>Yes, quite neat indeed, too bad Lamport signatures are so huge (a couple >kilobytes)... blocksize increase *cough*
Couldn't you significantly compress the signatures by using either Winternitz OTS or by using OP_CAT to build a merkle tree so that the full signature can be derived during script execution from a much shorter set of seed values? On Thu, Jul 8, 2021 at 4:12 AM ZmnSCPxj via bitcoin-dev <[email protected]> wrote: > > > Good morning Jeremy, > > Yes, quite neat indeed, too bad Lamport signatures are so huge (a couple > kilobytes)... blocksize increase *cough* > > Since a quantum computer can derive the EC privkey from the EC pubkey and > this scheme is resistant to that, I think you can use a single well-known EC > privkey, you just need a unique Lamport keypair for each UTXO (uniqueness > being mandatory due to Lamport requiring preimage revelation). > > Regards, > ZmnSCPxj > > > > Dear Bitcoin Devs, > > > > As mentioned previously, OP_CAT (or similar operation) can be used to make > > Bitcoin "quantum safe" by signing an EC signature. This should work in both > > Segwit V0 and Tapscript, although you have to use HASH160 for it to fit in > > Segwit V0. > > > > See [my blog](https://rubin.io/blog/2021/07/06/quantum-bitcoin/) for the > > specific construction, reproduced below. > > > > Yet another entry to the "OP_CAT can do that too" list. > > > > Best, > > > > Jeremy > > ----- > > > > I recently published [a blog > > post](https://rubin.io/blog/2021/07/02/signing-5-bytes/) about signing up > > to a > > 5 byte value using Bitcoin script arithmetic and Lamport signatures. > > > > By itself, this is neat, but a little limited. What if we could sign longer > > messages? If we can sign up to 20 bytes, we could sign a HASH160 digest > > which > > is most likely quantum safe... > > > > What would it mean if we signed the HASH160 digest of a signature? What the > > what? Why would we do that? > > > > Well, as it turns out, even if a quantum computer were able to crack ECDSA, > > it > > would yield revealing the private key but not the ability to malleate the > > content of what was actually signed. I asked my good friend and > > cryptographer > > [Madars Virza](https://madars.org/) if my intuition was correct, and he > > confirmed that it should be sufficient, but it's definitely worth closer > > analysis before relying on this. While the ECDSA signature can be malleated > > to a > > different, negative form, if the signature is otherwise made immalleable > > there > > should only be one value the commitment can be opened to. > > > > If we required the ECDSA signature be signed with a quantum proof signature > > algorithm, then we'd have a quantum proof Bitcoin! And the 5 byte signing > > scheme > > we discussed previously is a Lamport signature, which is quantum secure. > > Unfortunately, we need at least 20 contiguous bytes... so we need some sort > > of > > OP\_CAT like operation. > > > > OP\_CAT can't be directly soft forked to Segwit v0 because it modifies the > > stack, so instead we'll (for simplicity) also show how to use a new opcode > > that > > uses verify semantics, OP\_SUBSTRINGEQUALVERIFY that checks a splice of a > > string > > for equality. > > > > ``` > > ... FOR j in 0..=5 > > <0> > > ... FOR i in 0..=31 > > SWAP hash160 DUP <H(K_j_i_1)> EQUAL IF DROP <2**i> ADD ELSE > > <H(K_j_i_0)> EQUALVERIFY ENDIF > > ... END FOR > > TOALTSTACK > > ... END FOR > > > > DUP HASH160 > > > > ... IF CAT AVAILABLE > > FROMALTSTACK > > ... FOR j in 0..=5 > > FROMALTSTACK > > CAT > > ... END FOR > > EQUALVERIFY > > ... ELSE SUBSTRINGEQUALVERIFY AVAILABLE > > ... FOR j in 0..=5 > > FROMALTSTACK <0+j*4> <4+j*4> SUBSTRINGEQUALVERIFY DROP DROP DROP > > ... END FOR > > DROP > > ... END IF > > > > <pk> CHECKSIG > > ``` > > > > That's a long script... but will it fit? We need to verify 20 bytes of > > message > > each bit takes around 10 bytes script, an average of 3.375 bytes per number > > (counting pushes), and two 21 bytes keys = 55.375 bytes of program space > > and 21 > > bytes of witness element per bit. > > > > It fits! `20*8*55.375 = 8860`, which leaves 1140 bytes less than the limit > > for > > the rest of the logic, which is plenty (around 15-40 bytes required for the > > rest > > of the logic, leaving 1100 free for custom signature checking). The stack > > size > > is 160 elements for the hash gadget, 3360 bytes. > > > > This can probably be made a bit more efficient by expanding to a ternary > > representation. > > > > ``` > > SWAP hash160 DUP <H(K_j_i_0)> EQUAL IF DROP ELSE <3**i> SWAP DUP > > <H(K_j_i_T)> EQUAL IF DROP SUB ELSE <H(K_j_i_1)> EQUALVERIFY ADD ENDIF > > ENDIF > > ``` > > > > This should bring it up to roughly 85 bytes per trit, and there should be > > 101 > > trits (`log(2**160)/log(3) == 100.94`), so about 8560 bytes... a bit > > cheaper! > > But the witness stack is "only" `2121` bytes... > > > > As a homework exercise, maybe someone can prove the optimal choice of radix > > for > > this protocol... My guess is that base 4 is optimal! > > > > ## Taproot? > > > > What about Taproot? As far as I'm aware the commitment scheme (`Q = pG + > > hash(pG > > || m)G`) can be securely opened to m even with a quantum computer (finding > > `q` > > such that `qG = Q` might be trivial, but suppose key path was disabled, then > > finding m and p such that the taproot equation holds should be difficult > > because > > of the hash, but I'd need to certify that claim better). Therefore this > > script can nest inside of a Tapscript path -- Tapscript also does not > > impose a > > length limit, 32 byte hashes could be used as well. > > > > Further, to make keys reusable, there could be many Lamport keys comitted > > inside > > a taproot tree so that an address could be used for thousands of times > > before > > expiring. This could be used as a measure to protect accidental use rather > > than > > to support it. > > > > Lastly, Schnorr actually has a stronger non-malleability property than > > ECDSA, > > the signatures will be binding to the approved transaction and once Lamport > > signed, even a quantum computer could not steal the funds. > > > > -- > > @JeremyRubin > > > _______________________________________________ > bitcoin-dev mailing list > [email protected] > https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev _______________________________________________ bitcoin-dev mailing list [email protected] https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
