A processor generates an asymmetric crypto-key, such as an RSA crypto-key, which is associated with the user and includes a private key and a public key. It computes a first key portion based on a stored random number generation function, which has one or more constants such as a salt and/or iteration count, and a first value of a constant, and a second key portion based on the computed first key portion and one of the private key and the public key. It additionally computes another first key portion based on the stored random number generation function and a second value of that constant, and another second key portion based on the computed other first key portion and the one key. The computed first and second key portions and the computed other first and second key portions form first and second splits of the one key of the asymmetric crypto-key.