Secure Protocol

Encrypt

Encrypt module provides some encryption methods for data. It contains Paillier, RSA

Paillier encryption

Paillier encryption is a kind of addition homomorphic encryption which belongs to probabilistic asymmetric algorithm.

• Generate key pairs

  To generate key pairs for Paillier, two big prime numbers are needed. The generator will randomly pick two prime numbers, $p$ and $q$, whose bit length has been set. Then, p and q will be used as private keys to generate PrivateKey object.

  Then use $n = pq$ as public key to generate PublicKey object.

• Encrypt by PublicKey

  Encryption of Paillier follows the steps below.

  1. Encode: Paillier algorithm is applicable only to integer. Thus the input number will be encoded as a integer.

  2. Encrypt: The principle of encryption can be referred to here or this paper

  3. Apply Obfuscator: Apply an obfuscator so that every encrypted number is different even if the plaintext is the same.

• Decrypt by PrivateKey

  1. Decrypt: Same principle introduction with encrypt above.

  2. Decode: decode back as what it is.

• Addition and Scalar Multiplication

  Please refer to the links above with encrypt step for details.

RSA encryption

This encryption method generates three very large positive integers $e$, $d$ and $n$. Let $e$, $n$ as the public-key and $d$ as the privacy-key. While giving data $v$, the encrypt operator will do $$enc(v) = v^e \pmod{n},$$ and the decrypt operator will do $$dec(v) = enc(v) ^ d \pmod{n}$$

Hash Factory

Hash factory provides following data encoding methods: "md5", "sha1", "sha224", "sha256", "sha384", "sha512", "sm3". This module is meant to make hashing operation with more convenient. It also supports adding salt and outputing results to base64 format.

Diffne Hellman Key Exchange

Diffie–Hellman key exchange is a method to exchange cryptographic keys over a public channel securely

Protocol

1. keygen: generate big prime number $p$ and $g$, where $g$ is a primitive root modulo $p$
2. Alice generates random number $r_1$; Bob generates random number $r_2$.
3. Alice calculates $g^{r_1}\pmod{p}$ then send to Bob; Bob calculates $g^{r_2}\pmod{p}$ then sends to Alice.
4. Alice calculates $(g^{r_2})^{r_1}\pmod{p}) = g^{r_1 r_2} \pmod{p}$; Bob calculates $(g^{r_1})^{r_2}\pmod{p} = g^{r_1 r_2} \pmod{p}$; $g^{r_1 r_2}\pmod{p}$ is the share key.

How to use

from federatedml.secureprotol.diffie_hellman import DiffieHellman
p, g = DiffieHellman.key_pair()
import random
r1 = random.randint(1, 10000000)
r2 = random.randint(1, 10000000)
key1 = DiffieHellman.decrypt(DiffieHellman.encrypt(g, r1, p), r2, p)
key2 = DiffieHellman.decrypt(DiffieHellman.encrypt(g, r2, p), r1, p)
assert key1 == key2

SecretShare MPC Protocol(SPDZ)

SPDZ(Ivan Damg˚ard, Marcel Keller) is a multiparty computation scheme based on somewhat homomorphic encryption (SHE).

How To Use

• init

  from fate_arch.session import Session
  s = Session()
  
  # on guest side
  guest_party_id = 10000
  host_party_id = 10001
  guest_proxy_ip = "192.168.0.2"  # Generally, it is your current machine IP
  federation_id = "spdz_demo"     # choose a common federation id (this should be same in both site)
  session_id = "_".join([federation_id, "guest", str(guest_party_id)])
  s.init_computing(session_id)
  s.init_federation(federation_id,
                    runtime_conf={
                        "local": {"role": "guest", "party_id": guest_party_id},
                        "role": {"guest": [guest_party_id], "host": [host_party_id]},
                    },
                    service_conf={"host": guest_proxy_ip, "port": 9370})
  s.as_global()
  partys = s.parties.all_parties
  # [Party(role=guest, party_id=10000), Party(role=host, party_id=10001)]
  
  # on host side
  guest_party_id = 10000
  host_party_id = 10001
  host_proxy_ip = "192.168.0.1"   # Generally, it is your current machine IP
  federation_id = "spdz_demo"     # choose a common federation id (this should be same in both site)
  session_id = "_".join([federation_id, "host", str(host_party_id)])
  s.init_computing(session_id)
  s.init_federation(federation_id,
                    runtime_conf={
                        "local": {"role": "host", "party_id": host_party_id},
                        "role": {"guest": [guest_party_id], "host": [host_party_id]},
                    },
                    service_conf={"host": host_proxy_ip, "port": 9370})
  s.as_global()
  partys = s.parties.all_parties
  # [Party(role=guest, party_id=10000), Party(role=host, party_id=10001)]
  

• spdz env
  tensor should be created and processed in spdz env:

  from federatedml.secureprotol.spdz import SPDZ
  with SPDZ() as spdz:
      ...
  

