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Journals / Konuralp Journal of Mathematics / 2016 / Cilt: 4 - Sayı: 1

A SYMMETRIC KEY FULLY HOMOMORPHIC ENCRYPTION SCHEME USING GENERAL CHINESE REMAINDER THEOREM

Emin AYGÜN
Erkan LÜY
Pages
122–129
Publication Date
2016-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our scheme works with random numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The Fully Homomorphic Encryption (FHE) was an open problem up to 2009.
📊
Key Findings & Data:In 2009, Gentry solved the problem.
💡
Conclusion & Impact:Our scheme works with random numbers.
🔬Design:Research Article
📍Scope:2009 Verileri
⚙️Variables:Fully Homomorphic Encryption · Large Integer Factorization · General Chinese Remainder Theorem

Abstract

The Fully Homomorphic Encryption (FHE) was an open problem up to 2009. In 2009, Gentry solved the problem. After Gentry's solution, a lot of work have made on FHE. In 2012, Xiao et al suggested a new FHE scheme with symmetric keys. They proved that security of their scheme depends on large integer factorization. In their scheme, they used 2m prime numbers in keygen algorithm and they used Chinese Remainder Theorem (CRT) in encryption algorithm. In 2014, Vaudenay et al broken this scheme. In this paper we present a new FHE scheme with symmetric keys which is a little di erent from Xiao et al scheme. We extend the approach with using General Chinese Remainder Theorem (GCRT). With using GCRT, we obtained a new FHE scheme and also we achieved to avoid choosing 2m prime/mutually prime numbers. Our scheme works with random numbers.

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Cite This Article

AYGÜN, E., LÜY, E. (2016). A SYMMETRIC KEY FULLY HOMOMORPHIC ENCRYPTION SCHEME USING GENERAL CHINESE REMAINDER THEOREM. Konuralp Journal of Mathematics, Cilt: 4 - Sayı: 1, 122–129. https://ajindex.com/articles/786691

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