WannaCry NewsAvailable tools make a Dent in WannaCry Encryption
XP does not overwrite public key.
WannaKey, WannaDecrypt tools
WannaKey will recover the Public Key in XP.
Then, it is possible to rebuild the private key
With the private key, the WannaDecrypt tool will decrypt the files on the ransomed machine.
WannaKiwi will recover the Public Key in XP and Win 7 implying it will work in more recent Win OSs.
It does not look for the actual key, it searches through the wcry executable dropped by the ransomware in memory for the prime numbers from which the private key can be recomputed.