A stream stretcher is provided for securely expanding a key stream to match the length of a data block to be encrypted and/or decrypted. A key stream is obtained having a length of LZ bits. A length LD corresponding to a data block to be encrypted/decrypted is obtained, where LD>LZ. LD−LZ new bits are recursively generated by combining at least two bits of the key stream. The LD−LZ new bits are appended to the key stream to generate a stretched key stream. The data block may then be encrypted/decrypted with the stretched key stream. The at least two bits are selected to have offsets that form a full positive difference set.