Skip to main content
SpringerLink
Log in

SPA on Rabin variant with public key \(N=p^2q\)

  • Regular Paper
  • Published:
Journal of Cryptographic Engineering Aims and scope Submit manuscript

Abstract

Variants of the Rabin cryptosystem are built to overcome the decryption failure problem encountered by the cryptosystem. In this paper, we perform a theoretical simple power analysis on one of the variants that operates its decryption procedure via modular multiplication where the moduli \(N_1=pq\) is kept secret while the moduli \(N=p^2q\) is public. The attack utilizes Legendre’s theorem of continued fraction to successfully retrieve the secret key of the cryptosystem. An example of the attack is also included in this paper.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ariffin, M., Asbullah, M., Abu, N., Mahad, Z.: A new efficient asymmetric cryptosystem based on the integer factorization problem of \({N}=p^2q\). Malays. J. Math. Sci. 7(S), 19–37 (2013)

  2. Ariffin, M., Mahad, Z.: \(AA_{\beta }\) Public Key Cryptosystem–A Comparative Analysis against RSA and ECC. International Journal of Digital Content Technology and its Applications 7(7), 174–182 (2013)

  3. Asbullah, M., Ariffin, M.: Comparative analysis of three asymmetric encryption schemes based upon the intractability of square roots modulo \(N=p^2q\). In: 4th International Cryptology and Information Security Conference (2014)

  4. Asbullah, M., Ariffin, M.: Fast decryption method for a Rabin primitive based cryptosystem. Int. J. Adv. Comput. Technol. 6(1), 56–67 (2014)

    Google Scholar 

  5. Boneh, D., Durfee, G., Howgrave-Graham, N.: Factoring \(N= p^r q\). In: Advances in Cryptology, Crypto99, pp. 326–337. Springer, Berlin (1999)

  6. Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Advances in Cryptology, CRYPTO99, pp. 388–397. Springer, Berlin (1999)

  7. Kurosawa, K., Ito, T., Takeuchi, M.: Public key cryptosystem using a reciprocal number with the same intractability as factoring a large number. Cryptologia 12(4), 225–233 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mahad, Z., Ariffin, M.: \(AA_\beta \) public-key cryptosystem—a practical implementation of the new asymmetric cryptosystem. Int. J. Digit. Content Technol. Appl. 7(7), 165–173 (2013)

    Article  MathSciNet  Google Scholar 

  9. Mahad, Z., Ariffin, M., Asbullah, M.: A new improvement method on Rabin cryptosystem. In: International Conference on Computer Engineering and Mathematical Sciences (2014)

  10. Meneves, A., Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, New York (1997)

  11. Nishioka, M., Satoh, H., Sakurai, K.: Design and analysis of fast provably secure public-key cryptosystems based on a modular squaring. In: Information Security and Cryptology, ICISC 2001, pp. 81–102. Springer, Berlin (2002)

  12. Okamoto, T., Uchiyama, S.: A new public-key cryptosystem as secure as factoring. In: Advances in Cryptology, EUROCRYPT’98, pp. 308–318. Springer, Berlin (1998)

  13. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Advances in Cryptology, EUROCRYPT99, pp. 223–238. Springer, Berlin (1999)

  14. Rabin, M.O.: Digitalized signatures and public-key functions as intractable as factorization. Tech. Rep, DTIC Document (1979)

  15. Saldamli, G., Koç, C.K.: Spectral modular exponentiation. In: 18th IEEE Symposium on Computer Arithmetic. ARITH’07, pp. 123–132. IEEE, New York (2007)

  16. Schmidt, W.M.: Diophantine Approximation, vol. 785. Springer, Berlin (1996)

  17. Schmidt-Samoa, K., Takagi, T.: Paillier’s cryptosystem modulo \(p^2q\) and its applications to trapdoor commitment schemes. In: Progress in Cryptology—Mycrypt 2005, pp. 296–313. Springer, Berlin (2005)

  18. Takagi, T.: Fast RSA-type cryptosystem modulo \(p^kq\). In: Advances in Cryptology, CRYPTO’98, pp. 318–326. Springer, Berlin (1998)

  19. Williams, H.: A modification of the RSA public-key encryption procedure (Corresp.). IEEE Trans. Inf. Theory 26(6), 726–729 (1980)

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Malaysia

    Amir Hamzah Abd Ghafar & Muhammad Rezal Kamel Ariffin

  2. Department of Mathematics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400, Serdang, Malaysia

    Muhammad Rezal Kamel Ariffin

Authors
  1. Amir Hamzah Abd Ghafar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Rezal Kamel Ariffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amir Hamzah Abd Ghafar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abd Ghafar, A.H., Ariffin, M.R.K. SPA on Rabin variant with public key \(N=p^2q\) . J Cryptogr Eng 6, 339–346 (2016). https://doi.org/10.1007/s13389-016-0118-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13389-016-0118-5

Keywords

Search

Navigation