Destructible Authorization Factors

• Destructible authorization factors are secret credential components held by independent custodians that can be selectively released or irreversibly destroyed to control access within cryptographic systems.
• When integrated into CT-DAP, these factors enable condition-triggered activation and stateless revocation, ensuring that any destroyed element permanently disables the corresponding access path.
• Practical implementations leverage Argon2id for composite credential generation and HKDF-SHA256 for key derivation, balancing security with sub-second activation times for diverse custody applications.

A destructible authorization factor is a secret share or credential component within a cryptographic asset control system, held by an independent custodian who can either release or irreversibly destroy it. When employed in Condition-Triggered Dormant Authorization Paths (CT-DAP), these destructible factors underpin a mechanism for asset control that admits stateless, cryptographically enforced revocation and conditional delegation, without persistent key exposure, on-chain state mutation, or reliance on trusted intermediaries. This architecture is parameterized by a root-derivable framework supporting deterministic key derivation, strict context isolation, and authorization-bound revocation. The following exposition reviews definitions, key mechanisms, proof sketches, a concrete instantiation, and performance characteristics (Wang, 9 Mar 2026).

1. Formal Definition and Model

A destructible authorization factor is created and held by an independent custodian, distinct from the user, who possesses the power to either release the factor or permanently destroy it. In CT-DAP, each access pathway is formalized as a dormant authorization path $AP_j$, which comprises:

• $SA_{\rm root}$: a sealed artifact (AEAD ciphertext) of the root entropy $REV$,
• $s_j \in \{0,1\}^{128}$: a public, per-path salt,
• $UserCred_j$: a user-held secret credential,
• $\{AdminFactor_{j,i}\}$: the set of destructible factors.

The composite credential required to unlock the sealed artifact is produced as

$$Cred_{\rm composite} =\mathsf{Argon2id}\bigl(UserCred\parallel AdminFactor_1\parallel\cdots\parallel AdminFactor_n;\;s;\;m,t,p\bigr).$$

If any $AdminFactor_{j,i}$ is withheld, the path remains dormant and cryptographically inactive. The path becomes activated only when all custodial factors are present, permitting recovery of $REV$ via unsealing. If at least one factor is destroyed (secure erasure), the corresponding path is rendered irrevocably inactive without modifying the cryptographic root.

The CT-DAP protocol is parameterized over an abstract root-derivable framework

$$\Pi = (\mathsf{Setup}, \mathsf{Seal}, \mathsf{Unseal}, \mathsf{Derive})$$

with the following key features:

• Sealing Indistinguishability: AEAD encryption for $SA$ satisfies IND-CPA and INT-CTXT.
• Unsealing Correctness: Incorrect or partial credentials cause unseal to output $\bot$.
• Context Isolation: Derived keys for distinct contexts are cryptographically independent.
• Authorization-Bound Revocation: Erasure of any single factor makes unsealing of the relevant path impossible.

2. Cryptographic Mechanisms and Protocol Flow

Destructible authorization factors interact as follows:

1. Issuance: The system performs an initial setup to obtain the root entropy $REV$ and system parameters. The composite credential is generated using Argon2id with all components, and $REV$ is sealed using AEAD to yield $SA_{\rm root}$.
2. Conditional Activation: Upon satisfaction of a predefined condition (user consent, regulatory mandate, time lock, etc.), each custodian individually releases their factor. Only when all factors and the user credential are present can $REV$ be recovered using $\mathsf{Unseal}(\cdot)$; otherwise, the attempt fails.
3. Key Derivation: The recovered $REV$ is expanded using HKDF-SHA256 into a path-specific key based on an associated context $Ctx_j$, such that

$PRK = \mathrm{HKDF\text{-}Extract}("CT\text{-}DAP\text{-}v1", REV), \quad \KeyAP_j = \mathrm{HKDF\text{-}Expand}(PRK, \mathsf{Encode}(Ctx_j), L).$

1. Stateless Revocation: If a custodian executes a secure erase of their destructible factor, the composite credential can never be reconstructed, and access to the associated authorization path is permanently revoked. This action occurs independent of global state changes or on-chain events.

