Lux is not merely adding post-quantum signatures to a chain; it defines a hybrid finality architecture for DAG-native consensus, with protocol-agnostic threshold lifecycle, post-quantum threshold sealing, and cross-chain propagation of Horizon finality.

See LP-105 §Claims and evidence for the canonical claims/evidence table and the ten architectural commitments — single source of truth.

Lens is the curve-based threshold signing kernel for Lux. It is the classical sister to Pulsar (the lattice kernel at github.com/luxfi/pulsar).

Quick reference

Component	Pulsar	Lens
Math field	Module-LWE / R_q	Discrete log over a prime-order group
Sign math	Corona Sign1/Sign2/Combine	FROST 2-round (RFC 9591)
Pedersen commits	A·NTT(s) + B·NTT(r) over R_q	s·G + r·H over the curve
Genesis	Trusted-dealer Bootstrap	Trusted-dealer Bootstrap or FROST DKG
Per-epoch DKG	Never — VSR via `pulsar/reshare`	Never — VSR via `lens/reshare`
Lifecycle	LSS-managed	LSS-managed
LSS adapter	`threshold/protocols/lss/lss_pulsar.go`	`threshold/protocols/lss/lss_lens.go`

Curves shipped

Ed25519 — RFC 8032 / FIPS 186-5 EdDSA curve.
secp256k1 — SEC 2 / Bitcoin curve.
Ristretto255 — RFC 9496 prime-order group over Curve25519.

All three implement primitives.Curve. Per-curve secondary generators (H) are derived deterministically from a Lens-specific nothing-up-my-sleeve tag (lens.<curve>.h-base.v1); discrete log of H with respect to G is unknown to anyone, which is the only property Pedersen binding requires.

Package layout

primitives/  — curve abstraction, polynomial, Lagrange, Pedersen, Shamir, hash helpers
sign/        — FROST 2-round Schnorr threshold signing (RFC 9591)
threshold/   — GroupKey, KeyShare, Signer, Signature types
reshare/     — Refresh (HJKY97) + Reshare (Desmedt-Jajodia),
               Pedersen commits, complaints, transcript, pairwise KEX,
               activation cert
hash/        — HashSuite (Lens-SHA3 production / Lens-BLAKE3 legacy)
dkg/         — Distributed FROST key generation (proper distributed,
               no trusted dealer needed)
keyera/      — Bootstrap / Reshare / Reanchor lifecycle wrapper
cmd/         — KAT oracle binaries for cross-port byte-equal validation

Running

GOWORK=off go test ./...
GOWORK=off go run ./cmd/reshare_oracle -curve ed25519 -variant reshare -t_old 3 -t_new 3
GOWORK=off go run ./cmd/dkg_oracle -curve secp256k1 -n 5 -t 3

Lifecycle invariants

BLS lane:    each validator has its OWN keypair.
ML-DSA lane: each validator has its OWN keypair.
Lens lane:   each validator has a SHARE of one group key.
Pulsar lane: each validator has a SHARE of one group key.

Within a key era:

Master secret s is preserved across every Reshare.
Group public key X = s·G is byte-identical across resharing.
Only the share distribution rotates per epoch.

Across key eras (Reanchor): X and s are fresh.

References

Komlo, Goldberg 2020. FROST: Flexible Round-Optimized Schnorr Threshold Signatures. SAC 2020.
RFC 9591. The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures.
HJKY97. Proactive Secret Sharing or: How to Cope With Perpetual Leakage. CRYPTO.
Desmedt-Jajodia 1997. Redistributing Secret Shares to New Access Structures.
Wong-Wang-Wing 2002. Verifiable Secret Redistribution for Archive Systems.
Seesahai 2025. LSS MPC ECDSA: A Pragmatic Framework for Dynamic and Resilient Threshold Signatures. (LSS framework, paper-backed)
LP-103. Lens — Curve-Based Threshold Signatures with Dynamic Resharing. https://github.com/luxfi/lps/blob/main/LP-103-lens.md
LP-073. Pulsar — lattice threshold sister kernel.

License

Apache-2.0. See LICENSE.