t = modular_subtraction(target, r, modulus) assert (t + r) % modulus == target s = random_integer(s_size) >> 4 r += t % s ae = t / s e = modular_subtraction(ae, a, modulus) print log(a, 2), log(s, 2), log(e, 2), log(r, 2) assert e > 0 assert ((s * (a + e)) + r) % modulus == target, (((s * (a + e)) + r) % modulus, target) #if e < 0 or modulus - (s * (a + e) return s, e, r
def convergent_decrypt(ciphertext, key, public_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt): """ usage: convergent_decrypt(ciphertext, key, public_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt) => message or None Decrypts ciphertext using key; If the integrity is validated, then return the message; If not, then return None. """ public_key_ciphertext = modular_subtraction(ciphertext, key, n) ciphertext = (modular_inverse(public_key, n) * public_key_ciphertext) % n return _decrypt(key, ciphertext, decrypt, _hash)
def encrypt(m, public_key, security_level=SECURITY_LEVEL, _modulus=(2 ** (SECURITY_LEVEL * 8))): ciphertext = 0 value = 0 for element in public_key[:-1]: r = random_integer(security_level) ciphertext += element * r value += r final_r = modular_subtraction(m, value, _modulus) ciphertext += public_key[-1] * final_r return ciphertext
def generate_private_key(security_level=SECURITY_LEVEL, a=A, modulus=MODULUS): e = random_integer(security_level - 1) public_key = random_integer(security_level) while e < public_key: e = random_integer(security_level) public_key = random_integer(security_level) _as = modular_subtraction(public_key, e, modulus) s = _as / a e += _as % a assert ((a * s) + e) % modulus == public_key return s, e
def generate_private_key(security_level=SECURITY_LEVEL, a=A, modulus=MODULUS): e = random_integer(security_level - 1) public_key = random_integer(security_level) while e < public_key: e = random_integer(security_level) public_key = random_integer(security_level) _as = modular_subtraction(public_key, e, modulus) s = _as / a e += _as % a assert ((a * s) + e) % modulus == public_key return s, e
def encrypt(m, secret_key, security_level=SECURITY_LEVEL): modulus, encryption_key, decryption_key = secret_key ciphertext = 0 value = 0 for element in encryption_key[:-1]: r = random_integer(security_level) ciphertext += element * r value += r final_r = modular_subtraction(m, value, modulus) ciphertext += encryption_key[-1] * final_r return ciphertext % (modulus * random_integer(security_level))
def encrypt(m, public_key, security_level=SECURITY_LEVEL, _modulus=(2**(SECURITY_LEVEL * 8))): ciphertext = 0 value = 0 for element in public_key[:-1]: r = random_integer(security_level) ciphertext += element * r value += r final_r = modular_subtraction(m, value, _modulus) ciphertext += public_key[-1] * final_r return ciphertext
def convergent_decrypt(ciphertext, key, public_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt): """ usage: convergent_decrypt(ciphertext, key, public_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt) => message or None Decrypts ciphertext using key; If the integrity is validated, then return the message; If not, then return None. """ public_key_ciphertext = modular_subtraction(ciphertext, key, n) ciphertext = (modular_inverse(public_key, n) * public_key_ciphertext) % n return _decrypt(key, ciphertext, decrypt, _hash)
def backdoor_decrypt(ciphertext, private_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt): """ usage: backdoor_decrypt(ciphertext, private_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt) => message Decrypts a ciphertext using the private key; If the integrity is validated, then return the message; If not, then return None. This method can be used on any ciphertext that was created with the corresponding public key. """ p, pi, ri = private_key pikey_cr = (pi * ciphertext) % n cr = pikey_cr % pi pikey = modular_subtraction(pikey_cr, cr, n) ciphertext = (cr * ri) % n key = (pikey * p) % n return _decrypt(key, ciphertext, decrypt, _hash)
def encrypt(m, public_key, r_size=R_SIZE, q=Q, s_mask=secretkey.S_MASK + 1): ciphertext = 0 running_total = 0 for encryption_of_1 in public_key[:-1]: r = random_integer(r_size) ciphertext += encryption_of_1 * r running_total += r encryption_of_1 = public_key[-1] correction_factor = modular_subtraction(m, running_total, s_mask) # ensures r + r + r + ... == m # + 1 because it's a mask and not the modulus ciphertext += encryption_of_1 * correction_factor ciphertext += random_integer(160) ciphertext %= q #running_total += correction_factor #running_total &= s_mask #assert running_total == m, (running_total, m) return ciphertext
def backdoor_decrypt(ciphertext, private_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt): """ usage: backdoor_decrypt(ciphertext, private_key, n=N, _hash=hash_function, decrypt=symmetric_decrypt) => message Decrypts a ciphertext using the private key; If the integrity is validated, then return the message; If not, then return None. This method can be used on any ciphertext that was created with the corresponding public key. """ p, pi, ri = private_key pikey_cr = (pi * ciphertext) % n cr = pikey_cr % pi pikey = modular_subtraction(pikey_cr, cr, n) ciphertext = (cr * ri) % n key = (pikey * p) % n return _decrypt(key, ciphertext, decrypt, _hash)
def encrypt(m, public_key, r_size=R_SIZE, q=Q, s_mask=secretkey.S_MASK + 1): ciphertext = 0 running_total = 0 for encryption_of_1 in public_key[:-1]: r = random_integer(r_size) ciphertext += encryption_of_1 * r running_total += r encryption_of_1 = public_key[-1] correction_factor = modular_subtraction( m, running_total, s_mask ) # ensures r + r + r + ... == m # + 1 because it's a mask and not the modulus ciphertext += encryption_of_1 * correction_factor ciphertext += random_integer(160) ciphertext %= q #running_total += correction_factor #running_total &= s_mask #assert running_total == m, (running_total, m) return ciphertext
def _sum_geometric_series(a, p=P, z=Z): return modular_subtraction(z, z * a, p)
def invert_arithmetic_choice(d, b, c, modulus=256): return modular_subtraction(d, c, modulus) * (modular_inverse(a, modulus) * modular_subtraction(b, c, modulus)) % modulus, modulus)
def generate_key(size=SIZE, p=P): a = random_integer(size) b = random_integer(size) d = modular_inverse(modular_subtraction(b ** 2, a ** 2, p), p) return a, b, d
def invert_mix_columns(a, b, c, d, modulus=MODULUS): d ^= a b ^= c c = modular_subtraction(c, d, modulus) a = modular_subtraction(a, b, modulus) return a, b, c, d
def sign(m, x, p=P): r, priv_info = generate_keypair() e = hash(r + m) k = priv_info[0] s = modular_subtraction(k, (x[0] + e), p) return s, e
def _sum_geometric_series(a, p=P, z=Z): return modular_subtraction(z, z * a, p)
def _sum_geometric_series(point_count, a=A, p=P, z=Z): t = modular_subtraction(1, a, p) return (t * z) % p
def decrypt(c, secret_key, modulus=DEFAULT_MODULUS): k1, k2, k3 = secret_key _e = c #% k1 return (modular_subtraction(_e, k3, modulus) * modular_inverse(k2, modulus)) % modulus