Abstract: A new fast and secure elliptic curve scalar multiplication algorithm is presented. The method utilizes the front and back ratio coefficient of Pell sequence to produce new Pell Type Double-and-Add Chain（PTDAC）, its circulation fixed on simple operation like “double-and-addition”, which can be natural resistance to Simple Power Analysis（SPA） attack. PTDAC algorithm combined with Edwards elliptic curve can reduce the underlying operation time. Theoretical analysis and simulation experiments show that the PTDAC algorithm is 2.6% faster than the Euclid Addition Chain（EAC）, and 22.8% faster than the Golden Ratio Addition Chain（GRAC）.

Key words: scalar multiplication, Pell sequence, simple power attack, Pell Type Double-and-Add Chain（PTDAC）

摘要： 提出了一种新的椭圆曲线快速安全的标量乘算法。利用佩尔序列前后项分割比产生新的佩尔型点加-倍点链（Pell Type Double-and-Add Chain，PTDAC），其循环固定的“倍点-点加”操作可天然抵抗简单能量分析（Simple Power Analysis，SPA）攻击。PTDAC算法结合Edwards椭圆曲线可从底层域减少运算时间，进一步优化算法。经过理论分析和仿真实验表明，PTDAC算法在最优情况下比EAC-270和GRAC-258算法在时间效率上分别提高了2.6%和22.8%。

关键词: 标量乘, 佩尔序列, 简单能量攻击, Pell型点加-倍点链（PTDAC）