magnetar/SPEC.md

Magnetar v0.1 — Construction specification

Threshold FIPS 205 SLH-DSA via reveal-and-aggregate. Mirrors Pulsar's v0.1 reveal-and-aggregate pattern, ported to SLH-DSA's scheme-seed-as-secret model.

Status: v0.1 implementation specification. NOT yet independently reviewed. See BLOCKERS.md BLK-7 and BLK-9 for the proof-and-review path to Tier A.

1. Notation

Symbol	Meaning
n	committee size
t	reconstruction threshold (1 ≤ t ≤ n ≤ 256)
q	Shamir prime, fixed at 257 (smallest prime > 255)
seed_size	SLH-DSA scheme-seed length: 96 bytes for SHAKE-192s/192f, 128 bytes for SHAKE-256s
P_i	party i, 1 ≤ i ≤ n
x_i	Shamir x-coordinate of P_i, 1 ≤ x_i ≤ 256, distinct per party
c_i	P_i's contribution to the joint seed, c_i ∈ {0,1}^{8·seed_size}
S	joint master seed, S ∈ {0,1}^{8·seed_size}
share_i	P_i's Shamir share of the byte-sum used to mix to S
pk, sk	FIPS 205 SLH-DSA group public / private keypair derived from S

2. Hash domain separation

All cSHAKE / KMAC calls use function-name "Magnetar" and one of the following customisation tags:

Tag	Purpose
MAGNETAR-DKG-COMMIT-V1	committee-root digest
MAGNETAR-DKG-TRANSCRIPT-V1	DKG transcript digest
MAGNETAR-SIGN-R1-V1	threshold-sign Round-1 commit D_i
MAGNETAR-SIGN-R1-MAC-V1	(reserved for v0.2 MAC envelope)
MAGNETAR-SIGN-MASK-V1	per-attempt mask derivation
MAGNETAR-SEED-SHARE-V1	Shamir coefficient stream + seed mix

The protocol-wide domain-separation context is the ASCII string "lux-magnetar-v0.1" (tagDomainSep).

3. DKG protocol

Round 1 (dealer P_i)

1. Sample c_i ←$ {0,1}^{8·seed_size} from rng.
2. Sample seed_size · 2 · (t-1) bytes of coefficient material from rng (the random Shamir polynomial coefficients).
3. Run byte-wise Shamir-share-deal over GF(257):
   • For each byte position b ∈ [0, seed_size), define a polynomial f_b(x) = c_i[b] + a_{b,1}·x + ... + a_{b,t-1}·x^{t-1} (mod 257) where a_{b,j} are derived from the coefficient stream.
   • For each recipient P_j, compute share_{i→j}[b] = f_b(x_j) (mod 257) for every byte b. The result is a 2·seed_size-byte big-endian uint16 vector.
4. Construct one envelope per recipient:

   Envelope_{i→j} := (share_{i→j} || c_i)
   

   The full c_i is duplicated into every envelope so that at Round 2 each P_j can sum contributions to compute the joint master public key locally.
5. Broadcast DKGRound1Msg{NodeID = P_i, Envelopes = { P_j ↦ Envelope_{i→j} }_{j∈[n]}}.

Round 2 (party P_i)

1. Receive Round-1 broadcasts from every dealer in committee.
2. Validate: every broadcast contains an envelope for every recipient (no omissions); every envelope has the expected wire sizes; sender is in committee.
3. Compute the transcript digest binding the entire ordered envelope set:

   τ_dkg := lux-magnetar-v0.1 ‖ Mode ‖ t ‖ n ‖ committee_in_order
   D := cSHAKE256( τ_dkg ‖ for_each_dealer_in_order(for_each_recipient_in_order(share || contribution)),
                   N="Magnetar", S="MAGNETAR-DKG-TRANSCRIPT-V1", 32 bytes )
   

4. Broadcast DKGRound2Msg{NodeID = P_i, Digest = D}.

Round 3 (party P_i)

1. Receive Round-2 digests from every party.
2. Verify every received digest equals D (computed locally). A mismatch is identifiable abort with ComplaintKind = ComplaintEquivocation; the conflicting digest pair is the evidence blob.
3. Sum per-byte Shamir shares received from each dealer:

   my_share_sum[b] := Σ_{j∈[n]} share_{j→i}[b] (mod 257)  for b ∈ [0, seed_size)
   

4. Sum dealer contributions byte-by-byte over GF(257):

   master_byteSum[b] := Σ_{j∈[n]} c_j[b] (mod 257)  for b ∈ [0, seed_size)
   

5. Compute the committee root:

   committee_root := cSHAKE256( "MAGNETAR-COMMITTEE-V1" ‖ sorted_committee,
                                 N="Magnetar", S="MAGNETAR-DKG-COMMIT-V1", 32 bytes )
   

