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To: Bitcoin Development Mailing List <bitcoindev@googlegroups.com>
From: "'conduition' via Bitcoin Development Mailing List" <bitcoindev@googlegroups.com>
Subject: [bitcoindev] OP_CAT Enables Winternitz Signatures
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Hi list,
Jeremy Rubin's earlier work has already shown
OP_CAT enables Lamport signatures [0]. Jeremy's
approach gives us a script pubkey which is a little
less than 8600 bytes, plus a witness stack of 2121
bytes, for a total witness size of ~10721 bytes. The
scheme relied on using RMD-160 hashes to achieve these
sizes - SHA256 would've bloated the scheme
significantly.
I'd like to concretely demonstrate one more post-quantum
signature algorithm which OP_CAT enables: Winternitz
One-Time Signatures (WOTS) [1]. Specifically we instantiate
Winternitz using SHA256 hash chains of length 16 (AKA
"w = 16"), with a checksum compression technique
inspired by page 4 of the SPHINCS+ paper [2].
We use WOTS to sign the SHA256 hash of an EC signature,
which is validated by OP_CHECKSIG. We break this 256
bit hash up into 64 words of 4 bits each, and then use
script trickery to concatenate and verify the 64 words
match the EC signature's hash.
See a prototype implementation in pseudo-script on
github here.
https://gist.github.com/conduition/c6fd78e90c21f669fad7e3b5fe113182
With this approach, the script + witness stack are
substantially smaller than with Lamport signatures,
even when using 256-bit hashes. More concretely, the
serialized witness stack looks like this:
64 x SHA256 hashes 2112 bytes
64 x message words 128 bytes
1 x BIP340 EC signature 65 bytes
1 x Witness Script 5610 bytes
1 x Control block 33 bytes
--------------------------------------
Total 7948 bytes
I suspect you could shrink this by a few more kilobytes:
- If you were willing to compromise on security in favor
of compactness, you could use RMD-160 hash chains, or
sign RMD160(SHA256(ec_signature)) so that you only need
to sign 40 words instead of 64 words.
- One could experiment with Winternitz chains of length 4,
breaking the message into 2-bit words instead of 4-bit words.
- I'm no script wizard, so I'm sure there are optimizations
left to make on the witness script.
To be useful, this locking script would need to be
hidden as a tapscript leaf and revealed only after
OP_CAT activation. Naturally, this assumes key-path
spending is disabled, otherwise the whole scheme would
be easily defeated by a quantum attacker.
I successfully tested this protocol out using a Bitcoin
Inquisition [3] regtest node. A file containing example
transactions is attached to this email. The second TX
spends the first, using this Winternitz scheme. The
spending TX comes in at only 2070 vbytes after accounting
for the witness discount.
(Big thanks to kallewoof for making the btcdeb
debugging tool [4], without which I would've never
gotten the script working)
regards,
conduition
[0]: https://gnusha.org/pi/bitcoindev/CAD5xwhgzR8e5r1e4H-5EH2mSsE1V39dd06+TgYniFnXFSBqLxw@mail.gmail.com
[1]: https://eprint.iacr.org/2011/191.pdf
[2]: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10179381
[3]: https://github.com/bitcoin-inquisition/bitcoin
[4]: https://github.com/kallewoof/btcdeb
PS If anyone would like to test this on signet, I'd
be more than happy to help. I couldn't get my OP_CAT
transactions mined for some reason so i stuck to regtest.
--
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