Abstract
We present group encryption, a new cryptographic primitive which is the encryption analogue of a group signature. It possesses similar verifiability, security and privacy properties, but whereas a group signature is useful whenever we need to conceal the source (signer) within a group of legitimate users, a group encryption is useful whenever we need to conceal a recipient (decryptor) within a group of legitimate receivers.
We introduce and model the new primitive and present sufficient as well as necessary conditions for its generic implementation. We then develop an efficient novel number theoretic construction for group encryption of discrete logarithms whose complexity is independent of the group size. As part of achieving this we construct a new public-key encryption for discrete logarithms that satisfies CCA2-key-privacy and CCA2-security in the standard model (this gives the first Pailler-based system with the above two properties proven in the standard model).
Applications of group encryption include settings where a user wishes to hide her preferred trusted third party or even impose a hidden hierarchy of trusted parties while being required to assure well-formed ciphertexts, as well as oblivious storage settings where the set of retrievers need to be verifiable but the storage distribution should be oblivious to the server.
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Kiayias, A., Tsiounis, Y., Yung, M. (2007). Group Encryption. In: Kurosawa, K. (eds) Advances in Cryptology – ASIACRYPT 2007. ASIACRYPT 2007. Lecture Notes in Computer Science, vol 4833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76900-2_11
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