Constructing digital signature scheme based on the new hard problem on the elliptic curve
191 viewsDOI:
https://doi.org/10.54939/1859-1043.j.mst.CSCE7.2023.90-97Keywords:
Digital signature; Digital signature scheme; Discrete logarithm problem; Elliptic curve discrete logarithm problem; Elliptic curve cryptography.Abstract
In this paper, the authors propose a solution to improve the security of the digital signature scheme, this solution is implemented on two levels of digital signature scheme construction. At the first level, the authors propose a new hard problem, different from the hard problems used before, and importantly, this hard problem belongs to the class of hard problems for which there is currently no solution (except by the “brute force attack” method). At the second level, the authors propose a method to construct new digital signature algorithms based on this hard problem.
References
[1]. Nguyen Kim Tuan, Nguyen Vinh Thai, Luu Hong Dung, “A new construction method of digital signature scheme based on the discrete logarithm combining find root problem on the finite field”, Journal of Military Science and Technology - ISSN 1859-1403. (2022). DOI: 10.54939/1859-1043.j.mst.FEE.2022.164-170 DOI: https://doi.org/10.54939/1859-1043.j.mst.FEE.2022.164-170
[2]. ISO/IEC 15946: Information technology – Security techniques – Cryptographic Techniques Based on Elliptic Curves, (1999).
[3]. ANSI X9.62. Public Key Cryptography for the Financial Services Industry: Elliptic Cuve Digital Signature Algorithm (ECDSA), (1999).
[4]. National Institute of Standards and Technology, NIST FIPS PUB 186-4. Digital Signature Standard, U.S. Department of Commerce, (2013).
[5]. GOST R34.10 – 2012, Russian Federation Standard Information Technology. Government Committee of the Russia for Standards, (2012) (in Russian).
[6]. Federal Information Processing Standards Publication 180-3 (FIPS PUB 180-3). Secure Hash Standard (SHS), (2008).
[7]. A. Menezes, P. van Oorschot, and S. Vanstone. “Handbook of Applied Cryptography”. CRC Press, (1996).
[8]. J. Katz, Y. Lindell. “Introduction to Modern Cryptography”. Chapman & Hall/CRC (2008). DOI: https://doi.org/10.1201/9781420010756
[9]. Jeffrey Hoffstein, Jill Pipher and Joseph H. Silverman. “An Introduction to Mathematical Cryptography”. ISBN 978-0-387-77993-5. Springer - Verlag (2008).
[10]. L. C. Washington. “Elliptic Curves. Number Theory and Cryptography”. Chapman & Hall/CRC (2008).
[11]. D. R. Stinson. “Cryptography. Theory and Practice”. Chapman & Hall/CRC (2006). DOI: https://doi.org/10.1201/9781420057133
[12]. J. Talbot and D. Welsh. “Complexity and Cryptography: An Introduction”. Cambridge University Press, (2006). DOI: https://doi.org/10.1017/CBO9780511755286
[13]. J. H. Silverman. “Elliptic curves and cryptography”. In Public-Key Cryptography, volume 62 of Proc. Sympos. Appl. Math., pages 91–112. Amer. Math. Soc., Providence, RI, (2005). DOI: https://doi.org/10.1090/psapm/062/2211873
[14]. I. Shparlinski. “Cryptographic Applications of Analytic Number Theory”. Complexity Lower Bounds and Pseurandomness. Birkhäuser (2003). DOI: https://doi.org/10.1007/978-3-0348-8037-4
[15]. I. F. Blake, G. Seroussi, and N. P. Smart. “Elliptic Curves in Cryptography”, volume 265 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, (2000).
[16]. I. Blake, G.Seroussi & N. Smart. “Elliptic Curves in Cryptography”. Cambridge University Press (2000). DOI: https://doi.org/10.1017/CBO9781107360211
