A Public Key Encryption System Derived from the Pascal Parallelogram

The problem faced by all symmetric or private key cryptosystems is the difficulty of communicating the private key to all participants in the network. The degree of key sharing is on the order of the square of the number of nodes in the network. The concept of asymmetric or public key cryptology effectively solved this problem by dividing the key into two parts, one of which is made public. The remaining part need never be transmitted beyond the creator of the key. At the beginning of the era of public-key cryptology, many proposed cryptosystems were based on the classic subset sum knapsack problem. However most of these were shown to be insecure by the research of Lagarias and Odlyzko, and also Brickell. In this paper, we modify a previous method that we originally called the Pascal Knapsack Method. The current approach improves on security and computation time and provides a reasonable alternative to the most common public-key cryptosystem, the Rivest-Shamir-Adleman PKC.