Bitcoin multisignature: a practical guide

This guide is for readers who are new to Bitcoin and need a clear, practical understanding of multisignature (multisig) wallets and how three common approaches compare in cost (virtual size → fees), privacy, and complexity:

• SegWit multisig (P2WSH m-of-n)
• MuSig1 (embedded in Taproot scripts)
• MuSig2 (embedded in Taproot scripts)

At the end, you’ll find an appendix table with measured virtual sizes (vbytes) for many k-of-n policies gathered from real transactions.

1. What is multisignature (multisig)?

Multisig is a way to protect Bitcoin by requiring multiple approvals to spend coins. Instead of one person with one key, you can require k signatures out of n keys (a k-of-n policy).
Examples:

• 2-of-3: any 2 of 3 people (or devices/HSMs) must sign
• 3-of-5: any 3 of 5 signers must sign
• n-of-n: everyone must sign

Why it’s useful

• Security: No single lost/compromised key can spend alone.
• Shared control: Good for teams, companies, DAOs, or estates.
• Redundancy: Keep keys in different places/devices.

2. Key terms (fast glossary)

• SegWit (Segregated Witness): A Bitcoin upgrade that reduced signature data cost and enabled better scaling. “P2WSH” is the SegWit “Pay to Witness Script Hash” version used for script-based multisig.
• Taproot: A newer upgrade that improves privacy and efficiency. Lets you:
  • Spend via a key path (looks like a single key) or
  • Reveal only the script branch you use (hiding the rest).
• Schnorr signatures: The signature scheme used with Taproot (instead of ECDSA). Enables key aggregation protocols like MuSig2.
• MuSig: Family of protocols that let multiple parties produce one aggregated public key and one or many individual or aggregated signatures, making a multi-party spend look like a single-signer spend (for Musig2).
  • MuSig1: Early variant—more interactive, trickier nonce handling.
  • MuSig2: Newer, two-round protocol—simpler and safer in practice, more complex to implement.
• Virtual size (vsize): The size (in vbytes) the network uses to calculate fees. Your fee = vsize × feerate (sat/vB). Lower vsize → lower fees.

3. The three options (high level)

1. SegWit multisig (P2WSH m-of-n)
   • How it works: The spending rule (e.g., “k-of-n”) is a script that’s revealed when you spend.
   • Cost: Witness size grows with n; typically more expensive than MuSig for the same policy.
   • Privacy: Reveals your policy (m, n, and keys) on-chain when spending.
   • Limits: Script/witness size constraints make very large n impractical; the table below marks X once n > 16.
   • Good for: Legacy compatibility, simple committees already supported by existing tools.
2. MuSig1 (embedded in Taproot scripts)
   • How it works: All combinations of signatures are created and embedded in the tap tree, only the final tree is approved with the minimum amount of participants.
   • Cost: Often smaller than P2WSH multisig; good savings for typical committees.
   • Privacy: only the signers are revealed when signed (better than P2WSH).
   • Complexity: More complex than P2WSH multisig, adds complexity to the implementation.
3. MuSig2 (embedded in Taproot scripts)
   • How it works: Use Taproot + Schnorr with MuSig2 for a two-round signing flow. You can keep complex policies as Taproot scripts (hidden unless used) and spend through a key path when possible.
   • Cost: Best fee performance in our measurements—often lowest vsize across k-of-n.
   • Privacy: Best: key-path spends look like single-sig. Only reveal a script branch if necessary; unused branches stay hidden.
   • Complexity: More complex than MuSig1; requires Taproot-aware wallets/signers and 2 rounds of signatures.

4. Fees in practice (vsize → sats)

Your fee is vsize × feerate. Example at 10 sat/vB:

• 2-of-3: SegWit 212 vB → 2,120 sats; MuSig1 189 vB → 1,890 sats; MuSig2 164 vB → 1,640 sats (≈ 23% cheaper than SegWit).
• 3-of-3: SegWit 230 vB; MuSig1 198 vB; MuSig2 148 vB (≈ 36% cheaper than SegWit).

The gap grows with larger policies.

5. Privacy & complexity at a glance

Aspect	Best choice	Why
Privacy	MuSig2 (Taproot key path)	On-chain looks like single-sig; scripts/branches stay hidden unless used.
Fees	MuSig2	Our measurements show consistently lower vsize across many k-of-n.
Simplicity (small committees)	P2WSH	Straightforward and widely supported; fine when n is small and privacy isn’t critical.
Simplicity (modern setups)	MuSig2	Two-round protocol; integrates well with Taproot PSBT/HSM workflows.

