Strengthened Iterated Hill Cipher for encrypted processing

Majority of the homomorphic encryption schemes which are been used in many applications are asymmetric, required for the third party processing of encrypted data. Hardly few symmetric homomorphic schemes been proposed, most of them have been cracked. The Iterated Hill Cipher (IHC) is an additive symmetric homomorphic scheme. A novel generalized recurrence has been introduced for IHC in this work. The novelty of the Iterated Hill Cipher (IHC) of the present implementation lies on the fact that every time the cipher is invoked for processing of encrypted data, a random quasigroup along with a different initialization vector are generated dynamically. The existing IHC is based on an arbitrary matrix, which might cause a successful cryptanalytic attack on IHC. Almost all ciphers based on quasigroups consider a scenario where the quasigroup (which forms the part of key) to be used for encryption and decryption are pre determined. As a measure to strengthen the existing IHC the present work chooses the matrix to be a dynamically generated random latin square (no storage requirement of quasigroup), the method is illustrated to construct the latin square. The novelty of the present work lies on the fact that it elaborates the criteria of varying key parameters in a specified manner which enables the cipher to still retain its property to be used for encrypted processing as well as upgrading the cipher to a probabilistic cipher.