#LyX 2.1 created this file. For more info see http://www.lyx.org/ \lyxformat 474 \begin_document \begin_header \textclass article \begin_preamble % for subfigures/subtables \usepackage[caption=false,font=footnotesize]{subfig} \end_preamble \options journal \use_default_options false \maintain_unincluded_children false \language english \language_package none \inputencoding default \fontencoding global \font_roman default \font_sans default \font_typewriter default \font_math auto \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \default_output_format default \output_sync 0 \bibtex_command bibtex \index_command default \float_placement H \paperfontsize default \spacing single \use_hyperref true \pdf_title "Your Title" \pdf_author "Your Name" \pdf_bookmarks true \pdf_bookmarksnumbered true \pdf_bookmarksopen true \pdf_bookmarksopenlevel 1 \pdf_breaklinks false \pdf_pdfborder true \pdf_colorlinks false \pdf_backref false \pdf_pdfusetitle false \pdf_quoted_options "pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false" \papersize default \use_geometry false \use_package amsmath 1 \use_package amssymb 1 \use_package cancel 0 \use_package esint 0 \use_package mathdots 1 \use_package mathtools 0 \use_package mhchem 1 \use_package stackrel 0 \use_package stmaryrd 0 \use_package undertilde 0 \cite_engine basic \cite_engine_type default \biblio_style ieeetr \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false \justification true \use_refstyle 0 \index Index \shortcut idx \color #008000 \end_index \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \paragraph_indentation default \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle default \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Title Reaching The Ground With Lightning (draft 0.2) \end_layout \begin_layout Author Rusty Russell \end_layout \begin_layout Abstract The Lightning Network (as proposed by Joseph Poon and Thaddeus Dryja \begin_inset CommandInset citation LatexCommand cite key "Poon2015Lightning" \end_inset ) requires some new sighash modes in order to work with Bitcoin. This paper proposes a simplified variant which requires only modifications which are already proposed for bitcoin, and slightly simplifies the revocation of existing contracts. \end_layout \begin_layout Abstract Keywords: bitcoin, lightning, revocation hash, HTLC, BIP62, BIP65, BIP68 \end_layout \begin_layout Section Introduction \end_layout \begin_layout Standard The Bitcoin network \begin_inset CommandInset citation LatexCommand cite key "nakamoto2008bitcoin" \end_inset allows the transfer of value between peers using \emph on transactions. \emph default Each bitcoin transaction consists of one or more \emph on outputs \emph default (typically specifying the hash of the recipient's key), and one or more \emph on inputs \emph default (typically containing the recipient's key and a signature of the transaction). Thus one transfers value to another peer by creating a transaction which \emph on spends \emph default one or more outputs and creates an output which the recipient can spend using their private key. \end_layout \begin_layout Standard While such cryptographic transfer of value is near-instantaneous, ensuring that the transaction has been included in the consensus of the shared ledger (aka. \emph on blockchain \emph default ) creates delays ranging from a few minutes to hours, depending on the level of reliability required. Inclusion in the blockchain is performed by miners, who preferentially include transactions paying greatest fee per byte. \end_layout \begin_layout Standard Thus using the blockchain directly is slow, and too expensive for genuinely small transfers (typical fees are a few cents). \end_layout \begin_layout Section Previous Work \end_layout \begin_layout Standard To work around the bitcoin network's delays and fees, several forms of \emph on off-chain \emph default transaction patterns have been developed, where series of transactions are sent directly between two parties, with only the initial opening transactio n and final redemption transaction being included in the bitcoin blockchain. \end_layout \begin_layout Standard The Lightning Network paper proposed a solution, but at the cost of introducing new signature variants (sighash ops). Adding a new signature opcode would allow many other improvements \begin_inset Foot status collapsed \begin_layout Plain Layout Schnorr signatures offer faster batch validation, according