Cryptographic Foundations of Enygma

Enygma is built on a stack of well-established cryptographic primitives, each chosen to address a specific requirement of confidential, institutional-grade settlement. Together these components allow the network to enforce correctness, preserve privacy, and remain resilient against both classical and quantum adversaries, without relying on trusted intermediaries.

At the heart of the system are Zero-Knowledge Proofs (ZK-SNARKs, using the Groth16 proving system), which mathematically prove that a statement is true without revealing any of the underlying data. A bank can demonstrate that it holds sufficient balance to settle a payment without disclosing that balance to anyone on the network. Transaction validity is enforced cryptographically rather than through a trusted third party, and Enygma uses ZKPs to validate every transaction on the network. Amounts, sender and receiver are never exposed, yet correctness is always provable.

Token balances themselves are concealed using Pedersen Commitments, a cryptographic commitment scheme that hides a value while binding the committer to it, so that it cannot be changed after the fact. Balances remain hidden from the network while the token holder retains full sovereign control, since only they, or their designated auditor, can read the balance. The scheme also supports privacy-preserving arithmetic, so the network can verify that inputs equal outputs in a transaction without seeing any of the underlying numbers. That preserves token sovereignty, because the issuer cannot freeze, inflate or inspect balances without the holder's keys. Pedersen Commitments are the foundation of confidential token ownership in Enygma and represent shielded balances throughout the system.

To enable computation over confidential data, Enygma relies on the additively homomorphic property of Pedersen commitments, which allows commitments to be added and subtracted such that the result is a valid commitment to the sum or difference of the underlying values. Adding two commitments produces a commitment to the sum of the values they hide, so smart contracts can process, validate and update committed balances without ever seeing the actual values. This is what makes confidential delivery-versus-payment possible, since the system can verify both legs of a DvP transaction atomically without either party exposing their position. In practice, homomorphic addition over commitments is what enables programmable operations on confidential balances in Enygma, delivering privacy without sacrificing smart contract composability.

Recipients identify their incoming transactions through Private Tags, cryptographic identifiers based on SHA-256 that allow a recipient to detect and claim incoming transactions without scanning the entire chain publicly. Institutions can receive confidential payments without broadcasting their address or revealing monitoring activity to the wider network, which preserves anonymity at the receiving end so that no external observer can link an incoming transfer to a specific institution. Private Tags power the Enygma transaction detection model, in which recipients scan privately rather than publicly.

Enygma further separates authority over funds through a Separated Spending Key / Viewing Key architecture. Two distinct cryptographic keys govern any account, one authorising spending and the other authorising reading, and the two are mathematically independent and cannot be derived from each other. A regulator or auditor granted only the viewing key can inspect transaction history but cannot move, freeze or interfere with funds under any circumstances. This is a cryptographic separation of duties which, unlike a policy-based control, cannot be overridden by an administrator, a platform operator or a compromised internal party. It enables selective regulatory disclosure, so a bank can grant its central bank auditor a time-scoped or account-scoped view key without exposing the rest of its operations. The design is core to the Enygma audit model and underpins the Auditor View capability described in the academic papers.

Looking ahead to the post-quantum era, Enygma uses ML-KEM, the lattice-based key encapsulation mechanism standardised by NIST in 2024 as the post-quantum replacement for ECDH-based key exchange. Shared secrets generated during participant registration are protected against future quantum computers, which defeats "harvest now, decrypt later" attacks that would otherwise retroactively expose who transacted with whom. Adopting ML-KEM also aligns Enygma with the same post-quantum standard now being deployed across TLS and global communications infrastructure. ML-KEM has replaced CSIDH for auditor key exchange (QS-01, completed) and represents the most critical quantum upgrade in the Enygma stack.

Finally, Enygma adopts a UTXO-based transaction model, tracking individual token units rather than account balances. Each transaction consumes previous outputs and creates new ones, with no persistent account balance for an observer to monitor, which makes value flows across the network significantly harder to trace. The model also enables atomic multi-party settlement, so DvP and PvP flows can be constructed such that both legs either settle together or neither does, with no partial exposure. The UTXO model underpins the Enygma anonymity guarantees and is central to how confidential DvP is structured.