Is it possible to send a single encrypted data message to multiple users so that the users receiving the message can only decrypt certain parts of the message, depending on their rights.

For example, I send a message "Hello World", User A could decrypt and receive the whole message(hello world), but user B could only decrypt a certain part and receive the message as "hello" only.

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    $\begingroup$ You could trivially do this if you just encrypt "hello world" using A's public key and "hello" using B's public key and send both ciphertexts to both A and B. However, I expect this is not what you are after. Probably you want some additional properties of the scheme. Could you maybe describe those properties? Public-key encryption has many exotic variants so probably what you are looking for exists. $\endgroup$ – Guut Boy Feb 1 '16 at 9:15
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    $\begingroup$ For example, it is not clear how "distributed decryption" factors in to your question although you used that tag. $\endgroup$ – Guut Boy Feb 1 '16 at 9:16
  • $\begingroup$ I removed the distributed decryption tag, because as described this is not the same thing at all. Feel free to edit and add back if you can describe how it relates to your question. $\endgroup$ – otus Feb 1 '16 at 19:31
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    $\begingroup$ Cross-posted from Stack Overflow: multiparty encryption and decryption $\endgroup$ – Artjom B. Feb 1 '16 at 19:34

This is - in a way - Functional Encryption.

From Wikipedia:

Functional encryption is a type of public-key encryption in which possessing a secret key allows one to learn a function of what the ciphertext is encrypting.

So, YES, it is possible.

For more information this paper might prove useful.

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    $\begingroup$ It's important to note that there currently no such construction for arbitrary $f$. Even predicate encryption works only on inner-products and doesn't come even close. $\endgroup$ – Artjom B. Feb 1 '16 at 19:25

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