Rule of thumb: If you can, design for Taproot + MuSig2. Fall back to P2WSH for legacy tooling or small fixed committees. Prefer MuSig2 over MuSig1 unless you’re locked into MuSig1.

6. Implementation notes (practical)

• Key management: Distribute keys/devices/roles to avoid single points of failure.
• Backups: Document recovery for lost keys or role changes (thresholds help).
• Coordination: Even with MuSig2’s simpler flow, plan message passing (nonces, partial sigs) in your wallet/HSM/PSBT stack.
• Testing: Start with low-value spends and test unusual paths (e.g., time-lock or recovery branches) before going live.

Appendix — Virtual Sizes (vbytes)

Below is the measured table: k-of-n, SegWit, MuSig1, MuSig2, Best.
“X” indicates SegWit multisig wasn’t possible (e.g., n > 16).
We created the libraries for the three approaches and ran the same test with each one. These are the results:

k-of-n	Comb.	SegWit	MuSig1	MuSig2	Best
1-of-2	2	185	156	156	MuSig1
2-of-2	1	203	173	148	MuSig2
1-of-3	3	194	164	164	MuSig1
2-of-3	3	212	189	164	MuSig2
3-of-3	1	230	198	148	MuSig2
1-of-4	4	202	164	164	MuSig1
2-of-4	6	220	189	164	MuSig2
3-of-4	4	238	214	164	MuSig2
4-of-4	1	256	223	148	MuSig2
1-of-5	5	211	164	164	MuSig1
2-of-5	10	229	205	180	MuSig2
3-of-5	10	247	230	180	MuSig2
4-of-5	5	265	239	164	MuSig2
5-of-5	1	283	248	148	MuSig2
1-of-6	6	219	164	164	MuSig1
2-of-6	15	237	205	180	MuSig2
3-of-6	20	255	230	180	MuSig2
4-of-6	15	273	255	180	MuSig2
5-of-6	6	291	264	164	MuSig2
6-of-6	1	309	273	148	MuSig2
1-of-7	7	228	172	172	MuSig1
2-of-7	21	246	205	180	MuSig2
3-of-7	35	264	238	188	MuSig2
4-of-7	35	282	263	188	MuSig2
5-of-7	21	300	280	180	MuSig2
6-of-7	7	318	297	172	MuSig2
7-of-7	1	336	298	148	MuSig2
1-of-8	8	237	172	172	MuSig1
2-of-8	28	255	213	188	MuSig2
3-of-8	56	273	246	196	MuSig2
4-of-8	70	291	271	196	MuSig2
5-of-8	56	309	296	196	MuSig2
6-of-8	28	327	313	188	MuSig2
7-of-8	8	345	322	172	MuSig2
8-of-8	1	363	324	148	MuSig2
1-of-9	9	245	172	172	MuSig1
2-of-9	36	263	213	188	MuSig2
3-of-9	84	281	255	204	MuSig2
7-of-9	36	353	338	188	MuSig2
8-of-9	9	371	348	172	MuSig2
9-of-9	1	389	349	148	MuSig2
1-of-10	10	254	180	180	MuSig1
2-of-10	45	272	221	196	MuSig2
3-of-10	120	290	255	204	MuSig2
4-of-10	210	308	288	212	MuSig2
7-of-10	120	362	355	204	MuSig2
8-of-10	45	380	372	196	MuSig2
9-of-10	10	398	381	180	MuSig2
10-of-10	1	416	374	148	MuSig2
1-of-11	11	262	172	172	MuSig1
2-of-11	55	280	221	196	MuSig2
3-of-11	165	298	263	212	MuSig2
9-of-11	55	406	397	196	MuSig2
10-of-11	11	424	398	172	MuSig2
11-of-11	1	442	399	148	MuSig2
1-of-12	12	271	172	172	MuSig1
2-of-12	66	289	221	196	MuSig2
3-of-12	220	307	263	212	MuSig2
4-of-12	495	325	296	220	MuSig2
