Much has been written about the necessity of processing data in the encrypted form. However, no satisfactory method of processing encrypted data has been published to date. Ahitub et al.  have analyzed the possibilities of using some special algorithms to add encrypted data. Rivest et al.  have suggested the use of an algorithm based on homomorphic functions for processing encrypted data. The main limitation of this algorithm is that such functions can be broken by solving a set of linear equations, as noted by . The public-key crytosystem described in  can be used to multiply encrypted data but cannot be used to add encrypted data and is therefore not appropriate for some practical applications such as bank transactions. Abadi, Feigenbaum and Kilian  presented some general theorems concerning the problem of computing with encrypted data and formulated a framework to prove precise statements about what an encrypted instance hides and reveals; they also described encryption schemes for some well-known functions.
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