Oh you used the desktop apps too? (which is why you'd need syncing. The new Day One comes with Sync disabled.)

I did have the Day One Classic desktop app, but of late my journaling has been only on my phone. I understand though. I've never asked the question about security and you're right about pointing it out. Seems their FAQ admits it's not yet fully secure.

"Security. We've architected Day One Sync to securely store your data. In the future, we'll be offering end-to-end encryption on top of our current server-side encryption."

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