9-of-12	220	415	413	212	MuSig2
10-of-12	66	433	422	196	MuSig2
11-of-12	12	451	423	172	MuSig2
12-of-12	1	469	424	148	MuSig2
1-of-13	13	279	180	180	MuSig1
2-of-13	78	297	230	204	MuSig2
3-of-13	286	315	263	212	MuSig2
11-of-13	78	459	455	204	MuSig2
12-of-13	13	477	456	180	MuSig2
13-of-13	1	495	449	148	MuSig2
1-of-14	14	288	180	180	MuSig1
2-of-14	91	306	230	204	MuSig2
3-of-14	364	324	271	220	MuSig2
12-of-14	91	486	480	204	MuSig2
13-of-14	14	504	481	180	MuSig2
14-of-14	1	522	474	148	MuSig2
1-of-15	15	296	180	180	MuSig1
2-of-15	105	314	230	204	MuSig2
3-of-15	455	332	271	220	MuSig2
4-of-15	1365	350	312	236	MuSig2
12-of-15	455	494	496	220	MuSig2
13-of-15	105	512	505	204	MuSig2
14-of-15	15	530	506	180	MuSig2
15-of-15	1	548	499	148	MuSig2
1-of-16	16	305	180	180	MuSig1
2-of-16	120	323	230	204	MuSig2
3-of-16	560	341	271	220	MuSig2
4-of-16	1820	359	312	236	MuSig2
5-of-16	4368	377	345	244	MuSig2
12-of-16	1820	503	512	236	MuSig2
13-of-16	560	521	521	220	MuSig2
14-of-16	120	539	530	204	MuSig2
15-of-16	16	557	531	180	MuSig2
16-of-16	1	575	524	148	MuSig2
1-of-17	17	X	180	180	MuSig1
2-of-17	136	X	230	204	MuSig2
3-of-17	680	X	279	228	MuSig2
4-of-17	2380	X	312	236	MuSig2
14-of-17	680	X	554	228	MuSig2
15-of-17	136	X	555	204	MuSig2
16-of-17	17	X	556	180	MuSig2
17-of-17	1	X	549	148	MuSig2
1-of-18	18	X	180	180	MuSig1
2-of-18	153	X	230	204	MuSig2
3-of-18	816	X	279	228	MuSig2
4-of-18	3060	X	320	244	MuSig2
15-of-18	816	X	579	228	MuSig2
16-of-18	153	X	580	204	MuSig2
17-of-18	18	X	581	180	MuSig2
18-of-18	1	X	574	148	MuSig2
1-of-19	19	X	180	180	MuSig1
2-of-19	171	X	238	212	MuSig2
3-of-19	969	X	279	228	MuSig2
4-of-19	3876	X	320	244	MuSig2
16-of-19	969	X	604	228	MuSig2
17-of-19	171	X	614	212	MuSig2
18-of-19	19	X	606	180	MuSig2
19-of-19	1	X	599	148	MuSig2
1-of-20	20	X	180	180	MuSig1
2-of-20	190	X	238	212	MuSig2
3-of-20	1140	X	279	228	MuSig2
4-of-20	4845	X	320	244	MuSig2
5-of-20	15504	X	361	260	MuSig2
16-of-20	4845	X	620	244	MuSig2
17-of-20	1140	X	630	228	MuSig2
18-of-20	190	X	639	212	MuSig2
19-of-20	20	X	631	180	MuSig2
20-of-20	1	X	624	148	MuSig2
1-of-21	21	X	180	180	MuSig1
2-of-21	210	X	238	212	MuSig2
3-of-21	1330	X	287	236	MuSig2
4-of-21	5985	X	328	252	MuSig2
18-of-21	1330	X	663	236	MuSig2
19-of-21	210	X	664	212	MuSig2
20-of-21	21	X	656	180	MuSig2
21-of-21	1	X	649	148	MuSig2
1-of-22	22	X	180	180	MuSig1
2-of-22	231	X	238	212	MuSig2
3-of-22	1540	X	287	236	MuSig2
4-of-22	7315	X	328	252	MuSig2
19-of-22	1540	X	688	236	MuSig2
20-of-22	231	X	689	212	MuSig2
21-of-22	22	X	681	180	MuSig2
22-of-22	1	X	674	148	MuSig2
1-of-23	23	X	180	180	MuSig1
2-of-23	253	X	238	212	MuSig2
3-of-23	1771	X	287	236	MuSig2
4-of-23	8855	X	328	252	MuSig2
20-of-23	1771	X	713	236	MuSig2
