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Is there any good paper or research carried out till now that a data is encrypted by a single key or onwer(user) and their are 2 or more decryption keys. One key can decrypt the entire data. Other keys decrypt partial data or a portion of data. A person having no key cannot decrypt the data but those having keys can fully or partially decrypt data based on the keys.

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    $\begingroup$ Are you sure you actually need a special algorithm for this? You could just encrypt different parts with different keys and give persons subsets of those. $\endgroup$
    – otus
    Commented May 3, 2016 at 12:57
  • $\begingroup$ It depends what you mean by a "portion" of data. Many works have addressed issues which seem related to this question. The closest I can think of is the BCP cryptosystem. Each player can generate his own pair private/public key; the secret key of a player allows him to decrypt ciphertexts encrypted with his public key. Additionally, a master secret key can decrypt all the ciphertexts, whatever the public key used. (Other related and more powerful primitives are identity based and attribute based encryption). $\endgroup$ Commented May 3, 2016 at 15:24

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Functional encryption might fit your description; as far as I know it's still far from practical though.

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