Fully Homomorphic Encryption with Matrix based Public Key Crypto Systems

Abstract

In this work, a novel mechanism is considered for asymmetric mode of encrypting data. A generator matrix is used to generate a field with a large prime number. The generator matrix, prime number and quaternary vector are used as global variables. Those global variables are used to calculate public key and also sub keys which in turn are used in the ElGamal mode of encryption. The decryption of data is done with Private Key. The proposed algorithm supports the features like authenticity of users, security & confidentiality of data transmitted. The mechanism can well be used in homomorphic encryption where computations are carried out on cipher text and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintext. Going by the construction of the algorithm, encryption is being done on blocks of data for which it consumes less computing resources. Going by complexity of the algorithm, the key length needed is much less to provide sufficient strength against crypto analysis.

Keywords: Homomorphic Encryption, Public and Private Keys, Elgamal Mode, Crypto Analysis and Complexity

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