A homomorphic encryption scheme over integers based on Carmichael's theorem

The homomorphic properties of the cryptographic techniques take the attention of the scholars and makes it open research problem. The traditional encryption schemes don't support the operations to be computed on the encrypted data, which may compromise the privacy of the sensitive data. The homomorphic encryption supports the algebraic operations to be computed on the encrypted data. This property of the homomorphic encryption scheme have a wide application areas such as secure electronic voting, multiparty computation, private searching, delegation of computation and many more. In this paper we proposed a homomorphic encryption scheme based on the Carmichael's theorem over integers. The operations in the scheme are modular arithmetic. The paper also discuss the security scheme and further optimization are pointed out.