Threshold and availability model

The DeRec protocol uses a threshold-based recovery model to balance security and availability. This model defines how many Helpers participate in protection and how many must cooperate for recovery to succeed.

Parameters

Let:

• n = total number of Helpers in the Helper Set

• t = recovery threshold

Recovery succeeds only if at least t valid shares are obtained from distinct Helpers.

Condition for recovery:

t ≤ number of valid shares ≤ n

Security condition:

valid shares < t → reconstruction of the Secret is impossible

These guarantees derive from the underlying threshold secret-sharing scheme used by the protocol.

Protocol-enforced floor: t ≥ 2

Implementations MUST reject thresholds below 2. A threshold of 0 is meaningless; a threshold of 1 collapses the scheme to a single-share secret and lets any single Helper unilaterally reconstruct the Secret, defeating the entire point of threshold sharing. Two is the minimum value that preserves confidentiality against a single compromised Helper.

The protocol enforces this floor at configuration time — an attempt to build a protocol instance with t < 2 is rejected before any flow can be initiated.

Security vs Availability Trade-off

The choice of threshold directly affects both resilience and recoverability.

Higher threshold (t close to n):

• Stronger resistance to collusion

• Lower tolerance for Helper unavailability

Lower threshold (t much smaller than n):

• Higher availability

• Lower resistance to collusion

The protocol does not mandate a specific threshold beyond the t ≥ 2 floor above. Within that constraint, t is configured by the Owner based on risk tolerance and Helper independence.

Availability Model

Availability depends on the number of Helpers that are reachable and operational at recovery time.

• Recovery succeeds if — available_helpers ≥ t

• Recovery fails if — available_helpers < t

This means the system can tolerate up to:

• n - t unavailable Helpers

Example:

If n = 5 and t = 3:

• Up to 2 Helpers may be offline

• At least 3 must be available for recovery

Collusion Model

Security assumes that fewer than t Helpers collude. If t or more Helpers combine their shares independently of the Owner, reconstruction of the Secret becomes possible.

Therefore:

• Increasing t increases resistance to collusion

• Decreasing t reduces collusion resistance

Helper independence is critical. Operating multiple Helpers under the same administrative or security domain weakens the practical threshold guarantees.

Failure Scenarios

The threshold model behaves predictably under common failure conditions.

• Single Helper compromise — Security preserved if t > 1. The protocol-enforced floor of t ≥ 2 guarantees this baseline holds for every configuration the library will accept.

• Partial Helper compromise — Security preserved as long as compromised Helpers < t.

• Helper outages — Recovery possible if available Helpers ≥ t.

• Malicious Helper responses — Invalid or manipulated shares can be detected through protocol validation and cryptographic commitments.

• Threshold misconfiguration — Security or availability may be weakened due to operational choices, not protocol failure.

Practical Configuration Examples

n	t	Tolerates Offline Helpers	Collusion Resistance
3	2	1	1 compromised Helper
5	3	2	2 compromised Helpers
7	4	3	3 compromised Helpers

The optimal configuration depends on:

• Trust distribution across Helpers

• Operational reliability of Helpers

• Risk tolerance for collusion

• Desired recovery reliability

Replicas and the threshold model

The threshold model is defined entirely in terms of the Helper Set. Replicas — additional devices under the same Owner identity that hold a synchronized copy of the Secret — do not participate in threshold sharing and do not lower the threshold required for recovery from Helpers.

Replicas add an availability layer on top of the threshold model: a device that holds a current snapshot of the Secret already has the user-facing data and does not need to drive a recovery flow at all. The threshold-recovery path remains available as a fallback when no Replica has a fresh enough Secret. See Replicas for the full discussion.

Design Implication

The threshold model is the core security mechanism of DeRec. It ensures that recovery authority is distributed and that no single Helper can unilaterally enable reconstruction.

Availability and security are not fixed properties of the protocol. They are configuration outcomes determined by the chosen values of n and t, as well as the operational independence of Helpers.