This document analyses the capabilities of an adversary who controls a fraction of DA nodes and attempts to manipulate the data availability perception of validators. Unlike a simple denial-of-service adversary who tries to make data globally unavailable, this adversary exploits the statistical nature of the sampling protocol in two complementary directions.
Attack A — Available → Unavailable (Type II exploitation). The data is genuinely available, but the adversary causes targeted validators to conclude it is unavailable. This exploits Type II error. The adversary benefits by causing honest leaders to waste slots, disrupting liveness, or by creating asymmetric chain views across validators.
Attack B — Unavailable → Available (Type I exploitation). The data is genuinely unavailable or has been withheld by the adversary after dispersal, but the adversary causes targeted validators to conclude it is available. This exploits Type I error. The adversary benefits by inserting unrecoverable data into the chain.
Both attacks are governed by the same underlying combinatorial structure: how many subnetworks the adversary can influence, and how the sampling and retry decision rule responds to that influence. The analysis below derives general formulas in terms of all protocol parameters without fixing any specific numerical values.
Throughout this document the adversary is assumed to be silent — adversarial nodes do not respond to sampling requests from targeted validators. They do not send false proofs or invalid data. The analysis of adversarial nodes that respond with false proofs is deferred to a separate analysis.
| Symbol | Meaning |
|---|---|
| N | Total columns in expanded data = total number of subnetworks |
| e | RS expansion factor |
| K | Reconstruction threshold = N/e |
| n | Total DA nodes in the network |
| k | Number of adversarial DA nodes |
| $p_d$ | Fraction of adversarial nodes = k/n |
| R | Number of nodes assigned to each subnetwork |
| S | Number of subnetworks sampled per validation round |
| τ | Acceptance threshold: declare available if ≥ τ successes out of S |
| t | Number of nodes tried per subnetwork before declaring it failed (1 ≤ t ≤ R) |
The Logos Blockchain DA layer encodes blob data into $N = e·K$ columns using Reed-Solomon coding with expansion factor e, and distributes the columns across $N$ subnetworks, each holding $R$ nodes. The data is recoverable if at least $K+1$ of any columns are available. To verify availability, a validator samples $S$ subnetworks uniformly at random and queries up to $t$ nodes within each sampled subnetwork. If at least one of the $t$ queried nodes responds with a valid proof, that subnetwork is counted as a success. The validator declares the blob available if and only if at least $τ$ out of $S$ subnetworks succeed. An adversary controlling $k$ out of $n$ total DA nodes — a fraction $p_d = k/n$ — can exploit this decision rule in two directions, as described below.
Before the formal derivations, this section summarizes the key structural findings. The central question is: as the adversary controls a larger fraction $p_d$ of DA nodes, how effective do the two attacks become, and how does each protocol parameter change that relationship?
For given $(R, S, \tau, e)$, the adversarial fraction $p_d$ determines which attack regime the network is in.
🟢 Safe zone — $p_d < (\tau/S)^{1/R}$
Neither attack is meaningful. The adversary does not control enough subnetworks to cause targeted validators to fail sampling, and does not have enough fully captured subnetworks to push a validator above the $\tau$ threshold on fake successes.
🟡 Attack A only — liveness threat — $(\tau/S)^{1/R} \leq p_d < (1 - 1/e)^{1/R}$
The adversary can cause targeted validators to fail sampling by silently withholding responses. The data remains globally recoverable. The threat is to liveness: honest leaders waste slots, validators develop split views, chain growth slows. This is the primary practical threat zone — reachable well below majority control.
🔴 Attack A + B — safety threat — $p_d \geq (1 - 1/e)^{1/R}$
The adversary can both cause targeted validators to fail on available data (Attack A) and cause validators to accept genuinely unavailable data (Attack B). This regime requires near-majority or majority node control. The threshold always exceeds 50% for any $e \geq 2$ and $R \geq 1$.
| Parameter | Effect on Attack A | Effect on Attack B | Attack A threshold | Attack B threshold |
|---|---|---|---|---|
| τ ↑ | Stronger — only S−τ+1 failures needed | Weaker — more hits needed | $(τ/S)^{1/R}$ shifts right | unchanged |
| t ↑ toward R | Weaker (less partial capture) | No effect | unchanged | unchanged |
| R ↑ | Weaker (exponential) | Weaker (exponential) | shifts right | shifts right |
| e ↑ | No effect | Weaker (higher recovery threshold) | unchanged | shifts right |
| N ↑ | No effect | Stronger (more captured subnets) | unchanged | unchanged |
| S ↑ | Both attacks scale with S | Both attacks scale with S | $(τ/S)^{1/R}$ shifts | unchanged |
The Attack A threshold, $(\tau / S)^{1/R}$, is derived from the condition that the expected number of subnetwork failures in a sample of $S$ reaches $S - \tau + 1$, using the full-capture probability $p_d^R$ as the dominant term.