On using Aryabhatta Remainder Theorem to Decrypt a Message with RPrime and Rebalanced RSA

  • Authors

    • Ch J.L. Padmaja
    • V S.Bhagavan
    • B Srinivas
    2018-03-18
    https://doi.org/10.14419/ijet.v7i2.7.10940
  • Aryabhatta remainder theorem, Chinese remainder theorem, Rebalance, RPrime, Rebalanced.
  • RSA is the most world widely used asymmetric cryptosystem for network transactions. Through this article, we propose a new implementation of Aryabhatta Remainder theorem (ART) in place of the existing Chinese Remainder Theorem (CRT) to solve congruencies in the decryption phase for the faster variants of RSA such as RPrime RSA and Rebalanced RSA. Through our observations, we prove that using ART for CRT has improved the overall decryption speed of RPrime and Rebalanced RSA.

     

     

  • References

    1. [1] Boneh D, Shacham H., “Fast variants of RSAâ€. CryptoBytes, Vol. 5, No.1, pp. 1-9, (2001).

      [2] Fiat A, “Batch RSAâ€, Advances in Cryptology: Proceedings of Crypto ’89, Vol. 435, pp. 175–185, (1989).

      [3] Knuth DE, “The Art of Computer Programming – Volume 2: Seminumerical Algorithmsâ€, Addison Wesley, (1969).

      [4] Paixao CAM, “Implementacao e analise comparativa de variacoes do criptossistema RSA†Master’s thesis, Inst. de Matematica e Estatıstica, Univ. de Sao Paulo., (2003).

      [5] Paixao CAM., “An efficient variant of the RSA cryptosystemâ€, IACR Cryptology ePrint Archive, pp.159, (2003).

      [6] Rao TRN, Yang CH, “Aryabhatta Remainder Theorem: Relevance to Public-key Crypto-algorithmsâ€, Circuits, Systems and Signal Processing, Vol.25, No.1, (2006).

      [7] Rivest R, Shamir A, Adleman L, “A method for obtaining digital signatures and public-key cryptosystemsâ€, Commun. ACM, Vol.21, No.2, pp.120–126, (1978)

      [8] Singh A, “Improving the RSA Crypto Computationsâ€, Master Thesis, University of Louisiana, (2006).

      [9] Takagi T, “Fast RSA-type Cryptosystem Modulo p k qâ€, In H. Krawczyk, ed., Proceedings of Crypto ’98, 1462 of LNCS, Springer-Verlag, pp. 318–326, (1998).

      [10] WebLink to DataTrans Credit Card Data https://www.datatrans.ch/showcase/test-cc-numbers

      [11] WebLink to tutorial of RSA BiInteger Implementation using Java http://www.java2s.com/Code/Java/Security/SimpleRSApublickeyencryptionalgorithmimplementation.htm

      [12] Wiener MJ, “Cryptanalysis of short RSA secret exponentsâ€, IEEE Transactions on Information Theory, Vol.36, No.3, pp. 553–558, (1990).

  • Downloads

  • How to Cite

    J.L. Padmaja, C., S.Bhagavan, V., & Srinivas, B. (2018). On using Aryabhatta Remainder Theorem to Decrypt a Message with RPrime and Rebalanced RSA. International Journal of Engineering & Technology, 7(2.7), 758-762. https://doi.org/10.14419/ijet.v7i2.7.10940