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Novel Digital Signature Scheme with Multiple Private Keys on Non-commutative Division Semirings

  • G. S. G. N. AnjaneyuluEmail author
  • B. Davvaz
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this article, we propose a novel signature scheme connecting two private keys and two public keys generated on general non-commutative division semiring. The key notion of our technique engrosses three core steps. In the first step, we assemble polynomials on additive structure of non-commutative division semiring and execute them as underlying base work infrastructure. In the second step, we generate first set of private and public key pair using polynomial symmetrical decomposition problem. In the third step, we generate second set of private and public key pair using discrete logarithm. We use factorization theorem to generate the private key in discrete logarithm problem. By making so, we can execute a new signature scheme on multiplicative algebraic structure of the semiring using multiple private keys. The security of the designed signature scheme is depending on the intractability or hardness of the polynomial symmetrical decomposition problem and discrete logarithmic problem over the designed non-commutative division semiring. Hacking or tracking private keys should cross two mathematical hard problems. Hence, this signature scheme is much stronger than existing protocols in security point of view.

Keywords

Digital signature Factorization Discrete logarithm problem Symmetrical decomposition problem Non-commutative and division semiring 

2010 Mathematics Subject Classification:

16Y60 14G50 

References

  1. 1.
    Anjaneyulu, G.S.G.N., Vasudeva Reddy, P., Reddy, U.M., Secured digital signature scheme using polynomials over non-commutative division semirings. International Journal of Computer Science and Network Security. 8(8), 278–284 (2008).Google Scholar
  2. 2.
    Anjaneyulu, G.S.G.N., Venkateswarlu, B., Reddy, U.M., Diffie-Hellman-Like key agreement protocol using polynomials over non-commutative division semirings, International Journal of Computer Information Systems, 5(1), 37–41 (2012).Google Scholar
  3. 3.
    Diffie, W., Hellman, M.E., New directions in cryptography, IEEE Transaction on Information Theory, 22 (1976) 644–654.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Rivest, R.L., Shamir, A., and Adleman, L., A method for obtaining digital signatures and public key cryptosystems, Communications of the ACM, 27 (1978) 120–126.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Komaya,K., Maurer,V., Okamoto, T., Vanstone,S. New PKC based on elliptic curves over the ring \(\mathbb {Z}_n\), LNCS 516, PP. 252–266, Springer-verlag 1992.Google Scholar
  6. 6.
    Elgamal,T., A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Transactions on Information Theory, 31 (1985)469–472.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Maglivers,S.S., Stinson, D.R., Van Trungn, T. New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups,, Journal of Cryptology, 15 (2002) 285–297.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Shor, P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Computing, 5 (1997) 31484–1509.MathSciNetGoogle Scholar
  9. 9.
    Lee, E. Braid groups in cryptography, IEICE Trans. Fundamentals, E87-A (5) (2004) 986–992.MathSciNetGoogle Scholar
  10. 10.
    Sidelnikov,V., Cherepnev, M., Yaschenko, V.,Systems of open distribution of keys on the basis of non-commutation semigroups, Russian Acad. Sci. Dok L. Math., 48(2) (1993) 566–567.Google Scholar
  11. 11.
    Ko K.H.,Choi,D.H.,Cho,M.S., Lee J.W New signature scheme using conjugacy problem, Cryptology e print Archive: Report 2002/168, 2002.Google Scholar
  12. 12.
    Ko,K.H.,Lee,J.S.,Cheon J.H.,Han,Kang, J.S., Park C., New public-key cryptosystem using Braid Groups, Advances in cryptology, Proc. CRYPTO 2000. LNCS 1880, PP. 166–183, Springer-verlag, 2000.Google Scholar
  13. 13.
    Cao, Z. Dong, X., Wang, L., New public key cryptosystems using polynomials over non-commutative rings, Cryptography e-print archive, http://eprint.iacr.org/2007/

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsVIT - Vellore Institute of TechnologyVelloreIndia
  2. 2.Department of MathematicsYazd UniversityYazdIran

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