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In the DH algorithm $ a^x \bmod b $ where $ a $ is the generator and $b $ is the prime modulus does $b $ have to be bigger than $ a $ or could $ a $ be larger for example $ 19^x \bmod 17 $ . Because I don't see a problem with the generator being larger because the answer can still only be $ b \ge \text{answer} > 0 $ . Obviously the prime modulus would still have to be large enough to provide good security but I was just curious if the generator could be larger.

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I suppose there is really no requirement to have $a <b$. But then again, if you are using an $a>b$ why not reduce it modulo $b$ and save space?

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    $\begingroup$ I was just curios $\endgroup$ – Nat Jul 28 '17 at 17:58
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    $\begingroup$ It's good to be curious 😊 $\endgroup$ – Guut Boy Jul 28 '17 at 17:59
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    $\begingroup$ Ugh, emoji in comments. >:( $\endgroup$ – Wildcard Jul 29 '17 at 0:37

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