JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

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KEY MATRICES IN FULLY HOMOMORPHIC ENCRYPTION

Authors

  • Hakim Habri
  • Abdelhakim Chillali
  • Abdelkarim Boua

Keywords:

special matrices, encryption, decryption, public and private keys

DOI:

https://doi.org/10.17654/0972555522014

Abstract

This work investigates how to use special matrices in the encryption and decryption of messages. The key matrix is used to encrypt the messages, and its inverse is used to decrypt the encoded messages. The key matrices must be kept secret between the message senders and the intended recipients. If the key matrix or its inverse is discovered, then all intercepted messages can be easily decoded.

Received: March 2, 2022 
Revised: April 8, 2022 
Accepted: April 11, 2022

References

A. Boulbot, A. Chillali and A. Mouhib, Cryptographic protocols on the non-commutative ring R, International Journal of Mathematical and Computational Methods 2 (2017), 138-141.

M. Elhassani, A. Chillali and A. Mouhib, A heuristic method to approximate the closest vector problem, WSEAS Transactions on Mathematics 20 (2021), 745-755.

M. Elhassani, A. Boulbot, A. Chillali and A. Mouhib, Fully homomorphic encryption scheme on a non commutative ring R, International Conference on Intelligent Systems and Advanced Computing Sciences, ISACS, 2019.

C. Gentry, A fully homomorphic encryption scheme, PhD thesis, Stanford University, 2009.

P. Gille and T. Szamuely, Central simple algebras and Galois cohomology, Cambridge Studies in Mathematics 101, 2006.

R. L. Rivest, L. Adleman and M. L. Dertouzos, On data banks and privacy homomorphisms, Massachusetts Institute of Technology Cambridge, Massachusetts, 1978, pp. 160-179.

M. Zeriouh, A. Chillali and A. Boua, Cryptography based on the matrices, Bol. Soc. Parana. Mat. (3) 37(3) (2019), 75-83.

Published

2022-04-15

Issue

Section

Articles

How to Cite

KEY MATRICES IN FULLY HOMOMORPHIC ENCRYPTION. (2022). JP Journal of Algebra, Number Theory and Applications, 54, 35-50. https://doi.org/10.17654/0972555522014

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