21-of-23	253	X	714	212	MuSig2
22-of-23	23	X	706	180	MuSig2
23-of-23	1	X	699	148	MuSig2
1-of-24	24	X	188	188	MuSig1
2-of-24	276	X	238	212	MuSig2
3-of-24	2024	X	287	236	MuSig2
4-of-24	10626	X	336	260	MuSig2
21-of-24	2024	X	738	236	MuSig2
22-of-24	276	X	739	212	MuSig2
23-of-24	24	X	739	188	MuSig2
24-of-24	1	X	724	148	MuSig2
1-of-25	25	X	188	188	MuSig1
2-of-25	300	X	238	212	MuSig2
3-of-25	2300	X	287	236	MuSig2
4-of-25	12650	X	336	260	MuSig2
21-of-25	12650	X	762	260	MuSig2
22-of-25	2300	X	763	236	MuSig2
23-of-25	300	X	764	212	MuSig2
24-of-25	25	X	764	188	MuSig2
25-of-25	1	X	749	148	MuSig2
1-of-26	26	X	180	180	MuSig1
2-of-26	325	X	238	212	MuSig2
3-of-26	2600	X	295	244	MuSig2
4-of-26	14950	X	336	260	MuSig2
23-of-26	2600	X	796	244	MuSig2
24-of-26	325	X	789	212	MuSig2
25-of-26	26	X	781	180	MuSig2
26-of-26	1	X	774	148	MuSig2
1-of-27	27	X	188	188	MuSig1
2-of-27	351	X	246	220	MuSig2
3-of-27	2925	X	287	236	MuSig2
4-of-27	17550	X	336	260	MuSig2
24-of-27	2925	X	813	236	MuSig2
25-of-27	351	X	822	220	MuSig2
26-of-27	27	X	814	188	MuSig2
27-of-27	1	X	799	148	MuSig2
1-of-28	28	X	188	188	MuSig1
2-of-28	378	X	246	220	MuSig2
3-of-28	3276	X	295	244	MuSig2
4-of-28	20475	X	344	268	MuSig2
25-of-28	3276	X	846	244	MuSig2
26-of-28	378	X	847	220	MuSig2
27-of-28	28	X	839	188	MuSig2
28-of-28	1	X	824	148	MuSig2
1-of-29	29	X	188	188	MuSig1
2-of-29	406	X	238	212	MuSig2
3-of-29	3654	X	287	236	MuSig2
4-of-29	23751	X	336	260	MuSig2
26-of-29	3654	X	863	236	MuSig2
27-of-29	406	X	864	212	MuSig2
28-of-29	29	X	864	188	MuSig2
29-of-29	1	X	849	148	MuSig2
1-of-30	30	X	188	188	MuSig1
2-of-30	435	X	246	220	MuSig2
3-of-30	4060	X	295	244	MuSig2
4-of-30	27405	X	336	260	MuSig2
26-of-30	27405	X	887	260	MuSig2
27-of-30	4060	X	896	244	MuSig2
28-of-30	435	X	897	220	MuSig2
29-of-30	30	X	889	188	MuSig2
30-of-30	1	X	874	148	MuSig2
1-of-32	32	X	188	188	MuSig1
2-of-32	496	X	246	220	MuSig2
3-of-32	4960	X	303	252	MuSig2
4-of-32	35960	X	352	276	MuSig2
29-of-32	4960	X	954	252	MuSig2
30-of-32	496	X	947	220	MuSig2
31-of-32	32	X	939	188	MuSig2
32-of-32	1	X	924	148	MuSig2
1-of-35	35	X	188	188	MuSig1
2-of-35	595	X	254	228	MuSig2
3-of-35	6545	X	303	252	MuSig2
32-of-35	6545	X	1029	252	MuSig2
33-of-35	595	X	1030	228	MuSig2
34-of-35	35	X	1014	188	MuSig2
35-of-35	1	X	999	148	MuSig2
1-of-40	40	X	188	188	MuSig1
2-of-40	780	X	254	228	MuSig2
3-of-40	9880	X	311	260	MuSig2
37-of-40	9880	X	1162	260	MuSig2
38-of-40	780	X	1155	228	MuSig2
39-of-40	40	X	1139	188	MuSig2
40-of-40	1	X	1124	148	MuSig2
1-of-50	50	X	188	188	MuSig1
2-of-50	1225	X	254	228	MuSig2
3-of-50	19600	X	319	268	MuSig2
47-of-50	19600	X	1420	268	MuSig2
48-of-50	1225	X	1405	228	MuSig2
49-of-50	50	X	1389	188	MuSig2
50-of-50	1	X	1374	148	MuSig2