PPT Slide

Mod p

Let N be the smallest positive integer such that ZN º 0 mod p. Then N is the order of the point P on the curve E over Fp.

The sequence {Zk} is purely periodic with period tN for some t which divides p-1.

Example

Consider the sequence {Zk} generated by the curve

E:y2 + y = x3 - x over F5. We have N = 8 and t = 4 so the sequence is purely periodic with period 32 as follows:

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