\input zb-basic
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\iteman{io-port 05965007}
\itemau{Chen, Liqun; Chen, Yu}
\itemti{The $n$-Diffie-Hellman problem and its applications.}
\itemso{Lai, Xuejia (ed.) et al., Information security. 14th international conference, ISC 2011, Xi'an, China, October 26--29, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-24860-3/pbk). Lecture Notes in Computer Science 7001, 119-134 (2011).}
\itemab
Summary: The main contributions of this paper are twofold. On the one hand, the twin Diffie-Hellman (twin DH) problem proposed by Cash, Kiltz and Shoup is extended to the $n$-Diffie-Hellman ($n$-DH) problem for an arbitrary integer $n$, and this new problem is shown to be at least as hard as the ordinary DH problem. Like the twin DH problem, the $n$-DH problem remains hard even in the presence of a decision oracle that recognizes solution to the problem. On the other hand, observe that the double-size key in the Cash et al. twin DH based encryption scheme can be replaced by two separated keys each for one entity, that results in a 2-party encryption scheme which holds the same security feature as the original scheme but removes the key redundancy. This idea is further extended to an $n$-party case, which is also known as $n$-out-of-$n$ encryption. As examples, a variant of ElGamal encryption and a variant of Boneh-Franklin IBE have been presented; both of them have proved to be CCA secure under the computational DH assumption and the computational bilinear Diffie-Hellman (BDH) assumption respectively, in the random oracle model. The two schemes are efficient, due partially to the size of their ciphertext, which is independent to the value $n$.
\itemrv{~}
\itemcc{}
\itemut{the (strong) $n$-DH assumption; the (strong) $n$-BDH assumption; multiple public key encryption; multiple identity-based encryption}
\itemli{doi:10.1007/978-3-642-24861-0\_9}
\end