In order to determine the projected coordinate origin in the cone-beam CT scanning system with respect to the Feldkamp-Davis-Kress （FDK） algorithm, we propose a simple yet feasible method to accurately measure the p...In order to determine the projected coordinate origin in the cone-beam CT scanning system with respect to the Feldkamp-Davis-Kress （FDK） algorithm, we propose a simple yet feasible method to accurately measure the projected coordinate origin. This method was established on the basis of the theory that the projection of a spherical object in the cone-beam field is an ellipse. We first utilized image processing and the least square estimation method to get each major axis of the elliptical Digital Radiography （DR） projections of a group of spherical objects. Then we determined the intersection point of the group of major axis by solving an over-determined equation set that was composed by the major axis equations of all the elliptical projections. Based on the experimental results, this new method was proved to be easy to implement in practical scanning systems with high accuracy and anti-noise capability.展开更多
Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and...Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.展开更多
基金Supported by the National Natural Science Foundation of China (60872080)Peking Educational Committee Corporate Construction Project
文摘In order to determine the projected coordinate origin in the cone-beam CT scanning system with respect to the Feldkamp-Davis-Kress （FDK） algorithm, we propose a simple yet feasible method to accurately measure the projected coordinate origin. This method was established on the basis of the theory that the projection of a spherical object in the cone-beam field is an ellipse. We first utilized image processing and the least square estimation method to get each major axis of the elliptical Digital Radiography （DR） projections of a group of spherical objects. Then we determined the intersection point of the group of major axis by solving an over-determined equation set that was composed by the major axis equations of all the elliptical projections. Based on the experimental results, this new method was proved to be easy to implement in practical scanning systems with high accuracy and anti-noise capability.
基金Supported by the National Natural Science Foundation of China (60573031)
文摘Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to（φε^-1（P）, and compute [n]（φε^-1（P） on elliptic curve Eε, which is faster than computing [n]P on E, where φε is an isomorphism. Finally we calculate （φε（[n]φε^-1（P）） = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.
