Skip to main content

​
12.1 Temporal Correlation as a Primary Attack Vector

In public blockchains, one of the most powerful tools available to an adversary is temporal correlation. Even when transaction contents are cryptographically hidden, the relative timing between observable events can significantly reduce anonymity. If a deposit is closely followed by a withdrawal of a similar amount, the search space for linkage collapses. Abyss explicitly models time as a first-class privacy variable. Rather than enforcing protocol-level delays, which are rigid and gameable, Abyss provides the structural flexibility for users and applications to introduce temporal uncertainty organically.

​
12.2 Decoupling Deposits and Withdrawals

The protocol makes no assumption that a withdrawal must occur within any bounded time window after a deposit. Commitments persist indefinitely until fully exhausted. This allows users to delay withdrawals arbitrarily, spreading them across blocks, epochs, or even market cycles. Formally, there is no constraint of the form: 
withdraw_time - deposit_time ≤ T
The absence of this constraint is intentional. It ensures that temporal information alone cannot be used to eliminate candidate commitments.

​
12.3 Infinite Withdrawals and Time Smoothing

Because Abyss supports multiple withdrawals from a single commitment, users can smooth their activity over time: 
withdrawals := { w₁ at t₁, w₂ at t₂, …, wₙ at tₙ }
Where: 
t₁, t₂, …, tₙ are arbitrary and non-uniform
This behavior mimics natural spending patterns and resists timing-based heuristics. From an observer’s perspective, each withdrawal is statistically independent of the original deposit.

​
12.4 Application-Level Scheduling

Abyss is designed to support wallets and applications that manage withdrawal timing automatically. For example:
  • Randomized withdrawal delays
  • Batched merchant settlements
  • Periodic payroll disbursements
  • Event-triggered payouts
All of these increase entropy without requiring protocol-level intervention.

​
12.5 No Enforced Delays: Rationale

Protocols that enforce minimum delays create predictable patterns. Adversaries can adapt by aligning observation windows. Abyss avoids this by making time an emergent property of user behavior rather than a hard-coded rule.

​
12.6 Failure Modes

Temporal privacy degrades when:
  • A single user dominates pool activity
  • Deposits and withdrawals are immediately paired
  • Usage volume is extremely low
These are usage-level risks, not protocol failures.

​
12.7 Summary

Temporal privacy in Abyss is achieved through optionality, not enforcement. By allowing commitments to persist and withdrawals to occur freely over time, the protocol maximizes uncertainty and resists correlation without introducing brittle constraints.