Adaptively-Secure Proxy Re-Encryption with Tight Security

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(Bi-Directional) Proxy Re-Encryption ($\mathsf{PRE}$) is a public-key encryption scheme that allows a proxy, holding a re-encryption key from $i$ to $j$, to transform a ciphertext intended for $i$ into one intended for $j$. $\mathsf{PRE}$ has numerous applications, including secure data sharing and cloud computing. However, most existing $\mathsf{PRE}$ schemes experience significant security degradation when adversaries are allowed to adaptively corrupt re-encryption or secret keys. Prior to thi