JOURNAL ARTICLE

Noiseless homomorphic encryption for complex numbers and fully homomorphic encryption with modular arithmetic.

  • Published In: Journal of Algebra & Its Applications, 2026, v. 25, n. 7. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Chun, Jonghee; Han, Hee; Kang, Stefano V.; Wang, Hyo Keun 3 of 3

Abstract

In this paper, we construct a new noiseless homomorphic encryption scheme based on the hardness of AGCD problem. We give a succinct and efficient algorithm that produces necessary secret keys for homomorphic evaluation of higher degree polynomial circuits. We also show that our scheme can homomorphically evaluate all the integer polynomials, real polynomials and complex polynomials. Moreover, using Fermat's Little Theorem, we prove that the size of secret key is bounded above and hence it is a FHE in itself without having to rely on any bootstrapping procedure. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Algebra & Its Applications. 2026/06, Vol. 25, Issue 7, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2026
  • ISSN:0219-4988
  • DOI:10.1142/S021949882650060X
  • Accession Number:191103785
  • Copyright Statement:Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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