A cryptographic method, comprising receiving a public key belonging to a message recipient having a private key corresponding to the public key, selecting a numerical seed, having a first entropy, using the numerical seed and the public key, generating key recovery information having a second entropy, which is less than the first entropy, and generating a message key having a third entropy, which is less than the first entropy, encrypting a message using the message key, and transmitting the encrypted message and the key recovery information to the message recipient, whereby the recipient reconstructs the message key using the key recovery information and the private key and decrypts the encrypted message using the reconstructed message key. Related systems and methods are also included.