I have read “How does order-preserving encryption work?”. After that, I completed order-preserving encryption on integer data.

Now, I have four questions in this subject:

  1. Is it possible to apply sum operation on encrypted integer data.
  2. Is it available for string data?
  3. Can i make string operations like finding an encrypted string in a ciphertext, order encrypted strings ... ?
  4. If order-preserving encryption is not suitable for these operations, Does any algrotihm make the job ?
  • $\begingroup$ Regarding the second item: how do you want to add two strings? Concatenating them? Adding characterwise? $\endgroup$ – Hilder Vítor Lima Pereira Apr 13 '16 at 17:00

Paillier cryptosystem has the property that the product of 2 ciphertexts decrypt to the sum of the plaintexts.

Strings are integers. Only that they are usually large. So this algorithm is also available for strings.

This algorithm doesn't allow you to find encrypted string in a ciphertext.

If you want an encryption scheme in which you can do any operation with the ciphertext, see homomorphic encryption.

  • 1
    $\begingroup$ However, Paillier isn't order preserving. Actually, it's easy to see that no public key encryption system can be order preserving (if it was, then it wouldn't be secure) $\endgroup$ – poncho Apr 13 '16 at 13:51

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