A Certificateless Public Key Encryption Scheme Based On Quadratic Residues

Certificateless public key cryptography(CLPKC for short)is a new type of public key cryptography,which is developed on the foundation of identity based cryptography(ID-PKC for short).CLPKC elimilates the key escrow problem and the need for public key certificate.These two advantages are what makes it attractive to the research com-munity and industrial world form the beginning of its birth.It has been a very active research hot topic in the field of cryptology and information security.In several years,the study of CLPKC has advanced step by step,making its theories and techniques more and more enriching.there are many is implemented based on bilinear pairings In these schemes.However,in the practical application of bilinear pairings need large amount of cal-culation.The construction of certificateless encryption scheme without bilinear pairings is a promising research direction.This paper is based on the analysis of certificateless encryption scheme comparison,using the quadratic residue to construct a certificateless encryption scheme based on quadratic residue without bilinear pairings.Certificateless encryption combines the advantages of both,which eliminates the dis-advantages of both the traditional public key encryption(PKE)and identity based en-cryption(IBE)schemes.Therefore,it is quite natural to think of combining PKE and IBE to construct a certificateless encryption scheme,which is actually the idea of mul-tiple encryption.In this paper,We uses multiple encryption to construct a certificateless encryption scheme based on quadratic residues without bilinear pairs.The idea of con-struction is to ensure that the two sub-encryption schemes are IND-CPA secure,then convert them into IND-CCA2 secure encryption schemes,and then synthesize them into certificateless encryption scheme according to some conditions.The specific findings are as follows:(1)It is proved that Cocks’ identity based encryption scheme is IND-CPA secure;(2)Since the Cock’s identity based encryption scheme is a single-bit encryption scheme,the IND-CPA secure Cocks’scheme is transformed into the IND-CCA2 secure multi-bit Cocks’scheme;(3)Finally,the IND-CCA2 secure secure BG encryption scheme and the multi-bit Cocks’encryption scheme are used to synthesize an IND-CCA2 certificateless encryption scheme.