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Top1. Introduction
In this modern world, people use a wide range of applications and they rely on these applications for their data security. There are numerous encryption algorithms in the world and every algorithm serves a specific purpose. But as encryption methods evolve, the art of breaking encryption algorithms also evolved. Simple encryption methods are used till late 19th centuries. The problem with those were, they can be easily broken by a human mind without any additional resources. But after late 19th century encryption algorithms are made with super protection, so that a human could not break it without any resources. But all it took was days or weeks to break them. And then the invention of computers led to public key, private key encryption methods. An advanced hybrid scheme of public key encryption is discussed by Jung et. al., (2015) and elaborated a new method called homomorphic encryption which is explained below.
In Cryptography, encryption is a process of encoding certain sensitive information and store it in a manner that the encrypted data cannot be read without a secret key. With different security attacks being developed every day, there is a dire need for these algorithms to hold the data in an encrypted manner. Some of the common encryption algorithms known to the world are AES, DES, Blowfish, Twofish, RSA algorithms, etc. One such well used algorithm (Rajesh et. al., (2023) is Homomorphic encryption. It was proposed by Rivest, Adleman, and Dertouzos in 1978. The early stage of homomorphic encryption was really a tough process (Ryu et. al., (2023). Yang et. al., (2012) did an impressive job on finding and proving the homomorphic properties of integers, which provides a vivid view of homomorphic encryption. Almost 90 percent of banks either rent cloud storage or hire a group of technicians from an organization to help them store client’s data. They will encrypt and decrypt client’s data on sending and receiving. But while operating them they can’t do that. This particular vulnerability leads to a situation where everything that has been done before had gone wasted.
These kinds of problems can be solved using methods like Homomorphic encryption. A new fully homomorphic encryption method is discussed by Mahmood et. al., (2018). Besides that, how multiple and multistage partial homomorphic encryption is used to develop a fully homomorphic encryption method is described and these two technologies are used in cloud applications. Homomorphic encryption allows us to perform calculations on encrypted data without decrypting it in the first place, and when decrypted the output is the same as if these operations are performed on the unencrypted data. For example, there is an algorithm called Paillier, which can perform addition and multiplication on encrypted data. Other than these operations Homomorphic addition and paillier are used in many other departments. As in Li et. al., (2021) the privacy concern in IoT is a big challenge in IoT applications and services, so this problem is encountered with Homomorphic encryption. In addition to this, paillier is used in homomorphic volume rendering as discussed by Mazza et. al., (2021).
However, the classical paillier based Homomorphic encryption does provide results for few operations, the performance of paillier algorithm is not up to mark and it consumes more cycles during runtime. Paillier encryption method’s homomorphic properties are thoroughly analysed in Nassar et. al., (2015). This work theoretically stated an algorithm that can beat the traditional Paillier algorithm in addition operation. They named it Fast Additive Homomorphic Encryption, for sort FAHE. The basic idea of this paper is based on fast additive homomorphic encryption. ACD is also the same method that has been used in Eduardo et. al., (2020).