$ vagrant up
Bringing machine 'default' up with 'virtualbox' provider...
There are errors in the configuration of this machine. Please fix
the following errors and try again:
SSH:
* `private_key_path` file must exist: C:\cygwin64\home\USER/.vagrant.d/insecure_private_key
Solution:
Copy from : C:\Users\USER\.vagrant.d\insecure_private_key
To : C:\cygwin64\home\USER/.vagrant.d/insecure_private_key
An alternative override Solution (This is not a real solution but allow you to override the problem):
1. Add any (bad) private_key to C:\cygwin64\home\USER/.vagrant.d/insecure_private_key
2.Connect to the VM (vagrant ssh) using vagrant default user:password -> vagrant:vagrant