Searching for combined Wi‑Fi sign-in attacks without hints: a budgeted search and a complete one
A complete search of all 53,485 combinations of up to three attack families, on ten modelled designs, found no escape; a budgeted search of larger combinations found none either.
The lab hardened ten designs for quantum-resistant Wi‑Fi sign-in against known attacks. The worry is attacks that combine several known ones. An automated attacker with no hints searched such combinations within a fixed budget and found no escape. A complete search of every combination of up to three attack families found none either.
What it shows
Quantum-resistant sign-in for Wi‑Fi carries much larger messages than today's handshakes. The lab studied ten candidate designs for it and added repairs against known attacks, such as KRACK. A repair that stops each attack alone may still fail when two or three attacks are used at once. The question is whether any such combination gets through.
Two searches
The lab's claim answers in two parts. First, an attacker that was not seeded with known answers searched combined attacks across all ten designs, within a fixed budget of attempts. It found zero escapes, and every elite it kept, the best attack for each region of its search, was non-vacuous: a real attack rather than an empty one. Second, the lab listed every combination of one, two or three attack families on all ten designs and ran each one. That complete search also found zero escapes.
The two parts support each other. The complete search covers small combinations with certainty. The budgeted search reaches larger combinations, but only as a sample, so its silence is weaker evidence.
Why it matters, and to whom
Wi‑Fi chipset makers, access-point vendors and test labs will have to judge quantum-resistant sign-in designs before they ship. Designers tend to test the attacks they thought of. An attacker that was not seeded with known answers is a fairer test, and a complete search of small combinations removes doubt at that size, within the lab's own list of attack families and its models of the designs.
It also shows how to report a null result. The claim gives the size of the budget and of the complete search, so a reader can see how much ground was covered. "No attack found" then reads as a measured statement about a stated search, not as a proof that the designs are safe.
How it was checked
The claim's word elite comes from quality-diversity search methods such as MAP-Elites, which keep the best attempt in each of many regions of a search space so the search does not collapse onto a single idea; the served files do not name the method the lab used. Each attempt is judged by a verifier, and the scope note says a verifier crash counts as a failure, never as an escape. The evidence file records the command, a run on a clean copy of the code, and the run time: 224.1 seconds.
Testing the check
The lab tested the check by reopening a known attack, KRACK, in its repairs on purpose. The evidence file records that an escape then existed and the check failed, so a run that finds an escape is not reported as clean. The same record names a gap: shrinking the search budget left the check passing, so the check does not guard the budget size the claim states.
What was attacked
The designs, the repairs and the list of attack families are the lab's. The served files do not show the search running against the Wi‑Fi software that ships in real access points or phones.
What it does not claim
- It does not claim that no attack exists. Zero escapes within a budget is a null result, not a theorem. The complete search is exhaustive only up to three attack families, and only within the lab's own list of attack families. Attacks outside that list are not covered at all.
The lab's scope note, from the evidence file, reads: Exhaustive only up to three families per compound; budgeted above that. Every compound of one to three families from each design's composable alphabet was enumerated on all ten designs (53,485) and none escaped: a closure over this declared grammar at those orders only. Compounds of four to ten families are covered only by the MAP-Elites hunt, whose 11,200 evaluations are a budget: zero escapes within it is a null result, not a theorem. A verifier crash counts as FAILURE, never as an escape.
- It does not claim that the search method is new. MAP-Elites was published by Mouret and Clune. Recent work by Shihab and Afrin warns that filling every region of such a search does not bound the worst case that remains unexplored. That warning applies to the budgeted part of this result. It is also why the complete search of small combinations matters: at that size, nothing within the lab's list of attack families is left unexplored.
- It does not claim that the designs are ready to ship. The served files do not show the repairs tested in shipping Wi‑Fi software.
How to reproduce it
The evidence file names the command that re-runs the check. It needs the lab's code at the commit named in the evidence file.
A reader who wants to push harder has two clear options. The first is to extend the complete search to four attack families, which is larger but still finite. The second is to take the strongest combinations the attacker found and replay them against real open-source Wi‑Fi software in a simulated radio. A single escape in either test would show the zero to be an effect of the budget; the scope note already calls it a null result, not a theorem.
Prior art
- Mouret and Clune, "Illuminating search spaces by mapping elites": the MAP-Elites method, which keeps the best attempt, an elite, in each region of a search space
- Shihab and Afrin, "Quality-Diversity Stress Tests for Process Reward Models: What Archive Coverage Can and Cannot Certify": why filling every region of such a search does not bound the worst case left unexplored
Evidence
- The evidence file for this result
- Our claim file, with its limits
- All our published files, each with a fingerprint you can check
Related results across the group
- The chip netlist whose area and delay are published matches its design: a formal equivalence proof
- Ultra Ethernet ordered delivery: one recovery design checked in a model against the standard's rule
- Six slightly weakened bounds checks pass random fuzzing, and two coverage-guided fuzzers find all six
- The same result on VerifyCore Labs, our parent lab