SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 118101(2018) https://doi.org/10.1007/s11432-017-9287-6

• AcceptedOct 27, 2017
• PublishedMay 21, 2018
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### Abstract

In this paper our objective is to explore approaches of secure group-oriented communication with designation and revocation mechanisms simultaneously. In doing so, we present a new scheme of Revocation-Based Broadcast Encryption (RBBE) which is designed on Dan Boneh et al.'s scheme with the designation mechanism proposed in 2005. Moreover, we combine two above-mentioned schemes into a new cryptosystem, called Dual-Mode Broadcast Encryption (DMBE). Based on these work, we reach the following conclusions. First of all, we use the DMBE scheme as an example to show that it is feasible to construct a broadcast encryption scheme that supports designation and revocation mechanisms simultaneously. Moreover, the cryptosystem with dual modes is more efficient than that with single mode over computational costs, and the performance is improved to at most $O(\lceil \frac{N}{2} \rceil )$, where N is the total number of users in the system. Finally, we prove completely that both the RBBE scheme and the DMBE scheme are semantically secure against chosen plaintext attack with full collusion under the decisional bilinear Diffie-Hellman exponent assumption.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61472032), NSFC-Genertec Joint Fund for Basic Research (Grant No. U1636104), and Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao (Grant No. 61628201).

### References

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•
 Computational complexity Communication/storage complexity Setup $(2n)~\cdot~E(\mathbb{G})~+1\cdot~M(\mathbb{G})$ $(2n+1)~\cdot~l_{\mathbb{G}}$(PK), $2\cdot~l_{\mathbb{Z}_p^*}+1\cdot~l_{\mathbb{G}}$(MK) KeyGen $|U|~\cdot~(3~\cdot~E(\mathbb{G})+1\cdot~M(\mathbb{G})~+1\cdot~D(\mathbb{G}))$ (for $|U|$ users) $|U|~\cdot~l_{\mathbb{G}}$ (${\rm~sk}_i$, for $|U|$ users) Encrypt $~2~\cdot~E(\mathbb{G})+1~\cdot~E(\mathbb{G}_T)+(|R|-1)\cdot~M(\mathbb{G})~+1\cdot~D(\mathbb{G})+1~\cdot~B$ $2~\cdot~l_{\mathbb{G}}$ ($C_R$) Decrypt $(|R|-1)\cdot~M(\mathbb{G})~+1\cdot~D(\mathbb{G})+2~\cdot~B+~1~\cdot~D(\mathbb{G}_T)$ $1~\cdot~l_{\mathbb{G}_T}$ (ek)

a) $E(\cdot)$, $M(\cdot)$ and $D(\cdot)$ denote the exponentiation operation, multiplication operation and division operation in cyclic group, respectively. $B$ denotes the bilinear pairing $e:~\mathbb{G}~\times~\mathbb{G}~\rightarrow~\mathbb{G}_T$. $|U|$ and $|R|$ denote the number of users in set $U$ and $R$, respectively. $l_{\mathbb{Z}_p^*}$, $l_{\mathbb{G}}$ and $l_{\mathbb{G}_T}$ denote the length of elements in $\mathbb{Z}_p^*$, $\mathbb{G}$ and $\mathbb{G}_T$, respectively.

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