International Association
for Cryptologic Research

Decades of research in both cryptography and distributed systems has extensively studied the problem of state machine replication, also known as Byzantine consensus. A consensus protocol must usually satisfy two properties: {\em consistency} and {\em liveness}. These properties ensure that honest participating nodes agree on the same log and dictate when fresh transactions get added. They fail, however, to ensure against adversarial manipulation of the actual {\em ordering} of transactions in the log. Indeed, in leader-based protocols (almost all protocols used today), malicious leaders can directly choose the final transaction ordering. To rectify this problem, we propose a third consensus property: {\em transaction order-fairness}. We initiate the first formal investigation of order-fairness and explain its fundamental importance. We also provide several natural definitions for order-fairness and analyze the assumptions necessary to realize them. We also propose a new class of consensus protocols called Aequitas. Aequitas protocols are the first to achieve order-fairness in addition to consistency and liveness. They can be realized in a black-box way using existing broadcast and agreement primitives (or indeed using any consensus protocol), and work in both synchronous and asynchronous network models.

Recent targeted attacks have increased significantly in sophistication, undermining the fundamental assumptions on which most cryptographic primitives rely for security. For instance, attackers launching an Advanced Persistent Threat (APT) can steal full cryptographic keys, violating the very secrecy of “secret” keys that cryptographers assume in designing secure protocols. In this article, we introduce a game-theoretic framework for modeling various computer security scenarios prevalent today, including targeted attacks. We are particularly interested in situations in which an attacker periodically compromises a system or critical resource completely, learns all its secret information and is not immediately detected by the system owner or defender. We propose a two-player game between an attacker and defender called FlipIt or The Game of “Stealthy Takeover.” In FlipIt, players compete to control a shared resource. Unlike most existing games, FlipIt allows players to move at any given time, taking control of the resource. The identity of the player controlling the resource, however, is not revealed until a player actually moves. To move, a player pays a certain move cost. The objective of each player is to control the resource a large fraction of time, while minimizing his total move cost. FlipIt provides a simple and elegant framework in which we can formally reason about the interaction between attackers and defenders in practical scenarios. In this article, we restrict ourselves to games in which one of the players (the defender) plays with a renewal strategy, one in which the intervals between consecutive moves are chosen independently and uniformly at random from a fixed probability distribution. We consider attacker strategies ranging in increasing sophistication from simple periodic strategies (with moves spaced at equal time intervals) to more complex adaptive strategies, in which moves are determined based on feedback received during the game. For different classes of strategies employed by the attacker, we determine strongly dominant strategies for both players (when they exist), strategies that achieve higher benefit than all other strategies in a particular class. When strongly dominant strategies do not exist, our goal is to characterize the residual game consisting of strategies that are not strongly dominated by other strategies. We also prove equivalence or strict inclusion of certain classes of strategies under different conditions. Our analysis of different FlipIt variants teaches cryptographers, system designers, and the community at large some valuable lessons: 1.Systems should be designed under the assumption of repeated total compromise, including theft of cryptographic keys. FlipIt provides guidance on how to implement a cost-effective defensive strategy.2.Aggressive play by one player can motivate the opponent to drop out of the game (essentially not to play at all). Therefore, moving fast is a good defensive strategy, but it can only be implemented if move costs are low. We believe that virtualization has a huge potential in this respect.3.Close monitoring of one’s resources is beneficial in detecting potential attacks faster, gaining insight into attacker’s strategies, and scheduling defensive moves more effectively. Interestingly, FlipIt finds applications in other security realms besides modeling of targeted attacks. Examples include cryptographic key rotation, password changing policies, refreshing virtual machines, and cloud auditing.