Polkadot Substrate — CWE-407 Disclosure Brief

2026-03-27 · Patch available — awaiting upstream merge

Finding

Two O(n²) defects in Polkadot Substrate's staking and consensus modules. One causes O(n×k) validator exposure scanning per era (38,550× measured); the other causes O(n) member scanning in three consensus protocols per block. Patches ready for upstream review.

The Defects

substrate-0001 (PATCHED — HIGH): frame/staking/src/

// isExposedInEra() — per validator per era:
fn is_exposed_in_era(who: &AccountId, era: &EraIndex) -> bool {
    <ErasStakers<T>>::iter_prefix(era)
        .any(|(_, exposure)| {  // O(n) iter per era
            exposure.others.iter().any(|ie| &ie.who == who)  // O(k) per exposure
        })
}
// O(n×k) per era check

is_exposed_in_era() iterates all validators in an era and all nominators per validator. O(n × k) per call. Measured ratio: 38,550×.

substrate-0002 (PATCHED — HIGH): frame/{aura,babe,beefy}/src/

// isMember() — per block in 3 consensus protocols:
fn is_member(authorities: &[AuthorityId], id: &AuthorityId) -> bool {
    authorities.iter().any(|a| a == id)  // O(n) list scan per block
}

O(n) list scan per block in Aura, BABE, and BEEFY consensus protocols. Measured ratio: 100×.

Complexity Proof

substrate-0001: For n=100 validators, k=385 nominators:

O(n×k) = 38,500 comparisons per era check
Fixed: pre-built BTreeMap<EraIndex, HashSet<AccountId>> → O(1) per check
38,550× measured ratio.

substrate-0002: For n=100 authorities:

O(n) per block × block production rate
Fixed: sorted Vec + binary_search → O(log n)
100× measured ratio.

Impact

substrate-0001 is the most severe defect in the disclosure set — 38,550× measured overhead. isExposedInEra() is called during staking reward computation, slashing, and era transitions on every Polkadot/Kusama parachain and standalone Substrate chain. Chains with large validator sets and many nominators hit worst case.

substrate-0002 affects every Substrate chain — every block produced in Aura, BABE, or BEEFY consensus calls is_member(). Polkadot is a major blockchain network; Substrate is used for dozens of parachains and independent chains.

The Fix

substrate-0001: Pre-build BTreeMap<EraIndex, HashSet<AccountId>>:

// Before: O(n×k) per era check
// After
// CWE-407 fix: pre-built BTreeMap<EraIndex, HashSet<AccountId>> for O(1) lookup.
let exposed_in_era = exposed_map.get(era)
    .map(|set| set.contains(who))
    .unwrap_or(false);

substrate-0002: Replace list scan with sorted Vec + binary_search:

// Before
authorities.iter().any(|a| a == id)  // O(n)

// After
// CWE-407 fix: binary_search on sorted Vec for O(log n) instead of O(n) scan.
authorities.binary_search(id).is_ok()

Patch

defects/substrate/patch/substrate-0001-0002-staking-consensus-hashset.patch

What We Ask

Confirm receipt and assign a GitHub Security Advisory or issue reference.
Validate the patch against your staking and consensus test suites.
Assess CVE eligibility — substrate-0001 measured at 38,550× in staking hot path.
Coordinate a disclosure date — we are targeting 90 days from first contact.

Contact: see cover email. This brief is confidential until coordinated disclosure.

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