ENI6MA is not just an authentication platform—it is a next-generation proof infrastructure. At its core lies a novel cryptographic primitive, the Rosario–Wang Proof of Information Entanglement, a high-dimensional, zero-knowledge protocol that transforms human-memorable inputs into reusable, carrier-agnostic cryptographic proofs.
This architecture enables secure identity, data integrity, and authorization—without storing secrets, revealing credentials, or requiring specialized hardware. ENI6MA functions as a layer-zero trust substrate for post-quantum ecosystems, redefining authentication as an epistemic act, not a secret exchange.
The Rosario-Wang Accumulator cypher employs a novel approach to cryptographic accumulators, leveraging the Holographic Morphism with private languages. This cypher uses a set of enumerated alphabets with equal cardinality to create witnesses, ensuring efficient and secure membership proofs.
Witnesses in the cypher are lower-dimensional references that are expanded after determining the holographic morphism. This morphism identifies a subset of the projective alphabet sets containing character members of another alphabet, whose members are distributed equally across the new lower-dimensional projective set. The higher-dimensional set contains a larger number of members, representing the individual members of the secret key, from which the witness is provided in any $i^{\text{th}}$ round of a sigma protocol.
The Accumulator cypher defines the projective set $\Pi$ as a set containing elements arranged in a lower-dimensional space, which expands to identify specific subsets through holographic morphisms. The holographic morphism $\mathcal{H}$ is a hidden morphism linking two alphabets that have no intersection. This morphism is used to expand lower-dimensional witnesses. The lower-dimensional representation process maps higher-dimensional members of an alphabet into lower-dimensional projective sets.
\[\text{pk}_\chi = \text{HoloMorphism}(\nu_{i_k}) \quad \text{for} \quad \chi \in \Xi\] \[\Pi = \{\nu_{i_1}, \nu_{i_2}, \ldots, \nu_{i_r}\}\]In the setup phase, the projective set $\Pi$ is defined to model the domain $M$. A synonym relation to the emergent set is established via a hidden morphism.
During the accumulation phase, the short representation $\text{Acc}_\Xi$ of the set $X$ is created, partitioning it into subsets that form the basis of the projective set:
\[\text{Acc}_\Xi = \bigl\{\Pi = (\nu_{i_1}, \nu_{i_2}, \ldots, \nu_{i_r}),\; \Omega = (\nu_{j_1}, \nu_{j_2}, \ldots, \nu_{j_r})\bigr\}\]For membership holomorphic witness responses, a lower-dimensional reference is created using the Holographic Morphism, then expanded to identify a subset of the projective alphabet sets.
For non-membership witnesses, lower-dimensional references are generated and expanded to verify non-inclusion in the set $X$:
\[\text{pk}_\chi = \text{HoloMorphism}(\nu_{i_k}) \quad \text{for} \quad \chi \in \Xi\]The verification process utilizes the projective morphism to trace the exact path from the lower-dimensional witness to the accumulated representation $\text{Acc}_\Xi$:
\[\text{Verify}\!\bigl(\text{resp}(\chi, \text{pk}_\chi, \chi), \text{Acc}_\Xi\bigr) = \begin{cases} \text{True} & \text{if valid membership} \\ \text{False} & \text{otherwise} \end{cases}\]The primary equations and formulations in the RWP Accumulator cypher include the accumulator representation, membership holomorphic witness responses, non-membership holomorphic witness responses, and the sigma protocol for witness verification.
