Possible Prime Modified Fermat Factorization: New Improved Integer Factorization to Decrease Computation Time for Breaking RSA

  • Kritsanapong Somsuk
  • Sumonta Kasemvilas
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 265)


The aim of this research is to propose a new modified integer factorization algorithm, called Possible Prime Modified Fermat Factorization (P2MFF), for breaking RSA which the security is based upon integer factorization. P2MFF is improved from Modified Fermat Factorization (MFF) and Modified Fermat Factorization Version 2 (MFFV2). The key concept of this algorithm is to reduce iterations of computation. The value of larger number in P2MFF is increased more than one in each iteration of the computation, it is usually increased by only one in MFF and MFFV2. Moreover, this method can decrease the number of times in order to compute the square root of some integers whenever we can strongly confirm that square root of these integers is not an integer by using number theory. The experimental results show that P2MFF can factor the modulus faster than MFF and MFFV2.


RSA Scheme Modified Fermat Factorization (MFF) Modified Fermat Factorization Version 2 (MFFV2) Computation time Integer Factorization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Communications of ACM 21, 120–126 (1978)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bishop, D.: Introduction to Cryptography with java Applets. Jones and Bartlett Publisher (2003)Google Scholar
  3. 3.
    Somsuk, K., Kasemvilas, S.: MFFV2 and MNQSV2: Improved factorization Algorithms. In: International Conference on Information Science and Application, pp. 327–329 (2013)Google Scholar
  4. 4.
    Huang, Q., Li, Z.T., Zhang, Y., Lu, C.: A Modified Non-Sieving Quadratic Sieve For Factoring Simple Blur Integers. In: International Conference on Multimedia and Ubiquitous Engineering, pp. 729–732 (2007)Google Scholar
  5. 5.
    Ambedkar, B.R., Gupta, A., Gautam, P., Bedi, S.S.: An Efficient Method to Factorize the RSA Public Key Encryption. In: International Conference on Communication Systems and Network Technologies, pp. 108–111 (2011)Google Scholar
  6. 6.
    Pollard, J.: Monte Carlo methods for index computation (mod p). Math. Comp. 32, 918–924 (1978)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Sharma, P., Gupta, A.K., Vijay, A.: Modified Integer Factorization Algorithm using V-Factor Method. In: Advanced Computing & Communication Technologies, pp. 423–425 (2012)Google Scholar
  8. 8.
    Somsuk, K., Kasemvilas, S.: MVFactor: A Method to Decrease Processing Time for Factorization Algorithm. In: 17th International Conference on International Computer Science and Engineering Conference, pp. 339–342 (2013)Google Scholar
  9. 9.
    Silverman, J.H.: A Friendly introduction to number thoery, Pearson International Edition (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Electronics Engineering, Faculty of TechnologyUdon Thani Rajabhat University, UDRUUdon ThaniThailand
  2. 2.Department of Computer Science, Faculty of ScienceKhon Kaen University, KKUKhon KaenThailand

Personalised recommendations