Skip to main content
Log in

A new ElGamal-like cryptosystem based on matrices over groupring

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, we have developed a new ElGamal-like public key cryptosystem based on the matrices over a groupring. The underlying hard problem for this cryptosystem is the conjugacy search problem. That is, we have replaced the exponentiation of elements by conjugacy. This makes the key generation step more efficient. We also talk about different security aspects against known attacks. The proposed scheme is found to be secure against known plaintext attack when encryption uses a different random key for every new plaintext.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anshel I, Anshel M, Goldfeld D (1999) An algebraic method for public-key cryptography. Math Res Lett 6(287291):287–291

    Article  MathSciNet  MATH  Google Scholar 

  2. Cryptography and braid groups. http://www.tcs.hut.fi/helger/crypto/link/public/braid/

  3. Davis PJ (1994) Circulant matrices. Chelsea, New York

    MATH  Google Scholar 

  4. Dehornoy P (2004) Braid-based cryptography. In: Group theory, statistics, and cryptography, 533 (Contemporary Mathematics, vol. 360). American Mathematical Society, Providence

  5. Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory 22:644–654

    Article  MathSciNet  MATH  Google Scholar 

  6. ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theory 31:469–472

    Article  MathSciNet  MATH  Google Scholar 

  7. Fraleigh JB (1982) A first course in abstract algebra. Addison Wesley Pub., Reading

    MATH  Google Scholar 

  8. Hanoyamak T, Kusmus O (2015) On construction of cryptographic systems over units of group rings. Int Electron J Pure Appl Math 9:37–43

    MathSciNet  Google Scholar 

  9. Hurley B, Hurley T (2010) Group ring cryptography. Int J Pure Appl Math 69:67–86

    MathSciNet  MATH  Google Scholar 

  10. Mahalanobis A (2013) Are matrices useful in public-key cryptography. Int Math Forum 8:1939–1953

    Article  MathSciNet  MATH  Google Scholar 

  11. Mahalanobis A (2010) The discrete logarithm problem in the group of non-singular circulant matrices. Groups Complex Cryptol 2:83–39

    MathSciNet  MATH  Google Scholar 

  12. Passman DS (1977) The algebraic structure of group rings. Wiley, New York

    MATH  Google Scholar 

  13. Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public key cryptosystems. Commun ACM 21:120–126

    Article  MathSciNet  MATH  Google Scholar 

  14. Rososhek SK (2007) Cryptosystems in automorphism groups of group rings of abelian groups. Fundamentalnaya I prikladnaya matematica 13(8):157–164 (in Russian)

    MathSciNet  Google Scholar 

  15. Rososhek SK (2008) Cryptosystems in automorphism groups of group rings of abelian groups. J Math Sci 154(3):386–391. doi:10.1007/s10958-008-9168-2

    Article  MathSciNet  MATH  Google Scholar 

  16. Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput 26(5):1484–1509

    Article  MathSciNet  MATH  Google Scholar 

  17. Shpilrain V, Zapata G Combinatorial group theory and public key cryptography. arXiv:math/04100

  18. Silverman JH (1999) Fast multiplication in finite fields GF(2n). In: CHES’99, LNCS, vol 1717. pp 122–134

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saba Inam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Inam, S., Ali, R. A new ElGamal-like cryptosystem based on matrices over groupring. Neural Comput & Applic 29, 1279–1283 (2018). https://doi.org/10.1007/s00521-016-2745-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2745-2

Keywords

Mathematics Subject Classification

Navigation