6. Mix to the master seed:

   mix := (master_byteSum encoded as 2·seed_size big-endian uint16) ‖ committee_root
   S := cSHAKE256( mix, N="Magnetar", S="MAGNETAR-SEED-SHARE-V1", seed_size bytes )
   

7. Derive the group public key via FIPS 205:

   (pk, sk) := slhdsa.Scheme(SLH-DSA-SHAKE-{192s,192f,256s}).DeriveKey(S)
   

   Discard sk; publish pk as the joint group public key. (Each party can compute the same pk because every party has identical master_byteSum and committee_root inputs.)
8. Output: KeyShare{NodeID = P_i, EvalPoint = x_i = i, Share = my_share_sum, Pub = pk}.

DKG correctness

For any quorum Q ⊆ [n] with |Q| ≥ t:

Lagrange-interpolate({(x_i, my_share_sum_i) : i ∈ Q}) = master_byteSum

because my_share_sum_i = Σ_j share_{j→i} = Σ_j f_{j,b}(x_i) and the Lagrange interpolation at x=0 over GF(257) of the polynomial sums Σ_j f_{j,b} recovers Σ_j c_j[b] = master_byteSum[b].

Therefore any quorum's reconstructed seed S is identical to the one computed at Round 3.

4. Threshold signing

Round 1 (signer P_i, i ∈ T ⊆ [n], |T| = t)

1. Sample rngBytes ←$ {0,1}^{8·2·seed_size} from rng.
2. Derive per-attempt mask:

   maskMix := rngBytes ‖ session_id ‖ attempt(BE 4 bytes) ‖ NodeID
   r_i := cSHAKE256( maskMix, N="Magnetar", S="MAGNETAR-SIGN-MASK-V1", 2·seed_size bytes )
   

3. Mask the share byte-by-byte XOR:

   masked_i[b] := share_i[b] XOR r_i[b]  for b ∈ [0, 2·seed_size)
   

4. Compute Round-1 transcript binding:

   τ_1 := SP800-185-encode( session_id, attempt, quorum, NodeID, pk, message )
   

5. Compute commit:

   D_i := cSHAKE256( r_i ‖ masked_i ‖ τ_1, N="Magnetar", S="MAGNETAR-SIGN-R1-V1", 32 bytes )
   

6. Broadcast Round1Message{NodeID, SessionID, Attempt, Commit = D_i}.

Round 2 (signer P_i)

1. Validate Round-1 broadcasts (consistent session/attempt).
2. Reveal:

   Round2Message{NodeID, SessionID, Attempt, PartialSig = r_i ‖ masked_i}
   

Combine (aggregator)

1. For each Round-2 reveal (r_i, masked_i): a. Recompute D'_i = cSHAKE256(r_i ‖ masked_i ‖ τ_1_i, ...) and check D'_i == Round1Message.Commit. Reject on mismatch. b. Recover share_i = masked_i XOR r_i.
2. Collect t distinct shares. Pair each with its KeyShare.EvalPoint from the directory.
3. Run Lagrange interpolation over GF(257) at x=0:

   reconstructed_byteSum[b] := Σ_{i∈Q} λ_i · share_i[b] (mod 257)
   

   where λ_i = Π_{j≠i} (-x_j) / (x_i - x_j) (mod 257).
4. Compute committee_root from allShares (same definition as Round 3 step 5).
5. Mix to recover the master seed (identical to DKG Round 3 step 6):

   S := cSHAKE256( reconstructed_byteSum_BE ‖ committee_root, N="Magnetar", S="MAGNETAR-SEED-SHARE-V1", seed_size bytes )
   

6. Derive the SLH-DSA secret key:

   (pk_rec, sk_rec) := slhdsa.Scheme(...).DeriveKey(S)
   

   If pk_rec ≠ groupPubkey: abort with ErrPubkeyMismatch.
7. Sign:

   sig := slhdsa.SignDeterministic(sk_rec, message, ctx)
   

   (When randomized=true, SignRandomized is used with the caller's rng.)
8. Zeroize S, sk_rec, mix, reconstructed_byteSum.
9. Return Signature{Mode, Bytes = sig}.

5. Verify

Verify is a thin dispatch to slhdsa.Verify(pk, NewMessage(message), sig, ctx). No Magnetar-specific envelope. This is the Class-N1-analog property: any unmodified FIPS 205 verifier accepts Magnetar signatures.

6. Class-N1-analog byte-equality claim

Claim (Magnetar reveal-and-aggregate byte-equality). For any honest threshold-sign session over committee [n] with threshold t, any quorum Q of size t, message m, context ctx, session_id sid, attempt κ:

Combine(...) = slhdsa.SignDeterministic(slhdsa.DeriveKey(S), NewMessage(m), ctx)

where S is the master seed computed at DKG Round 3.

