Blockchain has a profound impact on all areas of society by virtue of its immutability, decentralization and other characteristics. However, blockchain faces the problem of data privacy leakage during the application process, and the rapid development of quantum computing also brings the threat of quantum attack to blockchain. In this paper, we propose a lattice-based certificateless fully homomorphic encryption (LCFHE) algorithm based on approximate eigenvector firstly. And we use the lattice-based delegate algorithm and preimage sampling algorithm to extract part of the private key based on certificateless scheme, which is composed of the private key together with the secret value selected by the user, thus effectively avoiding the problems of certificate management and key escrow. Secondly, we propose a post-quantum blockchain transaction privacy protection scheme based on LCFHE algorithm, which uses the ciphertext calculation characteristic of homomorphic encryption to encrypt the account balance and transaction amount, effectively protecting the transaction privacy of users and having the ability to resist quantum attacks. Finally, we analyze the correctness and security of LCFHE algorithm, and the security of the algorithm reduces to the hardness of learning with errors (LWE) hypothesis.

In 2008, Nakamoto [

With the rapid development of blockchain technology, the problem of sensitive data privacy disclosure is becoming more and more prominent. First of all, in blockchain transactions, the transaction record of the whole network is open to all nodes in the blockchain, and the transaction amount of users on the blockchain ledger is stored in plaintext, which causes the problem of privacy disclosure.

There have been some researches on blockchain data privacy protection [

At present, there is no quantum algorithm for solving difficult problems on the lattice, and the lattice cipher is simple to calculate and has high security. However, lattice cryptographic algorithms are mostly designed based on the traditional PKI cryptosystem or based on the identity-based cryptosystem, and there will be problems with certificate management and key escrow. In 2003, Al-Riyami et al. [

In this paper, we propose a post-quantum blockchain privacy protection scheme based on lattice homomorphic encryption. The main contributions of this paper are as follows:

We propose a lattice-based certificateless fully homomorphic encryption (LCFHE) algorithm. The security of the algorithm is based on LWE difficult problem and can resist quantum computing attacks. In addition, the algorithm can solve the key escrow and certificate management problems effectively based on the certificateless system.

Based on the LCFHE algorithm, we propose a post-quantum blockchain transaction data protection scheme, which effectively protects the user’s transaction privacy by homomorphically encrypting the available balance and transaction amount during the transaction process.

We analyze the algorithm and prove that the algorithm satisfies the correctness and has the security of chosen-plaintext attack.

In view of security issues such as exposure of sensitive transaction data faced by blockchain, relevant researchers have done a lot of studies [

Homomorphic encryption can achieve the same decryption result of ciphertext calculation as that of plaintext calculation, which can significantly improve the security of user data privacy. In 2009, Gentry [

In order to solve the problem of exposing the privacy of transaction data, some researchers study the block chain data privacy protection scheme based on homomorphic encryption. In 2015, Cheon et al. [

In view of the problem of exposing sensitive transaction data of blockchain, this project conducts in-depth research on high-performance homomorphic encryption algorithm based on lattice cryptography, mode exchange, key exchange and other technologies on blockchain. In addition, a lattice-fully homomorphic crypto blockchain scheme that can implicitly process sensitive transaction data is constructed to realize the privacy protection of blockchain sensitive data security processing.

The SLWE problem and the DLWE problem can be mutually regulated.

A homomorphic (public key) encryption algorithm

We design a lattice-based certificateless homomorphic encryption algorithm, in which the private key consists of part of the KGC private key and the secret value randomly selected by the user. The specific steps of the algorithm are as follows:

Input the safety parameter

Execute the trapdoor generation algorithm

Select secure Hash functions

Output public parameters

KGC generates part of the private key for the user and calculates

Calculate

Output public key

Output private key

Add(

Mult(

According to the above encryption algorithm, we have

For the additive homomorphism, we have

Therefore, the additive homomorphism satisfies the correctness. In the same way, it can be proved that multiplication satisfies correctness.

Conclusion: Based on the LWE difficulty hypothesis, given the security parameters required by the above LCFHE scheme, if the LWE difficulty hypothesis is true, the LCFHE algorithm we proposed is chosen-plaintext attack security, and the proof is as follows.

Proof: Let

We build a distributed discriminator

As shown in

Schemes | Public key size | Cryptography | |
---|---|---|---|

ABB10 [ |
IBE | ||

Wang16 [ |
IBE | ||

Our scheme | CLE |

According to the lattice-based certificateless homomorphic encryption algorithm mentioned above, we design a post-quantum blockchain transaction data protection scheme. There are three roles in the scheme: key generation center, transaction node and validation node. Specific definitions are as follows:

KGC: Used to generate system public parameters, system master keys, and user private keys.

Transaction node: The node on the blockchain for transactions, which are divided into the transaction sender and transaction receiver.

Validation node: The network-wide verification node on the blockchain that is responsible for verifying the transaction information and maintaining the public ledger. We designed the public ledger to store the real balance of the network accounts as homomorphic encrypted ciphertext.

The cryptic transaction scheme design of blockchain based on LCFHE mainly includes the following three parts: hiding transaction amount, transaction verification and updating account available balance. Compared with blockchain transactions without privacy protection, the research focus and difficulty lies in how to verify the ciphertext transaction after the encrypted transaction amount and dynamically update the available balance of the encrypted account in real time. The following are designed for these three parts respectively.

In blockchain hidden transactions, the amount to be hidden mainly consists of two parts: one is the balance of each account stored in the blockchain public ledger, and the other is the transaction amount in a transaction. The available balance exists in two forms: one is ciphertext stored in the global ledger after being encrypted by the LCFHE algorithm, and the other is plaintext stored locally only for the user to see personally. And there is

In this paper, a new lattice-based certificateless homomorphic encryption LCFHE algorithm based on approximate eigenvectors is proposed, which can satisfy the correctness of addition homomorphism and multiplication homomorphism. Certificateless system uses the advantages and disadvantages of certificate-based system and identity-based system to avoid certificate management and key escrow. Among them, lattice delegation algorithm and original image sampling algorithm are used to extract part of the private key, and the secret value selected by the user is combined to form the private key, which protects the security of the user private key. In addition, the correctness and security of LCFHE algorithm are analyzed, and it is proved that the algorithm satisfies the correctness and the security of selecting plaintext attack. Based on LCFHE algorithm, this paper puts forward the quantum block chain transaction privacy protection scheme, calculated by use of homomorphic encryption cipher decryption and clear again the calculation results of the same features, the account of the available amount into the remaining amount and transaction, and the user’s real balance stored encrypted in a public books, and the remaining amount in the trading and transaction amount for homomorphic encryption, It is invisible to other nodes, which effectively protects users’ transaction privacy and can resist quantum attacks.

In the next step, we will further study the application of zero-knowledge proof and other technologies to blockchain privacy protection to further improve the security and practicability of the scheme. The content proposed in this paper can provide new ideas for post-quantum blockchain research and promote the development of post-quantum blockchain.