Quantum-safe identity-based broadcast encryption with provable security from multivariate cryptography,Advances in Mathematics of Communications

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Quantum-safe identity-based broadcast encryption with provable security from multivariate cryptography
Advances in Mathematics of Communications ( IF 0.9 ) Pub Date : 2022-01-01 , DOI: 10.3934/amc.2022026
Ramprasad Sarkar,Mriganka Mandal,Sourav Mukhopadhyay

Identity-Based Broadcast Encryption (<inline-formula><tex-math id="M1">\begin{document}$\textsf{IBBE}$\end{document}</tex-math></inline-formula>) is a novel concept that can efficiently and securely transmit confidential content to a group of authorized users without the traditional Public-Key Infrastructure (<inline-formula><tex-math id="M2">\begin{document}$\textsf{PKI}$\end{document}</tex-math></inline-formula>). After carefully exploring these areas, we have observed that none of the existing works have adopted the quantum-attack resistant cryptographic machinery Multivariate Public-Key Cryptography (<inline-formula><tex-math id="M3">\begin{document}$\textsf{MPKC}$\end{document}</tex-math></inline-formula>) with provable security. We are the first to design a quantum-safe <inline-formula><tex-math id="M4">\begin{document}$\textsf{IBBE}$\end{document}</tex-math></inline-formula> that solely relies on the <inline-formula><tex-math id="M5">\begin{document}$\textsf{MPKC}$\end{document}</tex-math></inline-formula> framework. Our proposed protocol has achieved <inline-formula><tex-math id="M6">\begin{document}$ \mathcal{O}(n) $\end{document}</tex-math></inline-formula>-size communication bandwidth and <inline-formula><tex-math id="M7">\begin{document}$ {n^3}\cdot\mathcal{O}\big(\max\big\{N, {\delta}^4\big\}\big) $\end{document}</tex-math></inline-formula>-size overhead storage without any security breach. Here, <inline-formula><tex-math id="M8">\begin{document}$ n $\end{document}</tex-math></inline-formula> is the number of variables for each multivariate polynomial, <inline-formula><tex-math id="M9">\begin{document}$ N $\end{document}</tex-math></inline-formula> represents the total number of system users, and <inline-formula><tex-math id="M10">\begin{document}$ \delta $\end{document}</tex-math></inline-formula> denotes a positive fixed-length. More positively, our design has achieved the adaptive INDistinguishable Chosen-Ciphertext Attack (<inline-formula><tex-math id="M11">\begin{document}$\textsf{IND-CCA}$\end{document}</tex-math></inline-formula>) security in the Random Oracle Model (<inline-formula><tex-math id="M12">\begin{document}$\textsf{ROM}$\end{document}</tex-math></inline-formula>) under the hardness of standard Multivariate Quadratic (<inline-formula><tex-math id="M13">\begin{document}$\textsf{MQ}$\end{document}</tex-math></inline-formula>) problem. We emphasize that our system can also be immune against collusion attacks where several users come together to create an illicit decryption box.

更新日期：2022-01-01

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