docs(pattern): add Beasley lattice VOPRF preprint to vOPRF Nullifiers

CHANGELOG.md

@@ -17,6 +17,7 @@ All notable changes to the EthSystems Map are documented here.
 - feat(approach): link private-stocks, private-commodities, private-fx, and private-repo to [Private Trade Settlement](approaches/approach-private-trade-settlement.md), and private-treasuries to [Private Payments](approaches/approach-private-payments.md), as explicit variants ([#190](https://github.com/ethsystems/map/pull/190), part of [#138](https://github.com/ethsystems/map/issues/138))
 - feat(pattern): add [CMTAT](https://cmta.ch/standards/cmta-token-cmtat) as an alternative to ERC-3643 in [ERC-3643 Tokenized RWAs](patterns/pattern-erc3643-rwa.md), a blockchain-agnostic compliant-tokenization standard with an Aztec/Noir privacy-preserving implementation, cross-referenced in GLOSSARY.md and [Private RWA Tokenization](use-cases/private-rwa-tokenization.md) ([#190](https://github.com/ethsystems/map/pull/190), closes [#174](https://github.com/ethsystems/map/issues/174))
 - feat(vendor): [Gateway Open Privacy Suite](vendors/gateway-open-privacy-suite.md) — governed JSON-RPC access, selective disclosure, and compliance controls for private EVM networks and Gateway L2/validium deployments ([#189](https://github.com/ethsystems/map/pull/189))
+- docs: add the [Beasley](https://eprint.iacr.org/2026/2010) preprint to the [vOPRF Nullifiers](patterns/pattern-voprf-nullifiers.md) `## See also` section, an implemented lattice VOPRF and candidate post-quantum replacement for the DDH construction
 - docs: add Espalier preprint reference to [ZK Proof Systems](patterns/pattern-zk-proof-systems.md), [Post-Quantum Threats](domains/post-quantum.md), and [Safe Proof Delegation](patterns/pattern-safe-proof-delegation.md) `## See also` sections
 - feat(jurisdiction): [Indonesia / OJK (Digital Financial Assets)](jurisdictions/id-OJK.md) and [Singapore / MAS](jurisdictions/sg-MAS.md) -- adds ASEAN coverage, including the POJK 27/2024 listing criterion that bars assets whose features conceal ownership or transaction information ([#182](https://github.com/ethsystems/map/pull/182))
 - feat(jurisdiction): [EU / EUDR (Deforestation Regulation)](jurisdictions/eu-EUDR.md) -- Article 9 plot-level geolocation and the DDS reference-number model, ahead of the 30 December 2026 application date ([#181](https://github.com/ethsystems/map/pull/181))

patterns/pattern-voprf-nullifiers.md

@@ -105,3 +105,4 @@ A KYC issuer gives a user a credential with an internal credential identifier. A
 - [RFC 9576 (Privacy Pass Architecture)](https://www.rfc-editor.org/rfc/rfc9576.html)
 - [TACEO vOPRF writeup](https://core.taceo.io/articles/taceo-oprf/)
 - [TACEO Merces vendor page](../vendors/taceo-merces.md)
+- [Beasley (Li, Wang, Zhang, ePrint 2026/2010)](https://eprint.iacr.org/2026/2010): an implemented round-optimal, maliciously secure lattice VOPRF over MLWE/MSIS, and a candidate post-quantum replacement for the DDH-based construction above. It follows the ADDS21/LeOPaRd blueprint, a lattice analog of 2HashDH, with a generalized BLMR13 PRF that consumes 4 input bits per step and ring-switching sumcheck proofs in place of LaBRADOR; the authors report 520 ms to produce the client request and its NIZK proof, 15.3 ms server verification, and 109 KB of client communication (75.4 KB proof) on one AVX2 core. Round-optimality preserves the single round trip of the protocol above, but per-evaluation bandwidth is orders of magnitude above the elliptic-curve construction, and the paper benchmarks a single-server VOPRF rather than the threshold committee this pattern assumes.