Security Evaluation of Pailiar Homormophic Encryption Scheme

Main Article Content

Daniel Asiedu
Abdul-Mumin Salifu


In modern days of information security, much attention is drifted towards achieving the major security triad of privacy, authentication and availability. Pailiar homormophic encryption is one of the most widely area of pubic key encryption schemes researchers are exploring to enhance information security. In this paper, we presented an overview of the Pailiar cryptosystem. We further evaluated the security vulnerabilities in the cryptosystem. This was achieved through mathematical theorems and inductions. This is to present some open issues for further research to propose and implement a more robust security system based on the Pailiar homormophic encryption scheme. 

Homormophic encryption, RSA, security, cryptography.

Article Details

How to Cite
Asiedu, D., & Salifu, A.-M. (2020). Security Evaluation of Pailiar Homormophic Encryption Scheme. Asian Journal of Research in Computer Science, 6(3), 12-17.
Short Research Article


Paillier P. Public-Key Cryptosystems based on Composite Degree Residue Classes, Advances in Cryptology - EUROCRYPT ’99, LNCS. Springer Verlag. 1999;1592:223-238.

Okamoto T, Uchiyama S. A New Public-Key Cryptosystem as Secure as Factoring, Advances in Cryptology - EUROCRYPT ’98, LNCS. Springer Verlag. 1998;1403:308-318.

Fouque P-A, Poupard G, Stern J. Sharing Decryption in the Context of Voting or Lotteries, Financial Cryptography (2000), LNCS. Springer Verla. 2001;1962:90-104.

Damgard I, Jurik M, Nielsen JB. A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting, to appear in special issue on Financial Cryptography, International Journal on Information Security (IJIS). Springer Verlag.

Mads J. Jurik. Extensions to the Paillier Cryptosystem with Applications to Cryptological Protocols. PhD thesis. 2003;xii+117.

Sakurai K, Takagi T. (2002) On the Security of a Modified Paillier Public-Key Primitive. In: Batten L, Seberry J. (eds) Information Security and Privacy. ACISP. Lecture Notes in Computer Science, Springer, Berlin, Heidelberg. 2002;2384. Available:

Catalano D, Gennaro R, Howgraw-Graham N. The bit security of Paillier’s encryption scheme and its applications. Eurocrypt 2001, LNCS 2045. 2001;229-243.

Shukla V, Chaturvedi A, Srivastava N. Nanotechnology and cryptographic protocols: Issues and possible solutions, Nanomaterials and Energy. 2019;8(1):1-6. DOI:

Acar A, Aksu H, Uluagac AS, Conti M. A survey on homomorphic encryption schemes: Theory and implementation. ACM Comput. Surv. 2018;51:1–35.

Dowlin N, Gilad-Bachrach R, Laine K, Lauter K, Naehrig M, Wernsing J. Manual for using homomorphic encryption for bioinformatics. Proc. IEEE. 2017;105:552–567.

El Makkaoui K, Ezzati A, Beni-Hssane A, et al. Fast Cloud–Paillier homomorphic schemes for protecting confidentiality of sensitive data in cloud computing. J Ambient Intell Human Comput. 2020;11: 2205–2214. Available: