Adaptive Security Of Broadcast Encryption

With the rapid development of broadcast technology,the concerns about the security of broadcast communication system have received much more attention and broadcast encryptions have been one of the hot topics in cryptography.It is known that the security model is an important tool of capturing the security of cryptographic schemes.Research works in the last decade show that there are three kinds of security models on broadcast encryptions,which are static security,semi-static security and adaptive security,respectively.Since the internet envi-ronments in the real world are much more complex,multi-user,multi-challenge setting needs to be taken into account when constructing secure cryptograph-ic schemes.Therefore,a natural question is how to extend traditional security model of broadcast encryption to the multi-challenge setting.In this paper,we provide two strong security notions for broadcast encryption,called adaptive security in the multi-challenge setting(MA-security)and semi-static security in the multi-challenge setting(MS-security)respectively.We study the relation between the new security models and the one in the single challenge setting.Our general result shows that the reduction of the adaptive secure broad-cast encryption will lose a factor of q in the MA setting,where q is the maximum number of encryption queries.In order to construct tighter MA-secure broad-cast encryptions,we investigate Gentry and Water's transformation and show that their transformation can preserve MA-security at the price of reduction loss on the advantage of the underlying symmetric key encryption.Furthermore,we remove the q-type assumption in Gentry and Water's semi-statically secure broadcast encryption by using Hofheinz-Koch-Striecks techniques.The resulting scheme instantiated in a composite order group is MA-secure with constant size ciphertext header.