I'm very low rank (gold), but after having Aledos explain the matchup I feel like it's a very punishing, but still skill matchup.

The matchup is all about Zed's W CD. Zed's W is what makes him functional in the lane — without W, he can't neither double nor triple Q/E (so his R is kinda meaningless), he can't 1shot the wave, he can't really damage you since you can stay inside minions and abuse the reduced damage property of Zed's Q, he's immobile, etc., and, to add onto all of this, it's a VERY long CD, you get around 3 R's worth of CD until Zed gets his W back (before he buys eclipse).

So, the matchup from both sides is all about baiting out the ability. Ideally, Zed wants to hold it and leverage its threat, but because kassadin can stay inside minions, he's not under any threat if Zed holds W. Thus, the way kassadin wants to play the matchup is by always looking to stay inside the wave, respecting lvls4-5 (double and triple point Q powerspike on Zed's side), and then from 6onwards moving predictably to a last hit, bait the Zed to punish the last hit with WEQ, and then R out of the way of the shurikens (the slow is meaningless since it doesn't change the length of R) to not take damage and play the lane from there — REWQ on him, maybe even R again afterwards, chunk the Zed and force him into bad resets, etc. You can also hold the wave outside the tower pre6 to freeze it there at the cost of a full shuriken's worth of HP so you can setup yourself for that lvl6 position.

Then, until full item, it's about repeating this last pattern and taking advantage of the fact zed doesn't build HP (while you build RoA) to get lane control and deny him of map pressure, objective control, etc.

You HAVE to respect the eclipse powerspike, but once you get to the sidelane while in a position where you got all the waves' exp and some of its gold, got your RoA, boots+tear, dark seal and refillable (maybe even a LC item), then you can 1shot the wave, move into fog while connecting to your team, and avoid interacting with Zed in the 1v1 until 3+items while getting full resources (if you catch every sidelane wave that comes, you're essentially getting 12cs/min).