bm-pre

A Proxy Re-Encryption library using Bilinear Map. It contains basic functions like encryption, decryption, re-encryption, re-decryption, sign and verify.

Usage

Setup

Set the generators of G1 and G2. It must pefrom at first.

const PRE = require('bm-pre');
PRE.init({g: "this is g", h: "that is h", returnHex: true}).then(params => {
    console.log(params)
    //...
});

Generate Random Element in Fr

PRE is supposed to encrypt symmetric key.

It's recommended to get the key from a random element in Fr and convert it to hex string instead of generating a random key and mapping it to Fr.

const plain = PRE.randomGen();

Generate Key Pairs

Generate key pairs of Delegator(A) and Delegatee(B).

const A = PRE.keyGenInG1(params, {returnHex: true});
const B = PRE.keyGenInG2(params, {returnHex: true});

You can get public key from existing secret key using getPkFromG1 and getPkFromG1.

Encryption & Decryption

A can of course encrypt and decrypt.

const encrypted = PRE.enc(plain, A.pk, params, {returnHex: true});
const decrypted = PRE.dec(encrypted, A.sk, params);
console.log(plain === decrypted)

Generate Re-Encryption Key

A can generate reKey with A's secret key and B's public key.

const reKey = PRE.rekeyGen(A.sk, B.pk, {returnHex: true});

Re-Encryption & Re-Decryption

Anyone can convert encrypted with reKeyinto ciphertext that can be decrypted by B.

const reEncypted = PRE.reEnc(encrypted, reKey, {returnHex: true});
const reDecrypted = PRE.reDec(reEncypted, B.sk);
console.log(plain === reDecrypted)

Sign and Verify

Right now only signature by delegator is implemented, delegatee can have key pair with delegator's format (in G1) as well.

//create hash for msg
const crypto = require('crypto');
const msg = "1111";
const hash = crypto.createHash('sha256');
hash.update(msg);
const msgHash = hash.digest('hex');
//sign hash and verify
const sig = PRE.sign(msgHash, A.sk);
const C = PRE.keyGenInG1(params, {returnHex: false});
console.log("A's signature", sig);
console.log("verify A's signature by A's pk:", PRE.verify(msgHash, sig, A.pk, params));
console.log("verify A's signature by C's pk:", PRE.verify(msgHash, sig, C.pk, params))

Tips

Almost every input parameters can either be hex string or Object in group. It'll automatically check the type and convert it to Object during caculation if necessary.

Algrithom

• Setup

  $g$ and $h$ are the generators of $G_1$ and $G_2$

  $Z=e(g,h)$

  $e:G_1 \times G_2 \to G_T$

• Key Generation

  $sk_A \in F_r$, $pk_A=g^{sk_A} \in G_1$

  $sk_B \in F_r$, ​$pk_B=h^{sk_B} \in G_2$

• Encryption $$ C_1=((pk_A)^k,mZ^k) $$

• Decryption

  $$ \frac{\beta}{e(\alpha,h)^{\frac{1}{sk_A}}}=\frac{me(g,h)^k}{e((pk_A)^k,h)^{\frac{1}{sk_A}}}=\frac{me(g,h)^k}{e((g^{sk_A})^k,h)^{\frac{1}{sk_A}}}=m $$

• Re-Encryption Key Generation

  $$ rk_{A \to B}=(pk_B)^{\frac{1}{sk_A}} $$

• Re-Encryption

  From $C_I=(\alpha,\beta)$

  Caculate $\alpha{'}=e(\alpha,rk_{P \to D})$

  Output $C_2=(\alpha ^{'},\beta)$

• Re-Decryption

  $$ \frac{\beta}{(\alpha^{'})^{\frac{1}{sk_B}}}=\frac{me(g,h)^k}{e(\alpha,rk_{P \to D}))^{\frac{1}{sk_B}}}=\frac{me(g,h)^k}{e((pk_A)^k,(pk_B)^{\frac{1}{sk_A}})^{\frac{1}{sk_B}}}=\frac{me(g,h)^k}{e((g^{sk_A})^k,(h^{sk_B})^{\frac{1}{sk_A}})^{\frac{1}{sk_B}}}=m $$

• Sign

  $$ S=H^{sk_A} $$

• Verify

  $$ e(g,S)=e(g,H^{sk_A})=e(g^{sk_A},H)=e(pk_A,H) $$