Simple guide for sharing the same keypair in putty and cygwin (openssh).
Start by running puttygen.exe (not bundled with putty, must be downloaded separately)
Press "generate" to start.
Type in the machine name.
Export the (private) key in a format OpenSSH understands.
Save the file in C:\cygwin\home\USER\.ssh\id_rsa
Copy the public key (the select text in the image)
Paste it in a text editor.
Optionally change the line-ending to UNIX format.
Save the file in C:\cygwin\home\USER\.ssh\id_rsa.pub
Export private key in PPK format.