A SYMMETRIC KEY FULLY HOMOMORPHIC ENCRYPTION SCHEME USING GENERAL CHINESE REMAINDER THEOREM
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.
___
- [1] R. Rivest, L. Adleman and M. L. Dertouzos, On data banks and privacy homomorphisms
Foundations of Secure Computation, 169-170, 1978.
- [2] A. Silverberg, Fully Homomorphc Encrypton for Mathematcans sponsored by DARPA under
agreement numbers FA8750-11-1-0248 and FA8750- 13-2-0054. 2013.
- [3] S. Goldwasser and S. Micali, Probabilistic encryption and how to play mental poker keeping
secret all partial information in proceedings of the 14th ACM Symposium on Theory of
Computing, 365-377, 1982.
- [4] P. Pailler, Public-Key Cryptosystems Based on Composite degree Residuosity Classes in Advances
in Cryptology, EUROCRYPT, 223-238, 1999.
- [5] C. Gentry, A Fully Homomorphc Encrypton Scheme phd thesis, Stanford University, 2009.
- [6] V. Vaikuntanathan, Computing Blindfolded: New Developments in Fully Homomorphic En-
cryption 52nd Annual Symposium on Foundations of Computer Science,5-16, 2011.
- [7] L. Xiao, O. Bastani and I-Ling Yen, An Ecent Homomorphic Encryption Protocol for
Multi-User Systems iacr.org, 2012.
- [8] C. P. Gupta and I. Sharma, Fully Homomorphic Encryption Scheme with Symmetric Keys
Master of Technology in Department of Computer Science & Engineering, Rajasthan Technical
University, Kota, August - 2013.
- [9] C. P. Gupta and I. Sharma, A Fully Homomorphic Encryption scheme with Symmetric
Keys with Application to Private Data Processing in Clouds, Network of the Future (NOF)
Fourth International Conference on the Digital Object Identi er: 10.1109/NOF.2013.6724526,
Page(s): 1 - 4 IEEE CONFERENCE PUBLICATIONS, 2013.
- [10] H. E. Rose, A Course n Number Theory School of Mathematics , niversity of Bristol,1988.
- [11] W. J. Leveque, Topics in Number Theory Addison-Wesley Publishing Company, University
of Michigan, 35-35, 1965.
- [12] D. Vizar and S. Vaudenay, Cryptanalysis of Chosen Symmetric Homomorphic Schemes EPFL
CH-1015 Lausanne, Switzerland, 2014.