• create tenser
  We currently provide two implementations of fixed point tensor:

  1. one is based on numpy's array for non-distributed

     from federatedml.secureprotol.spdz.tensor.fixedpoint_numpy import FixedPointTensor
     
     # on guest side(assuming local Party is partys[0]): 
     import numpy as np
     data = np.array([[1,2,3], [4,5,6]])
     with SPDZ() as spdz:
         x = FixedPointTensor.from_source("x", data)
         y = FixedPointTensor.from_source("y", partys[1])
     
     # on host side(assuming PartyId is partys[1]):
     import numpy as np
     data = np.array([[3,2,1], [6,5,4]])
     with SPDZ() as spdz:
         y = FixedPointTensor.from_source("y", data)
         x = FixedPointTensor.from_source("x", partys[0])
     

  2. one based on a table for distributed

     from federatedml.secureprotol.spdz.tensor.fixedpoint_table import FixedPointTensor
     
     # on guest side(assuming PartyId is partys[0]): 
     data = s.computing.parallelize([np.array([1,2,3]), np.array([4,5,6])], include_key=False, partition=2)
     with SPDZ() as spdz:
         x = FixedPointTensor.from_source("x", data)
         y = FixedPointTensor.from_source("y", party[1])
     
     # on host side(assuming PartyId is partys[1]):
     data = session.parallelize([np.array([3,2,1]), np.array([6,5,4])], include_key=False, partition=2)
     with SPDZ() as spdz:
         y = FixedPointTensor.from_source("y", data)
         x = FixedPointTensor.from_source("x", party[0])
     

  When tensor is created from a provided data, data is split into n shares and every party gets a different one.

• rescontruct

  Value can be rescontructed from tensor

  x.get() # array([[1, 2, 3],[4, 5, 6]])
  y.get() # array([[3, 2, 1],[6, 5, 4]])
  

• add/minus

  You can add or subtract tensors

  z = x + y
  t = x - y
  

• dot

  You can do dot arithmetic:

  x.dot(y)
  

• einsum (numpy version only)

  When using numpy's tensor, powerful einsum arithmetic is available:

  x.einsum(y, "ij,kj->ik")  # dot
  

Oblivious Transfer

FATE implements Oblivious Transfer(OT) protocol based on work by Eduard Hauck and Julian Loss. For more information, please refer here.

Feldman Verifiable secret sharing

Feldman Verifiable secret sharing VSS is an information-theoretic secure method to share secrets between multi-parties.

Protocol

1. System parameters

   1. 1024-bits prime number $p$ and $g$ , 160-bits prime-order subgroup: $q$

   2. Set share_amount, it is the number of pieces the secret will be split into.

2. Encrypt

   1. Generate $k-1$ random numbers, which is ${a_0, a_1, a_2, ... ,a_{k-1}}$, denotes a polynomial of degree $k-1$, which is shown as $f(x)=a_0+a_1x+a_2x^2+...+a_{k-1}x^{k-1}$. where $a_0$ is the secret number, which requires a number of $k$ points to calculate.

   2. Take $k$ points on the polynomial, generate $k$ sub-keys, such as $\{\langle1, f(1)\rangle, \langle 2,f(2)\rangle,\dots, \langle k, f(k)\rangle\}$

   3. Generate commitments $c_i$ according to the $k$ coefficients, $c_i=g^{a_i}$

3. Sub-key holder performs validation: $g^y=c_0c_1c_2c_3...c_{k-1}$, verifies that the sub-key is valid.

4. Using Lagrange interpolation to recover secret.

How to use

from federatedml.secureprotol.secret_sharing.verifiable_secret_sharing.feldman_verifiable_secret_sharing import FeldmanVerifiableSecretSharing
vss = FeldmanVerifiableSecretSharing()
vss.key_pair()
vss.set_share_amount(3)
s = -5.98
sub_key, commitment = vss.encrypt(s) # generate sub-key and commitment
vss.verify(sub_key[i], commitment) # return True or False
x, y = zip(*sub_key)
secret = vss.decrypt(x,y) # assert s == secret

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最后更新: 2022-06-07