Towards minimizing memory requirement for implementation of hyperelliptic curve cryptosystems

  • Authors:

  • Pradeep Kumar Mishra;Pinakpani Pal;Palash Sarkar

  • Affiliations:

  • Centre for Information Security and Cryptography, University of Calgary, Calgary, Canada;Indian Statistical Institute, Kolkata, India;Indian Statistical Institute, Kolkata, India

  • Venue:
  • ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
  • Year:
  • 2007

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Abstract

Elliptic (ECC)and hyperelliptic curve cryptosystems (HECC) have emerged as cryptosystemsfor small hand-held andmobile devices.Extensive research has been carried out for their secure and efficient implementation on these devices. These devices come with very low amount of resources, efficient memory management is an important issue in all such implementations. HECC arithmetic is now generally performed using so called explicit formulas. The main goal of these formulas is to reduce the number of finite field operations (multiplications and squarings). On the other hand, reducing the memory requirement is also important.To the best of our knowledge, the literature onHECCimplementation does not seriously consider this aspect.This is the firstwork to obtainmemory efficient versions of various explicit formulas appearing in the literature. In certain cases, we are also able to determine theminimummemory requirement and obtain a memory optimal implementation.We believe that these formulas will be extremely useful to designers of HECC. Our basic technique is essentially an exhaustive search with heuristic strategies for improving the run-time.