3. Threat Model and Security Properties

The adversary model assumes a probabilistic polynomial time (PPT) adversary possessing:

• The ability to compromise up to $t < n$ custodians,
• Potential access to $SA_{\rm root}$,
• Observation of derived keys in unrelated paths,
• Interaction opportunities with the verifier, but
• No access to the full composite credential of a target path.

Security goals in the CT-DAP framework include:

• Unauthorized Control Resistance (UCR): Adversaries lacking full credentials for a path cannot derive $\KeyAP^*$.
• Cross-Path Isolation (CPI): Gaining control of one path yields no advantage on another (separation ensured via HKDF-derived keys and context separation).
• Stateless Revocation (SR): Destruction of any factor blocks all future attempts to recover $REV$ and derive the key, with the AEAD unseal operation yielding $\bot$ for all credential attempts.

Security is formalized using game-based proofs:

• In the UCR game, adversary success probability is bounded as

$$\Pr[A\text{ wins}] \le \mathrm{Adv}_{\rm Seal}^{\rm IND\text{-}CPA} + \mathrm{Adv}_{\rm MH} + \mathrm{Adv}_{\rm PRF} = negl(\kappa),$$

assuming the standard cryptographic assumptions (AEAD security of AES-GCM-SIV, PRF security of HKDF, memory-hardness of Argon2id, collision resistance of SHA-256).

4. Instantiation via the Atomic Cryptographic Entity Generative Framework (ACE-GF)

The ACE-GF instantiation demonstrates the practical application of destructible authorization factors within CT-DAP. System setup involves the following pseudocode:

PathSetup(1^κ, UserCred, {AdminFactor_i}) -> (REV, params) <- ACE-GF.Setup(1^κ) s <- {0,1}^128 Cred <- Argon2id(UserCred || ... || AdminFactor_n; s) SA <- ACE-GF.Seal(params, Cred, REV) Zeroize(REV) return (SA, s, params)

Conditional activation combines all secrets via Argon2id, then attempts to unseal $REV$:

Activate(SA, s, UserCred, {AdminFactor_i}, Ctx) -> Cred <- Argon2id(UserCred || ... ; s) REV <- ACE-GF.Unseal(params, SA, Cred) if REV == ⊥ then return ⊥ K <- ACE-GF.Derive(REV, Ctx) Zeroize(REV) return K

Revocation simply mandates secure erasure:

Revoke(i): custodian i securely erases AdminFactor_i → path becomes permanently unusable.

Dormant paths require simultaneous possession of all user and administrative credentials; only then can the cryptographic root and derived capabilities be reconstructed.

5. Performance Metrics and Security–Performance Trade-Offs

Benchmarks on contemporary consumer hardware (Apple M2, single core) demonstrate the following latencies:

• Argon2id ($m=256$ MiB, $t=3$, $p=4$): 482 ms
• AES-GCM-SIV seal/unseal: ≈0.003 ms
• HKDF-SHA256 derive: ≈0.005 ms
• Full path activation: ≈483 ms

Latency is dominated by Argon2id, which is configurable to tune the trade-off between brute-force resistance and usability:

Memory ($\mathrm{MiB}$)	Latency (ms)	Use Case
64	118	Mobile/IoT
128	239	Desktop wallets
256	482	Custody infra
512	971	Cold storage

For all configurations, activation remains sub-second, even at the highest security levels.

6. Context and Significance

Destructible authorization factors, as deployed in CT-DAP, advance cryptographic asset control by enabling reversible, stateless, and composable delegation/termination of access rights. The capability to cause irremediable path revocation without modification of cryptographic roots is especially significant for regulatory compliance, conditional transfers (such as inheritance or escrow), and scenarios demanding strong off-chain controls with no persistent exposure of sensitive keys. This approach circumvents limitations of multi-signature, threshold, and on-chain approaches, which inherently require key material or on-chain mutability with associated trust assumptions (Wang, 9 Mar 2026).

A plausible implication is increased adoption in regulated environments requiring event-driven activation and post hoc, provable revocation, as well as wider deployment for institutional-grade custodial security. The threat model and formal proofs in CT-DAP establish a rigorous baseline for further research on composable, revocable cryptographic delegation mechanisms.