Question Old Japanese sword

Hi. I was gifted an old Japanese sword from a veteran. It's in pretty bad shape but does look authentic. Can anyone tell me something about it?

The signature on the tang reads:
備州長船勝光
Bishū Ōsafune Katsumitsu

It means "Katsumitsu of Ōsafune in the province of Bishū made this". Ōsafune was a famous sword-making region in Japan, located in where Okayama Prefecture is today. I think there were a few swordsmiths who used the name Katsumitsu, so it might be difficult to pinpoint which one is the Katsumitsu in these photos. Also, there are plenty of fakes around, and this sword could have had a fake name put on it centuries ago. Some pictures of the sword itself would help.

Thank you, very interesting learning the history of those sword.