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Date: Thu, 21 Dec 2023 16:07:27 +0000
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>,
 Nagaev Boris <bnagaev@gmail.com>
From: yurisvb@pm.me
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Subject: Re: [bitcoin-dev] Lamport scheme (not signature) to economize on L1
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You are right to point out that my proposal was lacking defense against ra=
inbow-table, because there is a simple solution for it:
To take nonces from recent blocks, say, T0-6, ..., T0-13, for salting LSIG=
, and ECCPUB to salt LAMPPUB. Salts don't need to be secret, only unknown =
by the builder of rainbow table while they made it, which is the case, sin=
ce here we have 8*32=3D256 bits for LSIG, and the entropy of ECCPUB in the=
 second.

With rainbow table out of our way, there is only brute-force analysis to m=
ind. Honestly, Guess I should find a less 'outrageously generous' upper bo=
und for adversary's model, than just assume they have a magic wand to conv=
ert SHA256 ASICS into CPU with the same hashrate for memory- and serial-wo=
rk-hard hashes (therefore giving away hash hardness). That's because with =
such 'magic wand' many mining pools would, not only be capable of cracking=
 2^48 hashes far within the protocol's prescribed 48 hours, but also 2^64 =
within a block time, which would invalidate a lot of what is still in use =
today.

Please, allow me a few days to think that through.

YSVB

Sent with Proton Mail secure email.

On Wednesday, December 20th, 2023 at 10:33 PM, Nagaev Boris <bnagaev@gmail=
.com> wrote:


> On Tue, Dec 19, 2023 at 6:22=E2=80=AFPM yurisvb@pm.me wrote:
>
> > Thank you for putting yourself through the working of carefully analyz=
ing my proposition, Boris!
> >
> > 1) My demonstration concludes 12 bytes is still a very conservative fi=
gure for the hashes. I'm not sure where did you get the 14 bytes figure. T=
his is 2*(14-12) =3D 4 bytes less.
>
>
> I agree. It should have been 12.
>
> > 2) Thank you for pointing out that ECCPUB is necessary. That's exactly=
 right and I failed to realize that. To lessen the exposure, and the risk =
of miner of LSIG, it can be left to be broadcast together with LAMPPRI.
> >
> > 3) I avail to advocate for economizing down the fingerprint to just 12=
8 bits for the weakest-link-principle, since 128 bits is a nearly ubiquito=
us standard, employed even by the majority of seeds. Not an argument again=
st plain Schnorr, because Schnorr keys could use it too, but, compared wit=
h current implementations, we have that would be 20-16=3D4 bytes less.
>
>
> I think that the digest size for hash should be 2x key size for
> symmetric encryption. To find a collision (=3D break) for a hash
> function with digest size 128 bits one needs to calculate ~ 2^64
> hashes because of the birthday paradox.
>
> > 4) [Again, argument against plain, because it cuts for both sides:] To=
 economize even further, there is also the entropy-derivation cost trade-o=
ff of N times costlier derivation for log2(N) less bits. If applied to the=
 Address, we could shave away another byte.
> >
> > 5) T0 is just the block height of burying of LSIG doesn't need to be b=
uried. T2 can perfectly be hard-coded to always be the block equivalent of=
 T0 + 48 hours (a reasonable spam to prevent innocent defaulting on commit=
ment due to network unavailability). T1 is any value such as T0 < T1 < T2,=
 (typically T1 <=3D T0+6) of user's choosing, to compromise between, on on=
e hand, the convenience of unfreezing UTXO and having TX mining completed =
ASAP and, on the other, avoiding the risk of blockchain forking causing LA=
MPPRI to be accidentally leaked in the same block height as LSIG, which al=
lows for signatures to be forged. So this is 16 bytes less.
> >
> > Miners would keep record of unconfirmed BL's, because of the reward of=
 mining either possible outcome of it (successful transaction or execution=
 of commitment). Everything is paid for.
> >
> > So, unless I'm forgetting something else, all other variables kept equ=
al, we have 20 bytes lighter than Schnorr; and up to 25 bytes less the cur=
rent implementation of Schnorr, if items 3 and 4 are implemented too. Alre=
ady we have a reduction of between 21% and 26%, while, so far, nobody in t=
he mailing list has disputed how 'outrageously' conservative the 12 bytes =
figure is.
>
>
> 26% reduction of block space utilization would be great, but the price
> of relying on 12 bytes hashes (only need 2^48 hashes to find a
> collision) is too much for that, IMHO.
>
> Another consideration is about 12 byte hashes. Let's try to figure out
> if they are resistant to rainbow table attack by a large organization.
> Let's assume that the rainbow table has a chain length of 1024^3 (billio=
n).
> What storage size is needed? 2^96 * 12 / 1024^3 =3D 900 exabytes.
> Both chain length and storage size seems prohibitively high for today,
> but tomorrow the hash function can be optimized, memory can be
> optimized, storage can become cheaper etc. And this attack may be
> affordable for state level attackers.
>
> > Any other objections?
> >
> > YSVB
>
>
>
> --
> Best regards,
> Boris Nagaev
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