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From: Ethan Heilman <eth3rs@gmail.com>
Date: Sun, 24 Nov 2024 16:13:00 -0500
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Subject: [bitcoindev] Slashing covenants
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Slashing covenants is a protocol for covenants in Bitcoin via
incentives. A covenant is a set of rules about what transactions can
spend a Bitcoin output which is encumbered by that covenant. Typically
a covenant is enforced by preventing someone from spending that
output. In this protocol we instead allow the spending of the output
and then punish the spender by a loss of funds, i.e. we slash them, if
they do not follow the rules of the covenant. This is less secure than
a covenant enforced by an opcode, FE or ColliderScript, because it
relies on incentives over enforcement. The advantage of this approach
is that it is efficient, does not add new cryptographic assumptions
and is possible on Bitcoin today.

This protocol uses very similar mechanisms to BitVM, originally I
thought this was how BitVM worked, which is why I didn=E2=80=99t publish it=
.
After talking to many people it appears this technique is not used in
BitVM.


Notation
=3D=3D=3D=3D
By <x>32 we denote a value, x, in Bitcoin Script which is encoded as a
list of 32-bit stack elements. We can perform arbitrary computation on
such values using Bitcoin=E2=80=99s math opcodes, a.k.a., Small Script.

Protocol
=3D=3D=3D=3D
The essential problem for enforcing covenants in Bitcoin outputs is
showing that a signature s1 that will pass CHECKSIGVERIFY is equal to
a signature s2 encoded for Small Script. This is because once we get a
signature into Small Script, we extract the sighash and do transaction
introspection. ColliderScript gets us covenants by using hash
collisions to check equality between s1 and <s2>32. CAT gets us
covenants by simply concatenating all the <s2>32 and then comparing
against s1 using EQUAL:

s2 =3D CAT(<s2>32 [0], <s2>32 [1],  <s2>32 [2], =E2=80=A6 <s2>32 [15])
EQUAL s1, s2

Slashing covenants works by removing the requirement for this equality
check, but instead providing a fraud proof ifs1!=3Ds2, and posting that
fraud proof to punish the spending party. To do this we construct a
Bitcoin script output which takes as input:

s1 - the spending signature.
<s2>32 - the spending signature encoded in small script. An honest
spender will set s1 =3D s2.
L - a Lamport signature on <s2>32.
<txn data>32 - data about the spending transaction that we use to open
the sighash

The Bitcoin script covenant output then:
1. checks s1 is a valid spending signature.
2. Checks that <s2>32 is validly signed by the Lamport signature L
3. Supplies <s2>32 and <txn data>32 to Small Script which enforces the
covenant under the assumption that s1=3Ds2.

Covenant output (s1, <s2>32, L, <txn data>32):
  CHECKSIGVERIFY s1
  Lamport-Verify <s2>32, L
  SmallScript Enforce-Cov <s2>32, <txn data>32

As long as s1=3Ds2 the covenant is enforced. However if s1!=3Ds2 the
covenant can be broken. To punish spenders who set s1!=3Ds2, we create
an output that allows anyone to burn/slash the coins of the rule
breaker if and only if they spent a covenant and supplied s1 and s2
such that  s1!=3Ds2.

The Bitcoin script slash output takes as input: <s1>32, <s2>32, and L.

Slashing output (<s1>32, <s2>32, L):
  SmallScript CHECKSIGVERIFY <s1>32
  Lamport-Verify <s2>32, L
  IF <s1>32 !=3D <s2>32: Verify

Thus the slashing output can only be spent if the rule breaker spent
the covenant with s1!=3Ds2. SmallScript CHECKSIGVERIFY is used to prove
the rule breaker signed s1, the lamport signature is used to prove the
rule breaker signed s2. Thus, we have a fraud proof that the rule
breaker signed s1!=3Ds2.  The Lamport signature is only used here to
avoid having to do ECC math in Small Script in the covenant.

Note that because we are doing CHECKSIGVERIFY in Small Script, the
spending transaction will be massive. The slashing occurs because of
the fees incurred by spending the slashing transaction. Note that such
a slashing output could also be done on ethereum. This would simplify
the construction.

For the purposes of explanation, we assumed the spender is also the
party who is slashed. In actual practice it is more likely you could
have a set of N slashable cosigners who could attest to a spend not
violating the covenant. Using pre-signed transactions you could
recover an output if all n slashable cosigners were indefinitely
offline. If you could fit a SNARKS in Small Script, you could have
people join and leave the cosigner set dynamically for already posted
covenant outputs by simply proving they have posted slash outputs and
that the value in covenants < value in slash outputs.

--=20
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