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Special-q Techniques for Number Field Sieve to Solve Integer Factorization

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Smart Innovations in Communication and Computational Sciences

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 669))

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Abstract

Number Field Sieve is one of the best exist method for integer factorization. In this method, relation collection stage is the most time-consuming part and requires a large amount of memory. This paper reports comprehensive analysis between Pollard’s algorithm and FK algorithm of special-q lattice sieving in Number Field Sieve. The experiments are performed using two widely used factoring tools CADO-NFS and GGNFS on the data sets ranging between 100–120 digits; since CADO-NFS is based on FK algorithm and GGNFS is based on Pollard’s algorithm. Experiments are carried out using various parameters. The results are derived and influencing factors are reported. Through the results, it is shown that even though FK algorithm for sieving which avoids the lattice reduction compared with Pollard, the selection of special-q, influences on the performance of the sieving algorithm.

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Notes

  1. 1.

    GF is Galois field.

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Authors and Affiliations

  1. National Institute of Technology, Warangal, India

    Tanmay Sharma & R. Padmavathy

Authors
  1. Tanmay Sharma
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  2. R. Padmavathy
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Correspondence to Tanmay Sharma .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

    Bijaya Ketan Panigrahi

  2. Department of Computer Science and Engineering, ABES Engineering College, Ghaziabad, India

    Munesh C. Trivedi

  3. Department of Computer Science and Engineering, Motilal Nehru National Institute of Technology, Allahabad, Uttar Pradesh, India

    Krishn K. Mishra

  4. CSED, ABES Engineering College, Ghaziabad, Uttar Pradesh, India

    Shailesh Tiwari

  5. Department of Computer Science and Engineering, Jaypee University of Information Technology, Waknaghat, Solan, Himachal Pradesh, India

    Pradeep Kumar Singh

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Sharma, T., Padmavathy, R. (2019). Special-q Techniques for Number Field Sieve to Solve Integer Factorization. In: Panigrahi, B., Trivedi, M., Mishra, K., Tiwari, S., Singh, P. (eds) Smart Innovations in Communication and Computational Sciences. Advances in Intelligent Systems and Computing, vol 669. Springer, Singapore. https://doi.org/10.1007/978-981-10-8968-8_40

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