# Public-Key Encryption Based on Matrix Diagonalization Problem

### Jiande Zheng

#### Abstract

A research on the development of a new public-key encryption scheme based on matrix diagonalization problem over a ring of algebraic integers is reported in this paper. The research is original, although it is still in its early stage. The new public key encryption algorithm has three original features that distinguish it from existing ones: (a) it works on an infinite field instead of a Galois field; (b)it recognizes the ability of adversaries to factor big integers; (c) it requires only simple (without modulus) additions and multiplications for message encryption and decryption, no high-order exponentiation is required.

#### References

- J. D. Zheng, “A new public key cryptosystem for constrained hardware”, in LNCS 2433, New York: Springer-Verlag, 2002, 334-341
- D. Cantor, and H. Zassenhaus, “A new algorithm for factoring polynomials over finite fields”, Math. Comp., 1981, 36: 587-592.
- J. D. Zheng, “An Economical public-key crypto-device for C/S and B/S applications”, Journal of Xiamen University, 2004, vol. 43(2): 141-143
- J. D. Zheng “A fast digital signature scheme based on MDP”, Journal of Computer Research and Development, 2005, 42(2) to appear
- M O Rabin, Digital signatures and public key functions as intractable as factorization. MIT Laboratory for Computer Science, Technical Report: MIT/LCS/TR-212, 1979
- http://www.utm.edu/research/primes/howmany.html
- B. Schneier, Applied Cryptography, New York: John Wiley & Sons, 1996
- T. W, Hungerford, Algebra, New York: Springer-Verlag, 1974, pp. 114-145
- Raymond G. Ayoub, On the nonsolvability of the general polynomial, American Mathematical Monthly 89(1982), 397-401

#### Paper Citation

#### in Harvard Style

Zheng J. (2005). **Public-Key Encryption Based on Matrix Diagonalization Problem** . In *Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)* ISBN 972-8865-25-2, pages 102-112. DOI: 10.5220/0002543101020112

#### in Bibtex Style

@conference{wosis05,

author={Jiande Zheng},

title={Public-Key Encryption Based on Matrix Diagonalization Problem},

booktitle={Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)},

year={2005},

pages={102-112},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002543101020112},

isbn={972-8865-25-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)

TI - Public-Key Encryption Based on Matrix Diagonalization Problem

SN - 972-8865-25-2

AU - Zheng J.

PY - 2005

SP - 102

EP - 112

DO - 10.5220/0002543101020112