Proof sketch. Combine reconstructs master_byteSum from Q's shares via Lagrange interpolation (correct by Shamir's secret sharing over GF(257) for any quorum of size ≥ t). It then computes committee_root from the same allShares set that fixed it at DKG time, and applies the identical cSHAKE256 mix → produces the identical S. Sign on DeriveKey(S) is byte-deterministic over (S, m, ctx). ∎

Empirical validation. See n1_byte_equality_test.go: TestN1_ByteEquality_ThresholdMatchesCentralized and TestN1_ByteEquality_DifferentQuorumsSameSignature exercise the claim across three configurations and across distinct quorums.

7. Trust model — the v0.1 reveal-and-aggregate caveat

The aggregator process is in the trusted computing base (TCB) for the brief window the master seed is reconstructed in memory.

This is the same trust caveat Pulsar's v0.1 reveal-and-aggregate carries; it is documented honestly in Pulsar's DEPLOYMENT-RUNBOOK.md and is inherited verbatim by Magnetar.

Specifically:

• At step 6 of Combine (§4), the master SLH-DSA seed S is recomputed in aggregator memory.
• At step 7, FIPS 205 SignDeterministic consumes S to produce the signature.
• At step 8, all secret-bearing buffers (S, sk_rec, mix, reconstructed_byteSum) are explicitly zeroized.

During steps 6–7, an adversary with arbitrary code-execution on the aggregator host can extract S via:

• /proc/<pid>/mem
• a coredump
• a swap-file or hibernation image
• ptrace
• a malicious kernel/hypervisor

Operational mitigations are described in DEPLOYMENT-RUNBOOK.md "Aggregator hardening".

What this caveat does NOT cover:

• A passive network observer never sees S. Round-1 commits and Round-2 reveals collectively carry share_i values (masked + revealed), but reconstruction requires combining t of them with the matching EvalPoint directory. v0.1 v1 envelopes are plaintext (a passive observer can see committee shares); v0.2 will wrap them under ML-KEM-768 to the recipient's long-term identity public key, matching Pulsar's BLOCKERS.md CR-8 pattern.
• A single Byzantine committee member cannot forge a signature: forging requires reconstructing S, which requires t shares.
• A single Byzantine aggregator cannot forge a signature for a message it did not receive valid Round-2 reveals on: Combine's commit-bind check (step 1a) rejects tampered reveals.

8. Identifiable abort

The protocol commits to identifiable abort: every detected deviation produces verifiable evidence suitable for slashing.

Complaint	Detected at	Evidence
ComplaintEquivocation	DKG Round 3	Conflicting Digest from accused; honest party's local Digest
ComplaintBadDelivery	DKG Round 2 (envelope shape check)	Malformed envelope

The v0.1 protocol omits the per-pair MAC layer that Pulsar uses (BLOCKERS.md CR-7). This is documented; v0.2 adds MACs once the trust model tightens.

9. Parameter sets

Mode	NIST PQ Cat	Pub key	Priv key	Signature	Seed
Magnetar-SHAKE-192s	3	48 B	96 B	16,224 B	96 B
Magnetar-SHAKE-192f	3	48 B	96 B	35,664 B	96 B
Magnetar-SHAKE-256s	5	64 B	128 B	29,792 B	128 B

Recommended production target: Magnetar-SHAKE-192s (matches NIST Cat 3, smallest signature in its category).

10. Honest non-claims

Magnetar v0.1 does NOT claim:

• Full MPC threshold signing. v0.1 is reveal-and-aggregate; the aggregator process is TCB.
• Network-observer secrecy of envelopes in v0.1. Plaintext envelopes are visible to a passive observer; v0.2 closes this with ML-KEM-768 wrapping.
• Sub-second signing. SLH-DSA single-party signing on SHAKE-192s is ~10–50ms depending on hardware; race-detector runs are 5–10× slower.
• Formal verification. No EasyCrypt, Lean, or Jasmin artifacts ship in v0.1. See BLOCKERS.md BLK-7.

11. References

• FIPS 205: Stateless Hash-Based Digital Signature Standard (2024).
• Shamir, A. How to share a secret. Communications of the ACM, 1979.
• Pulsar v0.1 SPEC.md — reveal-and-aggregate pattern adapted from there.
• BLOCKERS.md — outstanding Tier B → A path.
• DEPLOYMENT-RUNBOOK.md — operator-facing trust-model disclosure.

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Document metadata

• File: SPEC.md
• Version: v0.1
• Date: 2026-05-18
• Status: implementation specification; not yet independently reviewed (see BLK-9).