References

Avanzi, R., C. Heuberger and H. Prodinger, 2011. Redundant τ-adic expansions I: Non-adjacent digit sets and their applications to scalar multiplication. Des. Codes Cryptography, 58: 173-202.
Direct Link  |  

Avanzi, R.M., C. Heuberger and H. Prodinger, 2006. On redundant τ-adic expansions and non-adjacent digit sets. Proceedings of the 13th International Workshop on Selected Areas in Cryptography, August 17-18, 2006, Springer, Berlin, Germany, ISBN:978-3-540-74461-0, pp: 285-301.

Blake, I.F., V.K. Murty and G. Xu, 2008. Nonadjacent radix-τ expansions of integers in Euclidean imaginary quadratic number fields. Canad. J. Math., 60: 1267-1282.
CrossRef  |  Direct Link  |  

Hadani, N.H. and F. Yunos, 2018. Alternative formula of T^m in scalar multiplication on Koblitz curve. AIP. Conf. Proc., Vol. 1974, 10.1063/1.5041533

Hakuta, K., H. Sato and T. Takagi, 2010. Explicit lower bound for the length of minimal weight τ-adic expansions on Koblitz curves. J. Math. Ind., 2: 75-83.
Direct Link  |  

Hankerson, D., Menezes, A.J. and S. Vanstone, 2006. Guide to Elliptic Curve Cryptography. Springer, Berlin, Germany, ISBN:9780387218465, Pages: 312.

Heuberger, C. and D. Krenn, 2013. Existence and optimality of w-non-adjacent forms with an algebraic integer base. Acta Math. Hungarica, 140: 90-104.
CrossRef  |  Direct Link  |  

Heuberger, C., 2010. Redundant τ-adic expansions II: Non-optimality and chaotic behaviour. Math. Comput. Sci., 3: 141-157.
CrossRef  |  Direct Link  |  

Koblitz, N., 1987. Elliptic curve cryptosystems. Math. Comput., 48: 203-209.
Direct Link  |  

Koblitz, N., 1992. CM-curves with good cryptographic properties. Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology, Aug. 11-15, Springer Verlag, London, pp: 279-287.

Solinas, J.A., 1997. An improved algorithm for arithmetic on a family of elliptic curves. Proceedings of the International Annual Conference on Cryptology, August 17-21, 1997, Springer, Berlin, Germany, ISBN:978-3-540-63384-6, pp: 357-371.

Solinas, J.A., 2000. Efficient Arithmetic on Koblitz Curves. In: Design, Codes and Cryptography, Solinas, J.A. (Ed.). Springer, Boston, Massachusetts, pp: 195-249.

Suberi, S., F. Yunos, S. Suberi, M.R.S. Said and S.H. Sapar et al., 2018. Formula of τ-adic non adjacent form with the least number of NON zero coefficients. J. Karya Asli Lorekan Ahli Math., 11: 23-30.

Suberi, S.M., F. Yunos and M.R.M. Said, 2016. An even and odd situation for the multiplier of scalar multiplication with pseudo τ-adic non-adjacent form. AIP. Conf. Proc., 1750: 1-9.
CrossRef  |  Direct Link  |  

Yunos, F. and K.A.M. Atan, 2016. Improvement to scalar multiplication on Koblitz curves by using pseudo τ-adic non-adjacent form. AIP. Conf. Proc., 1750: 1-8.
CrossRef  |  Direct Link  |  

Yunos, F. and S.M. Suberi, 2018. Even and odd nature for pseudo τ-adic non-adjacent form. Malaysian J. Sci., 37: 94-102.
Direct Link  |  

Yunos, F., 2015. Development of pseudo TNAF for aging calculate calling the curlcobitz. Ph.D Thesis, Universiti Putra Malaysia, Seri Kembangan, Malaysia.

Yunos, F., K.A.M. Atan, M.R.K. Ariffin and M.R.M. Said, 2015. Pseudo 𝝉-adic non adjacent form for scalar multiplication on Koblitz curves. Proceedings of the 4th International Conference on Cryptology and Information Security (Cryptology 2014), June 24-26, 2014, Institute for Mathematical Research, Serdang, Malaysia, pp: 120-130.

Yunos, F., K.A.M. Atan, M.R.K. Ariffin and M.R.M. Said, 2015. Pseudo-ADIC non adjacent form for scalar multiplication on Koblitz curves. Malaysian J. Math. Sci., 9: 71-88.
Direct Link  |  

Yunos, F., K.A.M. Atan, M.R.M. Said and M.R.K. Ariffin, 2014. A Reduced τ-Adic NAF (RTNAF) representation for an efficient scalar multiplication on Anomalous Binary Curves (ABC). Pertanika J. Sci. Technol., 22: 489-505.
Direct Link  |