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
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.
