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)


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.


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

2010 Mathematics Subject Classification:

16Y60 14G50 


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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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