Bankrupting DoS Attackers

TL;DR

The paper tackles whether a server can economically deter denial-of-service attackers by pricing service based on an estimator of past good-job arrivals. It introduces two online algorithms, LINEAR and LINEAR-POWER, that adjust prices using an estimator to ensure the defender’s total cost grows more slowly than the attacker’s cost, achieving asymptotic advantages under accurate estimators. A lower bound via Yao’s principle shows the results are tight for constant estimation gap $\\gamma$, and the authors develop several estimators (e.g., Poisson, Weibull/Gamma, adversarial queuing) to demonstrate broad applicability. The work connects DoS defense with resource-burning and online algorithms, showing how predictions (estimators) can yield robust cost guarantees even in adversarial settings and asynchronous communications. Overall, the framework provides a principled way to deter large-scale DoS by making attackers incur higher costs while preserving service for honest clients.

Abstract

Can we make a denial-of-service attacker pay more than the server and honest clients? Consider a model where a server sees a stream of jobs sent by either honest clients or an adversary. The server sets a price for servicing each job with the aid of an estimator, which provides approximate statistical information about the distribution of previously occurring good jobs. We describe and analyze pricing algorithms for the server under different models of synchrony, with total cost parameterized by the accuracy of the estimator. Given a reasonably accurate estimator, the algorithm's cost provably grows more slowly than the attacker's cost, as the attacker's cost grows large. Additionally, we prove a lower bound, showing that our pricing algorithm yields asymptotically tight results when the estimator is accurate within constant factors.

Figures (8)

• Figure 1: Pseudocode for LINEAR.
• Figure 2: Pseudocode for LINEAR-POWER.
• Figure 3: (Left) LINEAR with iterations of length $1/\lambda$, using the estimator from the zero-latency example in Section \ref{['s:scenarios']}. Black circles are good jobs, red circles are bad. Since the estimation gap is small, each iteration contains about $1$ good job. (Right) Blowup of the last iteration, with $b_i$ bad jobs followed by $1$ good job. The adversary's cost is $B_i = \Omega(b^2_i)$ and the algorithm's cost is $A_i = O(b_i)$, as described in Section \ref{['s:scenarios']}.
• Figure 4: The blue circle is a job that is repeatedly bounced, the black circles are other serviced jobs. Arrows are communication from the server to the client of the $\textrm{PRICE}\xspace$ value, and from the client to the server of fees. The blue job is bounced $3$ times and pays $1+2+4+8$.
• Figure 5: Illustration of an exchange of one bad job (a red ball) from iteration $k$ to iteration $i$, with all good jobs (black balls) remaining in place. The change in cost for iteration $i$ is $\delta(b_i)$, and change in cost for iteration $k$ is $\delta(b_k - 1)$. The Mean Value Theorem (MVT) says that for any integer $x$, the value of $\delta(x)$ equals $f'(y)$ for some $y \in [x,x+1]$. Using the convexity of $f'$ (for $\alpha\xspace \geq 1$), this implies that $\delta(b_i) \geq \delta(b_k - 1)$. This means that the exchange shown can only increase the algorithmic cost.

Theorems & Definitions (39)

• theorem 1
• theorem 2
• theorem 3
• proof
• lemma 1
• proof
• lemma 2
• proof
• lemma 3
• proof