Block ciphers, hash-based encryption, and public-key ciphers are examples of data encryption techniques with different desired features. Strong block ciphers, like AES, must run in some mode of operation to encrypt data larger than the block size. Public-key ciphers, like RSA, are costly and usually used for key-sharing rather than encrypting the data itself. Generic single-hash ciphers are less secure than block ciphers and vulnerable to some cryptanalysis techniques. In this paper, we review some cryptanalysis techniques on AES and some hash-based cryptosystems. We propose a new encryption scheme capable of encrypting big data and supporting both symmetric and asymmetric-key handling. We discuss its security strength against known cryptanalysis attacks. Unlike existing hash-based ciphers, the proposed scheme uses double hashing instead of a single hash function. With double hashing, the proposed scheme totally eliminates the threat of known cryptanalysis attacks and provides a highly secure stream ciphering scheme by its new design.