The hit row gives the toy secret exponent.

highlighted = computed this step

The table gives the exponent

Once the target row is found, the attacker has x=6.

x=6x=6
Recovered exponentThe recovered exponent is recomputed from the brute-force discrete-log rows.Recovered exponent - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

That exponent was the secret

The public value y hides x only when the group is too large to search. Here the table already found it.

gxmodp=yg^x\bmod p=y
Recovered exponentThe recovered exponent is recomputed from the brute-force discrete-log rows.Recovered exponent - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

The target check still holds

The recovered exponent maps base 5 to public value 8.

56mod23=85^6\bmod{}23=8
Recovered exponentThe recovered exponent is recomputed from the brute-force discrete-log rows.Recovered exponent - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8

Summary

Recovering x turns the public DH value back into the toy private exponent.

private exponent=6\text{private exponent}=6
Recovered exponentThe recovered exponent is recomputed from the brute-force discrete-log rows.Recovered exponent - recovered=6quantityvaluek=15k=22k=310k=44k=520k=6 recovered8