Improved RLCE public key encryption scheme based on Polar codes

Abstract

For PolarRLCE has no semantic security and be vulnerable to adaptively chosen ciphertext attacks. Based onrandom linear code encryptionscheme, the structure of the RLCE scheme and Polar code polarization propertieswere used to make the Polar code as underlying encoding scheme, and through the method of RLCEspad message padding, a kind of improved public key encryption scheme which considers semantic security and can resistant toadaptively chosen ciphertext attacks was proposed. The improved scheme transformed the public key matrix into a system matrix and reduces the storage space of the public key. Some pre-computation for private key are estimated to reduce the storage space of private key. Through analysis, this scheme does not change the structure of PolarRLCE scheme, which can resist structural attacks against hamming quasi-cyclic codes. At the 128 bit security level, compared with HermitianRLCE scheme, GRSRLCE scheme and GoppaMcEliece scheme, the public key size of this scheme decreased by 4%, 46.5% and 47.9% respectively.

Keywords

• polar code
• random linear code encryption
• message padding
• adaptively chosen ciphertext attacks
• structural attacks