Observations Concerning a Public-Key Cryptosystem Based on Iterated Morphisms

Abstract A public-key cryptosystem based on iterated morphisms and substitutions was introduced in 1983 by Salomaa and Welzl. The present paper studies this system further. Finding a standard key, that is, finding a decryption key like the secret one used by the designer of the system is the preprocessing method one first thinks of. This approach is shown to lead to an NP-hard problem. The important aspect of growth of the cryptotext with respect to the plaintext is also discussed. A simple tool to guarantee polynomial growth is given. Finally, a natural extension of the system, intuitively increasing its security, is presented.