Atomic Cryptographic Entity Framework (ACE-GF)

• ACE-GF is a cryptographic framework that deterministically derives context-bound keys without seed storage, enabling robust access control and identity attestation.
• It employs primitives like AEAD, HKDF, and Argon2id to support stateless revocation and compositional authorization through destructible factors.
• ACE-GF underpins models such as CT-DAP and AR-ACE, providing efficient, post-quantum secure mechanisms for cryptographic asset custody and blockchain protocols.

The Atomic Cryptographic Entity Generative Framework (ACE-GF) is a root-derivable, seed-storage-free cryptographic abstraction that underpins advanced access control, capability isolation, and identity attestation systems across cryptographic asset management and post-quantum blockchain protocols. Its fundamental contribution is a deterministic yet context-isolated key derivation architecture with strong support for stateless revocation and per-context capability binding, anchored in contemporary security reductions and efficient instantiations. ACE-GF has served as the core primitive for constructs such as Condition-Triggered Dormant Authorization Paths (CT-DAP) for asset custody and AR-ACE, a lightweight proof-off-path attestation relay suitable for post-quantum networks (Wang, 9 Mar 2026, Wang, 9 Mar 2026).

1. Formal Structure and Core Algorithms

ACE-GF is defined by a tuple of core algorithms: $$\text{ACE-GF} = (\mathsf{Setup}, \mathsf{Seal}, \mathsf{Unseal}, \mathsf{Derive})$$

• $\mathsf{Setup}(1^\lambda)$ samples a 256-bit root entropy $REV \in \{0,1\}^{256}$ and outputs public parameters $\mathsf{params}$ (e.g., AEAD IV size, HKDF label).
• $$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$ encrypts $REV$ using AES-256-GCM-SIV under a composite credential, outputting a BIP-39–encoded ciphertext $SA$.
• $\mathsf{Unseal}(\mathsf{params}, SA, Cred')$ reconstructs $REV$ if and only if authentication via derived decryption key (from $Cred'$) succeeds.
• $\mathsf{Setup}(1^\lambda)$0 computes a context-bound key $\mathsf{Setup}(1^\lambda)$1 via

$\mathsf{Setup}(1^\lambda)$2

Context encoding ensures unique, collision-resistant derivation for each $\mathsf{Setup}(1^\lambda)$3 triple.

This construction is seed-storage-free: root secret material is never directly persisted—only encrypted or KDF-hardened images are required for recovery, enforcing statelessness and minimizing persistent high-entropy key exposure (Wang, 9 Mar 2026).

2. Compositional Authorization via Destructible Factors

Authorization in ACE-GF can be composed of a user-held credential $\mathsf{Setup}(1^\lambda)$4 and $\mathsf{Setup}(1^\lambda)$5 independent administrative factors $\mathsf{Setup}(1^\lambda)$6, with the composite credential defined as

$\mathsf{Setup}(1^\lambda)$7

Here $\mathsf{Setup}(1^\lambda)$8 is a per-path salt and $\mathsf{Setup}(1^\lambda)$9 are memory, iteration, and parallelism parameters for the Argon2id memory-hard KDF. Destroying any $REV \in \{0,1\}^{256}$0 renders $REV \in \{0,1\}^{256}$1 and thus $REV \in \{0,1\}^{256}$2 permanently unrecoverable through that path, enabling stateless, cryptographically enforced revocation.

This factorization enables complex access semantics such as conditionally triggered reconstitution (e.g., via time-based, event-driven, or externally authorized factor release) and one-time activation, central to dormant authorization path architectures in regulated or policy-bound digital asset control (Wang, 9 Mar 2026).

3. Security Model and Guarantees

ACE-GF's instantiations rely on widely analyzed primitives: AEAD security of AES-GCM-SIV, PRF-security of HKDF, memory-hardness of Argon2id, and collision resistance of SHA-256.

Threat models are formalized through security games:

• Unauthorized Control Resistance (UCR): Adversary learns up to $REV \in \{0,1\}^{256}$3 credential components for a path and public metadata, then attempts key recovery for a challenge context $REV \in \{0,1\}^{256}$4. Success probability is negligible, bounded by the security of constituent primitives.
• Cross-Path Isolation (CPI): Compromise of $REV \in \{0,1\}^{256}$5 gives no advantage for recovering $REV \in \{0,1\}^{256}$6 for unrelated $REV \in \{0,1\}^{256}$7, ensured by context separator in HKDF-Expand.
• Stateless Revocation: Secure erasure of any $REV \in \{0,1\}^{256}$8 disables all paths relying on that factor, without root mutation or registry updates. The ACE-GF design achieves auditability via destruction logs but requires no state synchronization or rekeying (Wang, 9 Mar 2026).
• Attestation Unforgeability: In relay settings, existential unforgeability under chosen-message attack (EUF-CMA) and resistance to replay/cross-domain attacks is directly tied to the EUF-CMA property of the underlying signature and collision resistance of the object hash function (Wang, 9 Mar 2026).

