DH Key exchange attack: bad choice of g In the group $\mathbb{F}_p^*$, Bob reads Alice's parameters as $p=234917$ and $g=281$ and uses a secret key $b &lt; 400$ such that $h_b = g^b = 92646$.

Note that $p-1 = 2^2\cdot 11\cdot19\cdot281$

$281^{2\cdot11\cdot19\cdot281} \equiv 1 \mod 234917$

and that

$19452^{281} \equiv 1 \mod 234917$

Find $b$.

281 is too large for the Pohlig-Hellman attack by hand (which is how this question is supposed to be solved). I feel like the answer is staring me in the face but I cannot see it. Can anyone give a hint/help me? Basically we have $2\cdot(\text{order of g}) = p-1$...
I have solved the question by carrying out the Pohlig-Hellman attack for the smaller prime factors and finding that $b \equiv 3 \mod 11$ and $b \equiv 6 \mod 19$, then finding all the integers $&lt; 400$ satisfying this and testing them. The answer is $b=234$.

I am still interested in if anyone has a solution which usesthe order of $g$ though.