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Cryptography

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    $\begingroup$ You really shouldn't use the word "order" here. "Order" in group theory has a precise meaning, and using it to mean anything else creates confusion. $\endgroup$ Commented Jan 6, 2019 at 13:04
  • $\begingroup$ What word do you suggest to use instead of "order"? $\endgroup$ Commented Jan 6, 2019 at 16:15
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    $\begingroup$ The integer $a$ such that $P_1 = a\cdot G$ is called the discrete logarithm of $P_1$ (relative to $G$), and similarly for $P_2$, so you could say that you wish to show that the discrete logarithm of $P_2$ is larger than that of $P_1$. $\endgroup$ Commented Jan 6, 2019 at 16:21