The Graph Is the Message: Design and Analysis of an Unconventional Cryptographic Function

An algorithm is described for encrypting a graph to be transmitted securely from a sender to a receiver. In communications terminology, \the graph is the message": its vertices, its edges, and its edge weights are the information to be concealed. The encryption algorithm is based on an unconventional mapping, conjectured to be a trapdoor one-way function, designed for graphs. This function requires the sender and the receiver to use a secret one-time encryption/decryption key. It is claimed that a malicious eavesdropper with no knowledge of the key will be faced with a computational task requiring exponential time in the size of the input graph in order to extract the original plaintext from the ciphertext carried by the encrypted graph. A number of variants to the main algorithm are also proposed.