Take notes of studying this thesis .
Abstract
（1） Single key homomorphic encryption
Only one private key , And the ciphertexts encrypted by different public keys cannot be calculated with each other .
（2） Threshold homomorphic encryption （ Multi key encryption ）
Support multiple private keys , Ciphertexts encrypted by different public keys can be calculated with each other .
introduction
（1） big data Well developed , combination machine learning Better serve the society , But there is a problem ： The data of a single enterprise cannot support the landing of the algorithm in its own business scenario （ Your data volume is not enough , Need someone else's ）, So we need to Data interconnection , Data sharing .
（2） Privacy computing Can solve , Definition , effect , Common technologies , This paper mainly introduces Homomorphic encryption technology , And focus on the analysis Homomorphic encryption of single key and threshold homomorphic encryption technology , And the application advantages of the latter in privacy Computing .
Single key homomorphic encryption
Definition
summary ：
（1） In single key homomorphic encryption , Ciphertext that can perform homomorphic computation , Must be encrypted with the same key .
problem
here ,CA I'm sure I'll jump out and say , What do I do ！
summary ：
（1） Have to admit , Single key homomorphic encryption does have shortcomings in this aspect ！
Threshold homomorphic encryption
summary ：
（1） There are not only multiple private keys , The public key can also be multiple ！
Definition
Calculation key here \(evk\) And many ？\(k\) Private key ,\(N\) Public key and calculation key , Threshold homomorphic encryption true NB！
Current threshold homomorphic encryption scheme
Most of the current schemes are based on the improvement of single key homomorphic encryption algorithm , The encryption mode is roughly the same , That is, it supports multiple private keys , Ciphertext under different public keys （ Convert under the calculation key , key exchange ？） Can calculate each other .
threshold ：
- Different private keys , Different public keys , Different calculation keys
- When decrypting , Less need \(K\leq N\) To decrypt successfully
【12】：Efficient RSA key generation and threshold paillier in the two-party setting-2019
【4】：Multiparty homomorphic encryption: from theory to practice-2020
【2】：Efficient multi-key homomorphic encryption with packed ciphertexts with application to oblivious neural network inference-2019
【11】：Multi-key homomorphic encryption from TFHE-2019
application
Secure multi-party horizontal Federation modeling
The paper ：POSEIDON: privacy-preserving federated neural network learning-2020
Specific process ：
summary ：
（1） Parameter encryption
（2） The inquired data is encrypted with their own public key , To decrypt , All participants are required （ Inquirer + node ） The private key .
Security model reasoning
The paper ：Efficient multi-key homomorphic encryption with packed ciphertexts with application to oblivious neural network inference-2019
Specific process ：
summary ：
（1） Server as “ The mediation ” Deal with tenants and landlords , Data is always secret , And the private key is not exposed .
（2） Here are two copies of the public key , Two copies of private key , And you can decrypt with your own private key , But it needs to be aggregated to recover plaintext , This is different from the joint decryption of multiple private keys ！
Secure multi-party Cloud Computing
Multi-key privacypreserving deep learning in cloud computing-2017
Specific process ：
summary ：
（1） Different public keys , Different private keys
other
（1） With the help of threshold homomorphic encryption technology MPC frame , And with the existing MPC Scheme comparison
- Multiparty homomorphic encryption: from theory to practice-2020
- On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption-2012
- Multiparty computation with low communication, computation and interaction via threshold FHE-2012
- Multiparty computation from threshold homomorphic encryption-2001
（2） With the help of threshold homomorphic encryption, a federated integration tree model is proposed
Privacy preserving vertical federated learning for tree-based models-2020
（3） A federated learning scheme based on threshold homomorphic encryption is proposed
Privacy-preserving federated learning based on multi-key homomorphic encryption-2021
（4） With the help of threshold homomorphic encryption, a secure biometric authentication scheme is implemented
THＲIVE: threshold homomorphic encryption based secure and privacy preserving bIometric VErification system-2014
summary
summary ：
（1） Privacy data protection is currently highly valued .
（2） How to calculate in privacy , Data flow , share , Giving full play to the maximum value is very popular at present , Worthy of research input .
（3） Article content ： It introduces 、 Pointed out 、 Also on .. Analyzed and studied .
（4） Officially connected “Lifted ElGamal Threshold encryption algorithm ”
