Why is there a custom to eat cheese products on Hanoukah?

The Ran in Masechet Shabbat writes that women are also obligated to light candles for Hanoukah because they were also part of the miracle. He explains that the Greek generals and viceroys used to have sexual relations with newly married Jewish brides the first night after their wedding. In the midrash, we read of the daughter of Yohanan Kohen Gadol (High Priest), who was brought before the head of the Greek army. She fed him cheese products so he should be thirsty. She then gave him wine until he lay drunk and asleep. She promptly killed him. When the army received word that the mighty general had fallen, they fled. This ultimately contributed mightily to the victory of the Hashmonaim. To remember this event, we have the custom of eating cheese products on Hanoukah.