The construction of a public key cryptosystem is based on the idea of a trapdoor. Without the secret information in the trapdoor, the cryptanalyst who only has the public information finds it difficult to decode a ciphertext. The trapdoor information allows the legal recipient to decode the message easily.

The main purpose of this paper is to illustrate the usefulness of syntactic methods in the construction of public key cryptosystems for picture languages. The authors describe two types of public key cryptosystems. In the first system, pictures to be encrypted are represented in chain-code picture languages, while in the second system they are represented as arrays. In both systems, the basic idea is to make cryptanalysis equivalent to the membership problem for TOL systems (which is NP-complete). The public encryption key is a generative grammar, and the encryption algorithm uses a morphism for the conversion. The trapdoor hides information about this morphism.

The paper contains encryption and decryption algorithms and is peppered with examples. The authors assume a familiarity with the basic concepts of L-systems.