Most of the cryptosystems currently used are based on number theoretic problems. We focus on cryptosystems based on finite automata (FA) which are lightweight in nature and have relatively small key sizes. The security of these systems relies on the difficulties in inverting non-linear finite automata and factoring matrix polynomials. In symmetric or single key encryption, the secret key consists of two finite automata and their inverses. By applying the inverses of the automata to the cipher text, the plain text can be effectively calculated. In case of asymmetric or public key encryption, the public key consists of another automaton, which is the combination of the two finite automata while the private key consists of the inverse of the two individual automata. It is hard to invert the combined automaton without the knowledge of the private key automata. We propose a third variant which is based on a 128-bit key and uses a DES-based key generation algorithm. We implement and test all three cryptosystems - the standard single key and public key cryptosystems as well as our novel DES-based FA cryptosystem. We also extensively test the finite automata cryptosystems on a standard desktop machine as well as the Nokia N900 smartphone. All statistical tests carried out on the ciphertext are satisfactory. / Graduate