### The Beta Cryptosystem

#### Abstract

This paper, we introduce mainly the concept of beta cryptosystem, whose security is based on generalized discrete logarithm problem and integer factorization problem in the multiplicative group of finite fields. We show that the proposed public key cryptosystem based on generalized discrete logarithm problem and integer factorization problem, provides more security because of double computation comparing with the generalized discrete logarithm problem and integer factorization problem. Hence the adversary has to solve distinct discrete logarithm problems and integer factorization problem simultaneously in the multiplicative group of finite fields in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. We next show that, the newly developed scheme is efficient with respect to encryption and decryption and the validity of this algorithm is proven by applying to message that are text and returning the original message in numerical examples.

#### Keywords

#### References

. W. Diffie, M. Hellman, “New Directions in Cryptography”, IEEE Transactions On Information Theory, vol.22, no.6, pp. 644-654, 1976.

. R. L. Rivest, A. Shamir, L. Adleman., “A Method to Obtain Digital Signature and Public key Crytosystem” Commun. ACM, vol 21, pp 121-126, 1978.

. M. Rabin, “Digitalized Signatures and Public Key Functions as Intractable as Factorization”, 1st Edition, Massachusetts Institute of Technology, Laboratory for Computer Science, Ft. Belvoir Defense Technical Information Center, pp 18, 1979.

. T. ElGamal, “A public Key Cryptosystem and a Signature Scheme based on Discrete Logarithms”, IEEE Transactions On Information Theory, Vol 31, pp 469-472, 1985.

. L.Harn, “Public key cryptosystem design based on factoring and discrete logarithms”, IEE Proceeding of Computers Digital Techniques,IEEE Xplore, USA., pp: 193-195, May,1994.

. E.S. Ismail and M.S.N. Hijazi, “A New Cryptosystem Based on Factoring and Discrete Logarithm Problems” Journal of Mathematics and Statistics, vol.7 (3) , pp. 165-168, 2011.

. A. Ciss , A. Y. O. Cheikh and D. Sow “A Factoring and Discrete Logarithm based Cryptosystem” Cryptography and Security (cs.CR), arXiv:1205.1212 [cs.CR].

. A. Kiriyama, Y. Nakagawa, T. Takaoka and Z. Tu “A New Public-Key Cryptosystem and its Applications” Proceedings of the Eighth International Conference on Enterprise Information Systems: Databases and Information Systems Integration (ICEIS 2006), Paphos, Cyprus, May 23-27, 2006;

. S. M. Kalipha, J. W. A. Sada and H. A. Hussain “New public-key cryptosystem”, International Journal of Systems Science,Vol.21(1), pp. 205-215, 1990.

. N. Koblizt, A. Menezes, and S. Vanstone, “The state of elliptic curve cryptography”, Design, Codes Cryptography, vol. 19, pp. 173-193, 2000 .

. J. Gordon, Strong RSA keys, Electron. Letter, 20, No. 12 (1984),514-516.

. A.K.Lenstra and M.S. Manasse, “Factoring by electronic mail” Advances in CrvDtolorv - EUROCRYPT ’89 Chrineer Berlin, pp. 355-371, 1990.

. C. Meshram and S. Meshram “PKC Scheme Based on DDLP” International Journal of Information & Network Security (IJINS), Vol.2 (2), April 2013, pp. 154-159.

. C. Meshram and S. Meshram “A Public Key Cryptosystem based on IFP and DLP” International Journal of Advanced Research in Computer Science, vol.2 (5), 2011 pp. 616-619.

. C. Meshram, “A Cryptosystem based on Double Generalized Discrete Logarithm Problem” International Journal of Contemporary Mathematical Sciences, Vol. 6(6), 2011, pp. 285 – 297.

. C. Meshram and S. Agrawal, “Enhancing the security of A Public key cryptosystem based on DLP γ ≡ αaβb (mod p)” International Journal of Research and Reviews in Computer Science Vol.1 (4), pp.67-70, 2010.

. C. Meshram and S. Agrawal, “A New Design of Public Key Encryption Scheme Based on Double Discrete Logarithm Problem” Proceedings of International Conference on Challenges and Application of Mathematics in Science and Technology (CAMIST). January 11-13, 2010, pp. 495- 502.

. C..Meshram, “New PKC Technique based on DDLP in Metacyclic Group”- Proceedings of National Conference on Establishing Kinship between Mathematical Science and Society (NCKMS).October 30-31, 2009, pp. 141-147.

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