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I want to convert ciphertexts of one encryption scheme to another without decrypting them under the first scheme and then encrypting with the second scheme. For example convert OPE encryption to Paillier without decryption. Does anyone have any idea?

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    $\begingroup$ Related: Proxy re-encryption $\endgroup$ – CodesInChaos Feb 10 '16 at 13:01
  • $\begingroup$ A more appropriate way is "convert ciphertext encypted under one scheme to another .." $\endgroup$ – sashank Feb 11 '16 at 3:18
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I know of a proposal from Matsuo in 2007, called "Hybrid Proxy Re-Encryption", which allowed to transform PKE ciphertexts to IBE ciphertexts. This proposal is designed for a specific PKE and IBE scheme, not for generic ones. Note also that this is not what we usually understand by the term "proxy re-encryption", which is devoted to transforming ciphertexts from one key to another.

The only way to do what you ask with arbitrary schemes (e.g., OPE to Paillier) is to use fully homomorphic encryption. See these two answers (1 & 2) that could give you a hint of how to do this with FHE.

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