Cyber security adversaries and engagements are ubiquitous and ceaseless. We delineate Adversarial Genetic Programming for Cyber Security, a research topic that, by means of genetic programming (GP), replicates and studies the behavior of cyber adversaries and the dynamics of their engagements. Adversarial Genetic Programming for Cyber Security encompasses extant and immediate research efforts in a vital problem domain, arguably occupying a position at the frontier where GP matters. Additionally, it prompts research questions around evolving complex behavior by expressing different abstractions with GP and opportunities to reconnect to the Machine Learning, Artificial Life, Agent-Based Modeling and Cyber Security communities. We present a framework called RIVALS which supports the study of network security arms races. Its goal is to elucidate the dynamics of cyber networks under attack by computationally modeling and simulating them.