This book explores public key cryptographic systems, first investigating the question of cryptographic security of bits in the RSA encryption and then constructing a new knapsack type public key cryptosystem, based on arithmetic in finite fields. In Part I, two problems involving the RSA encryption of a message are proved to be equivalent. This equivalence implies that an adversary, given the ciphertext, can't do better than guessing unless s/he can break the RSA code. The results generated by the author's proof indicate that Rabin/RSA encryption can be directly used for pseudo random bit generation. A new knapsack type public key cryptosystem is introduced in Part II, along with a detailed description of its implementation. The system is based on a novel application of arithmetic in finite fields, following a construction by Bose and Chowla. By choosing appropriate parameters, the density of the resulting knapsack can be controlled. In particular, the density can be made high enough to foil low-density attacks against this new system. At present there are no known attacks capable of breaking the system in a reasonable amount of time.
Two Issues in Public Key Cryptography: RSA Bit Security and a New Knapsack Type System is a 1985 ACM Distinguished Dissertation.