4. Context-Isolated Derivation and Capability Binding

ACE-GF systematically binds contextual information to derived cryptographic keys and capabilities. For a given $REV \in \{0,1\}^{256}$9 and a context string $\mathsf{params}$0 (e.g., comprising algorithm identifiers, asset domains, relay types, application indices), the framework deterministically and exclusively derives a key unique to that tuple: $\mathsf{params}$1 This approach is exploited in AR-ACE for post-quantum blockchain relay protocols: different operational roles (such as mempool attestation, block production, or chain governance) each derive keys in domain-separated “contexts,” ensuring operational and security isolation without multiple master secrets (Wang, 9 Mar 2026).

5. Protocol Instantiations and Operational Roles

A. CT-DAP for Cryptographic Asset Control:

ACE-GF instantiates the CT-DAP model, where each dormant authorization path is an independent tuple $\mathsf{params}$2, binding to a unique $\mathsf{params}$3 and $\mathsf{params}$4. Activation requires factor release, and key derivation for usage is fully context-bound: $\mathsf{params}$5 Revocation of any $\mathsf{params}$6 disables only its path—other paths with independent $\mathsf{params}$7 sequences and context definitions are unaffected, providing strong per-capability isolation (Wang, 9 Mar 2026).

B. AR-ACE for Post-Quantum Blockchain Attestation:

With respect to relaying objects on post-quantum networks, ACE-GF-derived attestation keys allow participants to sign low-bandwidth eligibility attestations: $\mathsf{params}$8 Here relay context keys are derived as

$\mathsf{params}$9

facilitating proof-carrying object propagation while removing full proof objects (such as recursive STARKs) from the relay path entirely (Wang, 9 Mar 2026).

6. Performance Evaluation and Security-Performance Tradeoffs

Implementation profiling shows the cost of ACE-GF is dominated by the Argon2id key strengthening phase. On Apple M2 (single core, 3.49 GHz), representative timings are:

Operation	Mean Latency	Std Dev
$$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$0	0.02 ms	<0.01 ms
Argon2id (256 MiB)	482 ms	11 ms
$$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$1/$$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$2	0.003 ms	<0.001 ms
$$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$3	0.005 ms	<0.001 ms
End-to-end $$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$4	483 ms	11 ms

Performance is tunable via Argon2id memory usage:

Argon2id $$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$5 (MiB)	Latency (ms)	Use Case
64	118	Mobile / IoT
128	239	Desktop wallets
256	482	Custody infrastructure
512	971	Cold storage

Operations not involving Argon2id (e.g., AEAD, HKDF) are negligible on modern hardware. Even at high-security settings, sub-second activation latency is standard (Wang, 9 Mar 2026).

AR-ACE’s relay path removes all heavy proof-carrying overhead; relay nodes handle only small attestations (64–256 B classically, ~2.5 KB PQC) per object, removing up to order-of-magnitude bandwidth and CPU cost compared to recursive-STARK per-tick proofs (Wang, 9 Mar 2026).

7. Applications, Limitations, and Security Considerations

ACE-GF’s root-derivable, context-isolated, composable architecture renders it suitable for programmable, policy-governed cryptographic custody, survivable key management, and blockchain protocol roles requiring unified, domain-segregated key derivation. Its destructible factor mechanism establishes stateless, audit-friendly revocation without rekeying or on-chain mutation.

Stateless security comes with operational trade-offs: factor destruction is irrevocable, and recovery mechanisms rely entirely on redundant backup of remaining authorization factors. A plausible implication is that ACE-GF cannot natively handle reconstitution in adversarial loss-of-factor scenarios without separate recovery channels.

Security proofs anchor all main properties on strong security reductions to well-established primitives; for example, unauthorized control resistance and path isolation are both negligible in $$\mathsf{Seal}(\mathsf{params}, Cred_{\mathrm{composite}}, REV)$$6 under the AEAD, PRF, memory-hard, and collision-resistant assumptions specified (Wang, 9 Mar 2026).

• Condition-Triggered Cryptographic Asset Control via Dormant Authorization Paths (Wang, 9 Mar 2026)
• ACE-GF-based Attestation Relay for PQC - Lightweight Mempool Propagation Without On-Path Proofs (Wang, 9 Mar 2026)