Publications

**R.R. Goundar, K. Shiota, and M. Toyonaga, A Novel Method for Elliptic Curve Multi-Scalar Multiplication**,

International Journal of Applied Mathematics and Computer Sciences, vol. 4, no.9, pp. 1-5, 2009.**R.R. Goundar, K. Shiota, and M. Toyonaga, SPA Resistant Scalar Multiplication using Golden Ratio Addition Chain Method**,

IAENG International Journal of Applied Mathematics, vol. 38, issue 2, pp. 83-88, Jun. 2008.**R.R. Goundar, K. Shiota, and M. Toyonaga, New Strategy for Doubling-free Short Addition-Subtraction Chain**,

Applied Mathematics & Information Sciences -- An International Journal, vol.2, issue 2, pp.123-133, May 2008.**K. Ohta and K. Shiota, Construction of CM-Curves Suitable for Cryptosystems Using Weil Pairing**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 27(2006), No.1.**T. Saiki and K. Shiota, Cryptography using the trace map on elliptic curves**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 26(2005), No.4.**T. Shimaoka and K. Shiota, Secret sharing scheme on elliptic curves**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 25(2004), pp.173-178.**M. Ohshima and K. Shiota, Algorithm for computing n-th roots in modular operation**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 23(2002), pp.1-7.**N. Kikukawa and K. Shiota, On the codes constructed from orthogonal Latin square graphs**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 22(2001), pp.35-48.**K. Shiota, Table of left O-ideal classes in rational quaternion algebras I; II; III,**

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 14(1993), pp.15-94;

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 15(1994), pp.15-80;

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 15(1994), pp.81-122.**K. Shiota, On primitive forms of certain type of level q=q1q2q3**( in Japanese ),

Mem. Fac. Sci. Kochi Univ. ( Inf. Sci. ), 15(1994), pp.1-13.

As a continuation of the above, the author treats the case of composite levels.**K. Shiota, On theta series and the splitting of S2(Gamma0(q))**,

J. Math. Kyoto Univ., 31(1991), pp.909-930.

The author calculated the theta series appearing in 'the Basis Problem' for the cases of ellipitc modular forms of prime levels, and the linear degenerations of them. He found a lot of irregular degenerations, which cause some rational decomposition of the spaces of modular forms. Especially, he found a counter example for ( the weakest version of ) the conjecture of Hecke.**K. Shiota, On the explicit models of Shimura's elliptic curves**,

J. Math. Soc. Japan, 38(1986), pp.649-659.

The author determined the explicit models of Shimura's elliptic curves associated to the Neben type elliptic modular forms for the prime levels p=29,37 and 41. They are elliptic curves defined over real quadretic fields with good reduction everywhere, and have some rational torsion points.