| 摘要 |
PURPOSE: A Frobenius expansion method using an n-square root function of a unit circle in elliptic curve cryptosystem is provided to improve the computing speed of scalar product. CONSTITUTION: After inputting 'k', '0', and '0' to s1, s2, and i, respectively, the relational expressions of 'x= {as1+ bs2}/p' and 'y= {-bs1+ as2}/p' are calculated and each round-off value of the 'x' and 'y' is inputted to t1 and t2(S400,S410). After calculating the relational expressions of 'r1= s1- at1+ bt2' and 'r2= s2- bt1- at2', each value of 'r1' and 'r2' is inputted to R1(i) and R2(i)(S420). After checking whether the absolute values of the t1 and t2 are less than 2, or not, the relational expression of 'k= (R1(i)+ R2(i)λ)ψi+ (R1(i-1)+ R2(i-1)λ)ψi-1 +... +(R1(0)+ R2(0)λ)' is calculated when the absolute values of the t1 and t2 are less than 2(S430,S440).
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