As we know that in DH key exchange, both Alice and Bob would agree on the parameter $p$ and $g$. Next, Alice would choose a secret key $A$ while Bob would choose a secret key $B$. Alice would compute $g^A\mod p$ and Bob would compute $g^B\mod p$. They would exchange these computed values and each side would raise their secret key against the received computed value, i.e. $(g^A)^B\mod p = (g^B)^A\mod p$.
From Charlie's (external party) point of view, he would know values of $p$, $g$, $g^A\mod p$ and $g^B\mod p$. Assuming that $g^A\mod p$ and $g^B\mod p$ are 100 digits long, would he be able to determine a bound (in terms of digits or bits) for the respective secret key $A$ and $B$?
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