The main purpose of this paper is to introduce the LWE public key cryptosystem with its security. In the first section, we introduce the LWE public key cryptosystem by Regev with its applications and some previous res...The main purpose of this paper is to introduce the LWE public key cryptosystem with its security. In the first section, we introduce the LWE public key cryptosystem by Regev with its applications and some previous research results. Then we prove the security of LWE public key cryptosystem by Regev in detail. For not only independent identical Gaussian disturbances but also any general independent identical disturbances, we give a more accurate estimation probability of decryption error of general LWE cryptosystem. This guarantees high security and widespread applications of the LWE public key cryptosystem.展开更多
The main purpose of this paper is to give an extension on learning with errors problem (LWE) based cryptosystem about the probability of decryption error with more general disturbance. In the first section, we introdu...The main purpose of this paper is to give an extension on learning with errors problem (LWE) based cryptosystem about the probability of decryption error with more general disturbance. In the first section, we introduce the LWE cryptosystem with its application and some previous research results. Then we give a more precise estimation probability of decryption error based on independent identical Gaussian disturbances and any general independent identical disturbances. This upper bound probability could be closed to 0 if we choose applicable parameters. It means that the probability of decryption error for the cryptosystem could be sufficiently small. So we verify our core result that the LWE-based cryptosystem could have high security.展开更多
The Learning With Errors(LWE)problem is widely used in lattice-based cryptography,which is the most promising post-quantum cryptography direction.There are a variety of LWE-solving methods,which can be classified into...The Learning With Errors(LWE)problem is widely used in lattice-based cryptography,which is the most promising post-quantum cryptography direction.There are a variety of LWE-solving methods,which can be classified into four groups:lattice methods,algebraic methods,combinatorial methods,and exhaustive searching.The Blum–Kalai–Wasserman(BKW)algorithm is an important variety of combinatorial algorithms,which was first presented for solving the Learning Parity With Noise(LPN)problem and then extended to solve LWE.In this paper,we give an overview of BKW algorithms for solving LWE.We introduce the framework and key techniques of BKW algorithms and make comparisons between different BKW algorithms and also with lattice methods by estimating concrete security of specific LWE instances.We also briefly discuss the current problems and potential future directions of BKW algorithms.展开更多
文摘The main purpose of this paper is to introduce the LWE public key cryptosystem with its security. In the first section, we introduce the LWE public key cryptosystem by Regev with its applications and some previous research results. Then we prove the security of LWE public key cryptosystem by Regev in detail. For not only independent identical Gaussian disturbances but also any general independent identical disturbances, we give a more accurate estimation probability of decryption error of general LWE cryptosystem. This guarantees high security and widespread applications of the LWE public key cryptosystem.
文摘The main purpose of this paper is to give an extension on learning with errors problem (LWE) based cryptosystem about the probability of decryption error with more general disturbance. In the first section, we introduce the LWE cryptosystem with its application and some previous research results. Then we give a more precise estimation probability of decryption error based on independent identical Gaussian disturbances and any general independent identical disturbances. This upper bound probability could be closed to 0 if we choose applicable parameters. It means that the probability of decryption error for the cryptosystem could be sufficiently small. So we verify our core result that the LWE-based cryptosystem could have high security.
基金supported by National Natural Science Foundation of China(No.U1936209).
文摘The Learning With Errors(LWE)problem is widely used in lattice-based cryptography,which is the most promising post-quantum cryptography direction.There are a variety of LWE-solving methods,which can be classified into four groups:lattice methods,algebraic methods,combinatorial methods,and exhaustive searching.The Blum–Kalai–Wasserman(BKW)algorithm is an important variety of combinatorial algorithms,which was first presented for solving the Learning Parity With Noise(LPN)problem and then extended to solve LWE.In this paper,we give an overview of BKW algorithms for solving LWE.We introduce the framework and key techniques of BKW algorithms and make comparisons between different BKW algorithms and also with lattice methods by estimating concrete security of specific LWE instances.We also briefly discuss the current problems and potential future directions of BKW algorithms.
