为了提高椭圆曲线标量乘法的效率,根据将求逆转换为乘法运算的思想,提出了在二进制域F2n上用仿射坐标直接计算7P的两种算法。两种算法分别通过引入公因子和除法多项式来计算7P,其运算量分别为2I+7S+14M和I+6S+20M,比Purohit等提出的算法...为了提高椭圆曲线标量乘法的效率,根据将求逆转换为乘法运算的思想,提出了在二进制域F2n上用仿射坐标直接计算7P的两种算法。两种算法分别通过引入公因子和除法多项式来计算7P,其运算量分别为2I+7S+14M和I+6S+20M,比Purohit等提出的算法(PUROHIT G N,RAWAT S A,KUMAR M.Elliptic curve point multiplication using MBNR and Point halving.International Journal of Advanced Networking and Applications,2012,3(5):1329-1337)分别节省了一次和两次求逆运算。同时还给出直接计算7kP的快速算法,该算法比重复计算k次7P更有效。最后结合半点运算和扩展多基表示形式将这些新算法应用到标量乘法中。实验结果表明,在美国国家标准技术研究所(NIST)推荐的椭圆曲线上,当预存储点的个数为2和5时,新算法比Purohit算法效率提高了30%和37%,比洪银芳等所提的算法(洪银芳,桂丰,丁勇.基于半点和多基表示的标量乘法扩展算法.计算机工程,2011,37(4):163-165)效率提高了9%和13%。新算法以增加少量的预计算存储为代价,能有效降低标量乘法的运算量。展开更多
The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the a...The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.展开更多
文摘为了提高椭圆曲线标量乘法的效率,根据将求逆转换为乘法运算的思想,提出了在二进制域F2n上用仿射坐标直接计算7P的两种算法。两种算法分别通过引入公因子和除法多项式来计算7P,其运算量分别为2I+7S+14M和I+6S+20M,比Purohit等提出的算法(PUROHIT G N,RAWAT S A,KUMAR M.Elliptic curve point multiplication using MBNR and Point halving.International Journal of Advanced Networking and Applications,2012,3(5):1329-1337)分别节省了一次和两次求逆运算。同时还给出直接计算7kP的快速算法,该算法比重复计算k次7P更有效。最后结合半点运算和扩展多基表示形式将这些新算法应用到标量乘法中。实验结果表明,在美国国家标准技术研究所(NIST)推荐的椭圆曲线上,当预存储点的个数为2和5时,新算法比Purohit算法效率提高了30%和37%,比洪银芳等所提的算法(洪银芳,桂丰,丁勇.基于半点和多基表示的标量乘法扩展算法.计算机工程,2011,37(4):163-165)效率提高了9%和13%。新算法以增加少量的预计算存储为代价,能有效降低标量乘法的运算量。
基金Supported by the National Natural Science Foundation of China(6140220111326243+3 种基金612723001137117411501252)the Jiangsu Natural Science Foundation of China(BK20130117)
文摘The monotonicity of a rational Bezier curve, usually related to an explicit function, is determined by the used coordinate system. However, the shape of the curve is independent of the coordinate system. To meet the affine invariant property, a kind of generalized mono- tonicity, called direction monotonicity, is introduced for rational Bezier curves. The direction monotonicity is applied to both planar and space curves and to both Cartesian and affine co- ordinate systems, and it includes the traditional monotonicity as a subcase. By means of it, proper affine coordinate systems may be chosen to make some rational Bezier curves monotonic. Direction monotonic interpolation may be realized for some of the traditionally nonmonotonic data as well.
