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Is there an encryption decryption scheme in which a group of people are all given different keys, and of which each key can decrypt a file. (I’m not talking about a scenario where a file is encrypted with a single symmetric key, and then the symmetric key is separately encrypted with each individuals public key.)

I’ve read articles about broadcast encryption and multi-trapdoors but I'm unsure if any of these would match the correct scheme so I’m looking for.

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  • $\begingroup$ Why does each key have to be different? What would go wrong if every user had the same key? $\endgroup$ – Squeamish Ossifrage Jul 17 '18 at 14:12
  • $\begingroup$ Pretend we had to revoke access to one user. Since we used the same key for $$n$$ users, we now have to change the keys for $$n - 1$$ users. That means each revoke operation is linear instead of constant. $\endgroup$ – SlackOverflow Jul 18 '18 at 18:36
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You don't have to use any special asymmetric construct. Just give the group keys and encrypt the file with a unique random key and than encrypt the file key many times using the keys of the permitted users.

You can give each user multiple keys some of them shared by relevant groups. To prevent encrypting a file with too many keys. These can even be done ad-hoc, assuming groups repeat themselves. you can create a group key encrypt it with the keys of the members and reuse it if you want to give that group access to another resource later.

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  • $\begingroup$ How would encrypting the file key multiple times allow any one of the generated keys to decrypt the file? $\endgroup$ – SlackOverflow Mar 18 '18 at 8:18
  • $\begingroup$ you encrypt it once with each of keys, so anyone holding any of those keys can decrypt the file key and decrypt the file. $\endgroup$ – Meir Maor Mar 18 '18 at 8:37
  • $\begingroup$ But how can I make it such that each key is different? $\endgroup$ – SlackOverflow Mar 18 '18 at 18:04
  • $\begingroup$ All keys should be chosen at random from a secure random number generator. Obviously no two keys chosen this way with sufficient length will be the same. $\endgroup$ – Meir Maor Mar 19 '18 at 5:48
  • $\begingroup$ The OP specifically rules out encrypting the key with individual keys: "I’m not talking about a scenario where a file is encrypted with a single symmetric key, and then the symmetric key is separately encrypted with each individuals public key". $\endgroup$ – zaph Oct 15 '18 at 15:32

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