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Date: Tue, 19 Dec 2023 14:07:23 +0000
To: Nagaev Boris <bnagaev@gmail.com>
From: yurisvb@pm.me
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: [bitcoin-dev] Lamport scheme (not signature) to economize on L1
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Thank you for the question, Boris. That was an easy one:

Short answer is Lamport hashes are protected by long hash of key fingerpri=
nt an ECC (Schnorr or otherwise conventional) public-key, which is not pub=
lished until first transaction. For clarity:

HL(.) =3D serial-work- and memory-*hard* hash with *short* digest (ex.: Ar=
gon2 with ~ 12 bytes output. "L" for "Lamport");
HC(.) =3D nonspecific representation of conventional, serial-work- and mem=
ory-*easy* hashes with *long* (brute-force-resistant) digest length. "C" f=
or "Conventional";
KDF(.) =3D conventional key deriving function
ECCPUB =3D public key correspondent to ECCPRI
ECCPRI =3D KDF(seed, tag) //conventional BTC signing key (could be Schnorr=
 instead)
LAMPPUB =3D HL(LAMPPRIi)
LAMPPRI =3D HL(seed, tag) //Though it is (more) feasible to crack a seed S=
 that works as pre-image to LAMPRI, such seed can only be deemed valid if =
the public key correspondent to KDF(s) =3D ECCPUB, so ultimately, cracking=
 seed is still as hard as cracking a conventional seed.
ADDR =3D H(ECCPUB, LAMPPUB) //Conventional BTC key fingerprinting with con=
ventionally used hashes and their respective brute-force-resistant digest =
lengths
TX =3D plaintext transaction
LSIG =3D HL(TX, LAMPPRI)
COMMITMENT =3D Smart contract stating "This UTXO is frozen until one of th=
e following happens: A) publishing of a L such that HL(TX,L) =3D LSIG befo=
re T2 in which case TX is deemed valid and executed, or B) T2 blocks from =
now, when miner of LSIG has gets F1+FF1, and the miner of COMMITMENT gets =
FC, both from UTXO"
BL =3D "Bundle of Lamport scheme" =3D (TX, LSIG)
BC =3D "Bundle of Commitment and Conventional Signing" =3D (COMMITMENT, EC=
CPRI(COMMITMENT), ECCPUB, LAMPPUB)	//LAMPPUB is added here to allow easy v=
erification that ECCPUB corresponds to ADDR
BT =3D "Total Bundle" =3D (BL, BC)
F1 =3D fee offered to mine BL
FF1 =3D fine offered to miner of BL to compensate for delay
FC =3D fee offered to mine BC in case of default
T0 =3D Block height of broadcasting of BT
T1 =3D Block height owner should aim at broadcasting LAMPPRI  block ~ T0+1=
 to T0+6 blocks. This is to protect owner from dissensus (revealing LAMPPR=
I in a block and have it utilized to forge transaction in a competing bloc=
k of same height).
T2 =3D Block height of expiration of commitment ~ T0+24 hours to T0+ a few=
 days to protect user from execution of commitment being triggered by inno=
cent unavailability.

From ADDR alone, Miners, cannot forge a valid LSIG, nor try to ascertain L=
AMPPUB or LAMPPRI, because of pre-image-resistance of H(.) and brute-force=
 resistance of ECCPUB before being published. The saving happens because, =
safe from T2 passing without LAMPRI being broadcasted, only BL and LAMPPR,=
 and not BC, end up in Blockchain.

The proposed scheme, therefore allows for only 1 instance of Lamport schem=
ed-based economic transaction, which has to be the first transaction of AD=
DR (because of publishing of ECCPUB). After this first transaction, ADDR i=
s stil valid, just no longer able to issue transactions.

The proposed scheme, therefore, favors the good practice of non-address re=
use.

YSVB

Sent with Proton Mail secure email.

On Tuesday, December 19th, 2023 at 1:45 AM, Nagaev Boris <bnagaev@gmail.co=
m> wrote:


> On Mon, Dec 18, 2023 at 7:44=E2=80=AFPM yurisvb@pm.me wrote:
> =


> > I beg to disagree: key owner broadcasts first bundle (let's call it th=
is way) so that it is on any miner's best interest to include said bundle =
on their's attempted coinbase because they know if they don't any other co=
mpeting miner will in the next block.
> =


> =


> What if an attacker broadcasts the first bundle? He spent a lot of
> time cracking the hash which is the part of the address in the
> proposed scheme. Then he cracked the second layer of hashing to have
> both hashes ready. If the utxo has enough sats, the attack is
> economically viable.
> =


> =


> --
> Best regards,
> Boris Nagaev
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