In this paper, we propose an efficient encryption algorithm, without exchanging session keys of a symmetric cryptosystem. The proposed scheme, called as the FAKE(Fast Asymmetric Key Encryption), first scrambles an entire input message and then encrypts small parts of the scrambled message using an asymmetric key encryption scheme. We use the all-or-nothing transform based on the hash function as a scrambling function, which was proposed by Shin, et al. Furthermore, the proposed scheme can additionally provide a digital signature service with only small overhead. AMS Mathematics Subject Classification : 94A60