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Date: Mon, 18 Dec 2023 22:43:48 +0000
To: Nagaev Boris <bnagaev@gmail.com>,
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: yurisvb@pm.me
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Subject: [bitcoin-dev]  Lamport scheme (not signature) to economize on L1
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I beg to disagree: key owner broadcasts first bundle (let's call it this w=
ay) so that it is on any miner's best interest to include said bundle on t=
heir's attempted coinbase because they know if they don't any other compet=
ing miner will in the next block.

Once more I think it's worth mentioning the principle of weakest link: if =
cracking this Lamport chain within the stipulated few blocks time is harde=
r than the double-spending attack, by definition, it's (much!) more than h=
ard enough.

Consider a 12 bytes =3D 96 bits Lamport hash link (Less than half a Schnor=
r signature). Assume a cracking power of one order of magnitude higher tha=
n the current global hash rate of say 10^21 H/s. Already our assumption is=
 outrageously pessimistic for more that two reasons: 1) The whole premise =
of Bitcoin being secure is presumptive unfeasibility of that attack (weake=
st-link argument); 2) Memory-hard hashes, by definition, are ASIC-resistan=
t in the first place (so, being less efficient than ASICS, the CPUs necess=
ary to match that hashing power would be far *more* costly than today's to=
tal global mining hardware). In other words, we are giving away the hardne=
ss of the hash.

Let's assume a generous window of 1M seconds, so 10^27 hashes. Multiplying=
 that by log2(10), we have shy of 2^89 hashes (actually it's 2^ 'shy of 89=
', but again: erring on the side of safety). That divided by our 2^96 poss=
ible pre-images gives a probability of approximately 2^-6 < 0.02. This doe=
sn't sound very impressive, but an important thing to have in mind is that=
 this attack would destroy utility only of its specific victim (owner of t=
arget UTXO), unlikely the 50%+epsilon attack, in which the adversary may b=
lock whomever they want from ever having a transaction mined. Again, we ar=
e giving away over 11 days for good measure to safeguard against loss of c=
onnection.

More importantly, the economic viability of that attack: if your UTXO has =
less than ~50 times the cost of that operation, which we could lower bound=
 for, say, half of blocks rewards (again, generously assuming 100% ROI for=
 mining). Let's be generous once again disregard mining fees, which would =
give us (block reward)*(seconds)/((1+ROI)*(second per block)*(prob. succes=
s)) =3D 6.25*10^6 / (2*600*0.02)BTC ~ 260416 BTC.

So mine is an argument of economic viability: clearly adversary's economy =
of scale is positive, and it doesn't make sense to consider an adversary w=
ith more scale than that necessary for double spending. Even at that unrea=
listically large scale, however, and even assuming your adversary would ga=
in 1000 times more utility than what they make their victim loose, it woul=
d still be unworthy to conduct such attack to an UTXO of less than 1K BTC.

In retrospect, I'm beginning to think that 12 bytes is rather an overkill.

YSVB

Sent with Proton Mail secure email.

On Monday, December 18th, 2023 at 6:48 PM, Nagaev Boris <bnagaev@gmail.com=
> wrote:


> On Mon, Dec 18, 2023 at 2:22=E2=80=AFPM yurisvb@pm.me wrote:
> =


> > Most Wallets implement BIP39 with 12 words, which corresponds to 128 b=
its of entropy + 4 of checksum (so really only 128 bits).
> > =


> > 2 times that would get even to one Schnorr signature, as you say.
> > Going lower than 128 per hash is, IMO admissible under the same premis=
e of memory-hard hashes like Argon2, Scrypt, CryptoNight, Catena, Balloon =
Hashing, or Krypton8 (the latter of my authoring, a fully homomorphically =
encryptable memory-hard hash). You make hashing N times more time-costly u=
nder some conservative assumption and allow for the alleviation of log2(N)=
 bits from your key. It's widely adopted in passwords (Argon2, for instanc=
e, being the 2015 Password Hash Competition) since human memorization of p=
assword is a critical weak link in security and UX. BIP39 itself resorts t=
o PBKDF2 with 2048 iterations with the same goal, even though it's not mem=
ory-hard. But there is more:
> > =


> > By design, my proposed Lamport chain needs only to resist brute-force =
for a few blocks time, so key strength can be cheapened even further. Keep=
 in mind that before its first transaction, the public-key of an address i=
s not published, so the window of opportunity for brute-forcing a key with=
 lower strength really only opens upon the broadcasting of the transaction=
, and closes within a few blocks time.
> =


> =


> IIRC, miner M1 is the only party who verifies the ECC signature in the
> proposed protocol. If M1 is malicious, he can crack the short hash of
> an address in advance (spending as much time as needed). He should do
> it twice to know the next two hashes. Then mines the first transaction
> (in which he steals coins from the address) with the first hash and
> then publish the second hash a few blocks later to finalize the theft.
> =


> > YSVB
> > =


> > Sent with Proton Mail secure email.
> > =


> > On Monday, December 18th, 2023 at 5:45 PM, Nagaev Boris bnagaev@gmail.=
com wrote:
> > =


> > > Hey Yuri,
> > =


> > > On Mon, Dec 18, 2023 at 6:19=E2=80=AFAM Yuri S VB via bitcoin-dev
> > > bitcoin-dev@lists.linuxfoundation.org wrote:
> > =


> > > > down from 136 from ECC.
> > =


> > > Schnorr signature has size 64 bytes (serialized format consists of x
> > > coordinate of R and of s, 32 bytes each).
> > =


> > > > The whole point is that, in the typical use case in which pre-imag=
e of hash is, in fact, successfully broadcasted before maturity, commitmen=
t, the only ECC signature in this protocol is discarded, and only two Lamp=
ort hashes end up being buried at L1.
> > =


> > > Two SHA256 hashes are 64 bytes in total, the same as one schnorr sig=
nature.
> > =


> > > > To push economy even further, we could implement a memory-hard has=
h like Argon2 to do the same entropy-processing trade-off already utilized=
 for passwords, so we could have hashes of, say 12 bytes, making it 24 in =
total
> > =


> > > 12 bytes security for spending bitcoins is not enough, is it?
> > =


> > > --
> > > Best regards,
> > > Boris Nagaev
> =


> =


> =


> =


> --
> Best regards,
> Boris Nagaev
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