The middle person sends her own public value to both sides.

highlighted = computed this step

Eve chooses her own secret

Eve chooses e=10 and publishes E=9.

E=510mod23=9E=5^{10}\bmod{}23=9
Eve replaces the valuesUnauthenticated DH replacement values are recomputed from p, g, a, b, and Eve's exponent.Eve replaces the values - E=9quantityvaluee (Eve secret)10E=g^e mod p9Eve-Alice secret3Alice computes E^a3Eve-Bob secret6Bob computes E^b6real A-B shared never forms2

The same E is sent both ways

Alice receives E instead of B, and Bob receives E instead of A.

both sides see E\text{both sides see }E
Eve replaces the valuesUnauthenticated DH replacement values are recomputed from p, g, a, b, and Eve's exponent.Eve replaces the values - E=9quantityvaluee (Eve secret)10E=g^e mod p9Eve-Alice secret3Alice computes E^a3Eve-Bob secret6Bob computes E^b6real A-B shared never forms2

The real pair never meets

Alice does not use B=19, and Bob does not use A=8.

A=8B=19A=8\quad B=19
Eve replaces the valuesUnauthenticated DH replacement values are recomputed from p, g, a, b, and Eve's exponent.Eve replaces the values - E=9quantityvaluee (Eve secret)10E=g^e mod p9Eve-Alice secret3Alice computes E^a3Eve-Bob secret6Bob computes E^b6real A-B shared never forms2

Summary

The replacement makes each endpoint do correct math with the wrong public value.

same table, different transcript\text{same table, different transcript}
Eve replaces the valuesUnauthenticated DH replacement values are recomputed from p, g, a, b, and Eve's exponent.Eve replaces the values - E=9quantityvaluee (Eve secret)10E=g^e mod p9Eve-Alice secret3Alice computes E^a3Eve-Bob secret6Bob computes E^b6real A-B shared never forms2