i-manager Publications

New Digital Signature Scheme Based on MDLP and Multinacci Matrices

Manju Sanghi*

Alliance University, Karnataka, India.

Periodicity:January - March'2023
DOI : https://doi.org/10.26634/jit.12.1.19775

Abstract

A new digital signature scheme based on Matrices Discrete Logarithm Problem (MDLP) and generalized Fibonacci or Multinacci matrices is proposed. The security of the scheme is based on the difficulty of solving the Discrete Logarithm Problem (DLP) in matrices. MDLP is a new one-way function based on matrices that provides the same security as the DLP. The use of matrices increases the complexity of the scheme, as it involves matrix exponentiation rather than integers. In the proposed scheme, the signer uses a Multinacci matrix F^k_nto generate the signature and an inverse Multinacci matrix F_n^-kto verify it. The computational complexity and security of the scheme are also discussed.

Keywords

Digital Signature, Fibonacci Matrices, Multinacci Matrices, DLP, MDLP.

How to Cite this Article?

Sanghi, M. (2023). New Digital Signature Scheme Based on MDLP and Multinacci Matrices. i-manager’s Journal on Information Technology, 12(1), 1-7. https://doi.org/10.26634/jit.12.1.19775

References

[1]. Bani-Ahmad, F., Shatnawi, M., Tahat, N., & Shatnawi, S. (2016). A new kind of digital signature scheme using golden matrices based on factoring problem. International Journal of Pure and Applied Mathematics, 107(1), 49-57.

[2]. Basu, M., & Das, M. (2014). Tribonacci matrices and a new coding theory. Discrete Mathematics, Algorithms and Applications, 6(1), 1450008.

[3]. Chiou, S. Y. (2016). Novel digital signature schemes based on factoring and discrete logarithms. International Journal of Security and Its Applications, 10(3), 295-310.

[4]. Diffie, W., & Hellman, M. (1976). New directions in cryptography. IEEE Transaction on Information Theory, 22(6), 644-654.

[5]. Ding, L., & Laih, C. S. (2002). Comment: Digital signature scheme based on factoring and discrete logarithms. IEEE, 49(12), 2374-2391.

[6]. ElGamal, T. (1985). A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31(4), 469-472.

[7]. He, W. H. (2001). Digital signature scheme based on factoring and discrete logarithms. Electronics Letters, 37(4), 1-2.

[8]. Ismail, E. S., Tahat, N. M. F., & Ahmad, R. R. (2008). A new digital signature scheme based on factoring and discrete logarithms. Journal of Mathematics and Statistics, 4(4), 222-225.

[9]. Koblitz, N. (1987). Elliptic curve cryptosystems. Mathematics of Computation, 48(177), 203-209.

[10]. Nayak, R., & Jayaram, P. (2011). NTRU Digital signature scheme-A matrix approach. International Journal of Advanced Research in Computer Science, 2(1), 49-52.

[11]. Rivest, R. L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120-126.

[12]. Rososhek, S. (2016). Fast and secure modular matrix based digital signature. British Journal of Mathematics & Computer Science, 13(1), 1-20.

[13]. Sagheer, A. M., Rahama, A. M. S., & Sadiq, A. T. (2012). Design of public-key cryptosystems based on matrices discrete logarithm problem. Journal of University of Babylon, 20(4), 1113-1128.

[14]. Shao, Z. (1998). Signature schemes based on factoring and discrete logarithms. IEE ProceedingsComputers and Digital Techniques, 145(1), 33-36.

[15]. Stakhov, A. P. (2006). Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory. Chaos, Solitons & Fractals, 30(1), 56-66.

[16]. Tzeng, S. F., Yang, C. Y., & Hwang, M. S. (2004). A new digital signature scheme based on factoring and discrete logarithms. International Journal of Computer Mathematics, 81(1), 9-14.

[17]. Yanlin, Q., & Xiaoping, W. (2009, August). New digital signature scheme based on both ECDLP and IFP. In 2009 2nd IEEE International Conference on Computer Science and Information Technology (pp. 348-351). IEEE.

New Digital Signature Scheme Based on MDLP and Multinacci Matrices

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