计算机工程与应用
計算機工程與應用
계산궤공정여응용
Computer Engineering and Applications
2015年
22期
115-118
,共4页
椭圆曲线密码体制%标量乘法%底层域运算%仿射坐标%雅克比坐标
橢圓麯線密碼體製%標量乘法%底層域運算%倣射坐標%雅剋比坐標
타원곡선밀마체제%표량승법%저층역운산%방사좌표%아극비좌표
elliptic curve cryptosystem%scalar multiplication%field operation%affine coordinate%jacobian coordinate
为了提高椭圆曲线底层域运算的效率，基于将乘法转换为平方运算的思想，提出在素数域FP上用雅克比坐标直接计算2k P和3k P的改进算法，其运算量分别为(3k-1)M+(5k+3)S和(6k-1)M+(9k+3)S ，与DIMITROY和周梦等人所提的算法相比，算法效率分别提升了6.25%和5%。另外，利用相同的原理，给出了素数域FP上用在仿射坐标系直接计算3k P的改进算法，其运算量为I+(6k+1)M+(9k+1)S ，与周梦和殷新春等人所提的算法相比，效率分别提升了3.4%和24%。
為瞭提高橢圓麯線底層域運算的效率，基于將乘法轉換為平方運算的思想，提齣在素數域FP上用雅剋比坐標直接計算2k P和3k P的改進算法，其運算量分彆為(3k-1)M+(5k+3)S和(6k-1)M+(9k+3)S ，與DIMITROY和週夢等人所提的算法相比，算法效率分彆提升瞭6.25%和5%。另外，利用相同的原理，給齣瞭素數域FP上用在倣射坐標繫直接計算3k P的改進算法，其運算量為I+(6k+1)M+(9k+1)S ，與週夢和慇新春等人所提的算法相比，效率分彆提升瞭3.4%和24%。
위료제고타원곡선저층역운산적효솔，기우장승법전환위평방운산적사상，제출재소수역FP상용아극비좌표직접계산2k P화3k P적개진산법，기운산량분별위(3k-1)M+(5k+3)S화(6k-1)M+(9k+3)S ，여DIMITROY화주몽등인소제적산법상비，산법효솔분별제승료6.25%화5%。령외，이용상동적원리，급출료소수역FP상용재방사좌표계직접계산3k P적개진산법，기운산량위I+(6k+1)M+(9k+1)S ，여주몽화은신춘등인소제적산법상비，효솔분별제승료3.4%화24%。
To raise the efficiency of field operation on elliptic curve, based on the idea of trading multiplications for squares, two modified algorithms are proposed to compute 4P and 5P directly over prime field FP in terms of affine coor-dinates, their computational complexity are (3k-1)M+(5k+3)S and (6k-1)M+(9k+3)S respectively, which are improved to 6.25% and 5% respectively than those of Dimitroy’s and Zhou meng’s method. Moreover, using the same idea, an improved method is given to compute 3k P directly in terms of affine coordinates, its computational complexity is I+(6k+1)M+(9k+1)S , and the efficiency of the new method is improved to 3.4% and 24% respectively than those of Zhong meng’s and Yin xin-chun’s method.