Consider a set $X = {\chi_1, \chi_2, \chi_3, \chi_4}$. The accumulator represents this set in projective form:
\[\text{Acc}_X = \bigl\{\Pi = (v_1, v_2, v_3, v_4),\; \Omega = (v_5, v_6, v_7, v_8)\bigr\}\]For membership witness $\chi_1$:
\[\text{pk}_{\chi_1} = \text{HoloMorphism}(v_1)\]Verification:
\[\text{Verify}\!\bigl(\text{resp}(\chi_1, \text{pk}_{\chi_1}, \chi), \text{Acc}_X\bigr)\]In setup, $\Pi$ models the domain $\mathcal{M}$. The accumulate phase creates the short representation $\text{Acc}_\Xi$ of the set $\Xi$, partitioning it into projective subsets:
\[\text{Acc}_\Xi = \bigl\{ \Pi = (\nu_{i_1}, \ldots, \nu_{i_r}),\; \Theta = (\nu_{j_1}, \ldots, \nu_{j_r}) \bigr\}\]Membership witnesses:
\[\text{pk}_\xi = \mathcal{H}(\nu_{i_k}) \quad \text{for} \quad \xi \in \Xi\]Non-membership witnesses:
\[\text{pk}_{\xi'} = \mathcal{H}(\nu_{j_k}) \quad \text{for} \quad \xi' \in \mathcal{M} \setminus \Xi\]Accumulator Representation
\[\text{Acc}_\Xi = \bigl\{ \Pi = (\nu_{i_1}, \ldots, \nu_{i_r}),\; \Theta = (\nu_{j_1}, \ldots, \nu_{j_r}) \bigr\}\]Membership Public Key Generation
\[\text{pk}_\xi = \mathcal{H}(\nu_{i_k}) \quad \text{for} \quad \xi \in \Xi\]Non-Membership Public Key Generation
\[\text{pk}_{\xi'} = \mathcal{H}(\nu_{j_k}) \quad \text{for} \quad \xi' \in \mathcal{M} \setminus \Xi\]Sigma Protocol for Witness Verification
Challenge: $\chi \in {0,1}^n$ Response:
\[\text{resp}(\xi, \text{pk}_\xi, \chi) = \text{Expand}\bigl(\mathcal{H}(\nu_{i_k}), \chi\bigr)\]Verification:
\[\text{Verify}\!\bigl(\text{resp}(\xi, \text{pk}_\xi, \chi), \text{Acc}_\Xi\bigr) = \begin{cases} \text{True} & \text{if valid membership} \\ \text{False} & \text{otherwise} \end{cases}\][Bellare1999]8 [Benaloh1993]9 [Pointcheval1996]10
ENI6MA introduces a universal symbolic language:
Above this geometric layer operates the Rosario–Wang Protocol:
The result is a zero-knowledge password proof (ZKPP)—a cognitive authentication primitive that is:
| Threat Class | Defense Mechanism | Result |
|---|---|---|
| Replay Attacks | Entropy-gated morphisms $\Pi_{e^R}$, non-reusable nonces | Observed transcripts become invalid |
| Phishing / Keylogging | Symbol shuffling $\Sigma(A) \rightarrow X^R$ per round | Recorded keystrokes don’t replay secrets |
| Quantum Attacks | Hilbert lattice traversal over multiple combinatorial spaces | Grover and Shor ineffective |
| Storage Breach | Stateless commitments, no persistent secrets | Server-side breaches yield nothing usable |
Mathematically, soundness and zero-knowledge are formalized via:
| Probabilistic guarantees of security: $\Pr[\text{forgery}] \le ( | \Sigma | ^{-1})^{nk}$. |
ENI6MA’s symbolic core and modular deployment model allow it to anchor secure communication, identity, and verification in:
| Layer | Role | Patent Anchor |
|---|---|---|
| Commitment Engine | Builds $C = (s_k, \Sigma_j, t_k)$ from user-secret + nonce | Claim 1, Axiom 3 |
| Projection Driver | Generates session-specific slice of manifold $X^R \subset \mathbb{M}$ | Eq. 10, Claim 8 |
| Verifier Module | Sensory matching $|\mathbf{v} - \varphi(s)| < \varepsilon$ | Eq. 12–13 |
The system requires no vault, no shared secrets, and no device registration. Each login projects a new slice of the manifold, verified via entropic gating and human-memory input.