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Explanation of Homomorphic Encryption Research Paper

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Updated: Dec 25th, 2019


Homomorphic encryption has been created to improve services in cloud computing. The encryption will enable organizations to use cloud computing in analyzing and mining data. Public cloud providers need the intervention of homomorphic encryption to promote security on the access of information.

Researchers have suggested that this system has the ability of analyzing information without decrypting (Geiselmann & Steinwandt, 2002). It shows that homomorphic encryption develops a key that performs mathematical operations on encrypted data and enables the same results on unencrypted information (Kalai, 2003).

Therefore, the connection between functions on unencrypted data and operations to be done on encrypted information in defined as homomorphism. Studies have showed that this invention would be used to provide security on the Internet because many people access this media to seek information. The growth of technology has made people consult the Internet using cloud providers such as Google and Yahoo.


Homomorphic encryption assists companies to encrypt their database of emails and post them to the cloud. The cloud assists the company to use the stored information to confirm how its workers are collaborating. Initially, when a firm is installing the new system, it may be able to run a few basic programs. However, as it continues with the system, it can apply it to all other operations.

This indicates that after the data has been stored in the database, it can be downloaded without exposing any information (Lipmaa, 2005). The access of information on the Internet may be dangerous because other competitors may be able to access policies that the firm plans to initiate to dominate the market. Companies have classified information which should not be accessed by everyone.

Therefore, when competitors are able to get such information, they can use it against the company. The company should device a safety device which will protect data from other cloud users. Some systems break down, and, as a result, people are able to get information stored. In this case, homomorphic encryption protects such information from being reached as the system is being reset.

Firms face competition from other companies, which offer similar goods or services (Limpaa, 2005). These competitors will work to outshine other so as win customers and dominate the market. The company may use the information acquired to develop strategies so as to fulfill its interest.

The above information shows that homomorphic encryption promotes business by safeguarding the firm’s data. Homomorphic encryption enables programs to be effectively evaluated so as produce encryption on the output. The system has an enormous impact on outsourcing of private programs such as cloud computing.

During the invention period, the system was challenging because people did not believe in full homomorphic encryption. It was supporting evaluation of an unlimited number of additions but could offer functions to one multiplication. The homomorphic encryption scheme is given as c =pq + m where c symbolizes the cipher text, m the marked text message, p is the key and q the random number (Mulmuley & Sohoni, 2002).

Addition, subtraction, and multiplication described the function of homomorphic encryptions. This system is efficient in arithmetic because it involves small numbers, which could be solved in parallel. Arithmetic performance is improved with the application of Residue Number System, RNS.


Homomorphic computations are designed to function on data without exposing or accessing actual modulus so as to ensure security of data in programs. It promotes the confidentiality of data by adding confusion to the modulus.

This indicates that, in cloud computing, homomorphic encryption transforms the modulus randomly through multiplication. Gentry (2010) indicates that a fully homomorphic encryption scheme was announced in 2009. This scheme supported evaluation of low polynomials on encrypted data (Endsuleit, Geiselmann, & Steinwandt, 2002).

According to Craig, the security of this scheme overlooked two problems, which were low weight sum problems and worst case on ideal lattices. The cipher texts in Gentry’s scheme did not depend on the length of the operations that evaluated encrypted data. Instead, it relied on the number of operations the computation time performed.

Homomorphic computation promotes confidentiality by distributing the program to various clouds, and it verifies that the outcome of the cloud is exactly valid (Canetti, Krawczyk, & Nielsen, 2003).

This shows that homomorphic encryption prevents clouds from tampering with the module. It follows by developing a strategy to each cloud, which can reduce the impact of security because of collusion. This shows that researchers at every level were working on how to protect data from being accessed by unnecessary people.

Cloud computing involves a network of machines to a single program for efficient monitoring and significant service delivery. However, these machines are independent in their operation. Therefore, homomorphism promotes confidentiality of information.

It protects them from being reached by other machines on the Internet, and protects the security of data. Last but least, homomorphic encryption can make the computation on multiple systems so as to compare results. The client can use several ways to make sure that the cloud does not access the module set because it can affect the confidentiality of the program.


Canetti, R., Krawczyk, H. & Nielsen, J. B. (2003). Relaxing chosen-cipher text security. In Proc. of Crypto ’03, pages 565-582.

Endsuleit, R.W. Geiselmann, & Steinwandt, R. (2002).Attacking a polynomial-based cryptosystem: Polly Cracker. Int. Jour. Information Security, (1):143-148.

Geiselmann, W. & Steinwandt, R. (2002).Cryptanalysis of Polly Cracker. IEEE Trans. In- formation Theory, (48):2990-2991.

Gentry, C. (2010). Computing arbitrary functions of encrypted data. Commun. ACM, 53(3):97–105, 2010

Kalai. A. (2003) Generating Random Factored Numbers, Easily. J. Cryptology, vol. 16, no. 4, pages 287-289.

Lipmaa. L (2005). An Oblivious Transfer Protocol with Log-Squared Communication. Proc. of ICS ’05 pages 314-328,

Mulmuley, K. & Sohoni, M. (2002). Geometric complexity theory I: An approach to the P vs. NP and related problems. SIAM J. Comput., 31(2):496-526.

Van Dam, W., Hallgren, S. & Ip, L. (2006). Quantum algorithms for some hidden shift problems. In Proc. of SODA ’03, pages 489{498. SIAM J. Comput. 36(3): 763-778.

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