Efficient Lattice-Based Cryptosystems with Key Dependent Message Security

Applied Sciences

Bo Yang¹  Ruwei Huang¹  Jianan Zhao¹ 

[1] School of Computer and Electronic Information, Guangxi University, Nanning 530004, China;

关键词: key-dependent message;    RLWE problem;    invertible;    challenge functions;   

DOI  :  10.3390/app112412161

来源: DOAJ

【 摘 要 】

Key-dependent message (KDM) security is of great research significance, to better analyse and solve the potential security problems in complex application scenarios. Most of the current KDM security schemes are based on traditional hard mathematical problems, where the public key and ciphertext are not compact enough, and make the ciphertext size grow linearly with the degree of the challenge functions. To solve the above problems and the inefficient ciphertext operation, the authors propose a compact lattice-based cryptosystem with a variant of the RLWE problem, which applies an invertible technique to obtain the ${\mathrm{RLWE}}^{*}$ problem. It remains hard after the modification from the RLWE problem. Compared with the ACPS scheme, our scheme further expands the set of challenge functions based on the affine function of the secret key, and the size of public key and ciphertext is $\tilde{O}\left(n\right)$, which is independent of the challenge functions. In addition, this scheme enjoys a high level of efficiency, the cost of encryption and decryption is only $\mathrm{ploylog}\left(n\right)$ bit operations per message symbol, and we also prove that our scheme is KDM-CPA secure under the ${\mathrm{RLWE}}^{*}$ assumption.

【 授权许可】

Unknown