to https://github.com /ElementsProject/elementsproject.github.io#schnorr-signature-validation \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Plain Layout DER encoding adds unnecessary bytes and is a cause of malleability \end_layout \end_inset but that is precisely why it's a matter for longer term research and unlikely to be deployed in Bitcoin in the immediate future. \end_layout \begin_layout Subsection Payment Channels \end_layout \begin_layout Standard The concept of \emph on payment channels \emph default (sometimes called micropayment channels) has existed in various forms for several years \begin_inset CommandInset citation LatexCommand cite key "BitcoinChannels" \end_inset . The simplest form is as follows, and allows A to quickly and cheaply pay B a stream of slightly increasing amounts: \end_layout \begin_layout Enumerate A creates an \emph on anchor \emph default transaction to \emph on open the channel \emph default which: \end_layout \begin_deeper \begin_layout Enumerate Outputs $1, \end_layout \begin_layout Enumerate Requires the signatures of both A and B to redeem. \end_layout \end_deeper \begin_layout Enumerate A sends the transaction ID of the anchor, which output to spend, and the amount of that output to B. \end_layout \begin_layout Enumerate B signs a \begin_inset Quotes eld \end_inset refund \begin_inset Quotes erd \end_inset transaction which: \end_layout \begin_deeper \begin_layout Enumerate spends that anchor output, \end_layout \begin_layout Enumerate outputs the $1 to an address controlled by A, and \end_layout \begin_layout Enumerate can only be spent in 24 hours (using the \emph on locktime \emph default field) \end_layout \end_deeper \begin_layout Enumerate B sends A the refund transaction. \end_layout \begin_layout Enumerate A broadcasts the anchor transaction, knowing she can get the funds back in 24 hours using the refund if B vanishes. \end_layout \begin_layout Standard A can now pay B 1 cent by signing a new \emph on commitment \emph default transaction to send to B, which spends the anchor output and has two outputs: one pays A 99c, and the other pays B 1 cent. A can later pay B another cent by signing another transaction ( \begin_inset Quotes eld \end_inset updating the commitment \begin_inset Quotes erd \end_inset ) for B which pays A 98c and B 2c, etc. \end_layout \begin_layout Standard At any point, B can \begin_inset Quotes eld \end_inset close the channel \begin_inset Quotes erd \end_inset by signing and broadcasting the latest commitment transaction to collect the money. B should do this before 24 hours pass, otherwise A can use the refund transacti on. \end_layout \begin_layout Subsubsection Limitations Of Simple Payment Channels \end_layout \begin_layout Standard Simple channels have several limitations: \end_layout \begin_layout Description Single \begin_inset space ~ \end_inset recipient. A new recipient requires a new channel, which must wait for consensus on the anchor transaction. \end_layout \begin_layout Description One \begin_inset space ~ \end_inset way. They cannot be reversed: A can sign a transaction which pays B less money than the last, but B could still broadcast the older transaction. \end_layout \begin_layout Description Vulnerable \begin_inset space ~ \end_inset to \begin_inset space ~ \end_inset malleability. The anchor transaction could be altered in several ways (without invaliding it completely) before inclusion in the blockchain: this alters its transaction id and thus makes the refund transaction unusable. \end_layout \begin_layout Standard This last issue is a common one with complex bitcoin transactions, and BIP62 \begin_inset CommandInset citation LatexCommand cite key "BIP62" \end_inset is proposed to prevent non-signing parties from being able to malleate transactions. \end_layout \begin_layout Subsection Generalized Payment Channels Using Revocable Transactions \end_layout \begin_layout Standard The Lightning network introduced generalized, bi-directional payment channels, referred to here as \emph on Poon-Dryja channels \emph default . These use a mutual anchor, which both create to provide the channel funding, and a symmetrical \emph on pair \emph default of updatable commitment \emph on \emph default transactions rather than the single transaction used in the one-way channel case, as shown in figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Figure-1-from" \end_inset \begin_inset Foot status collapsed \begin_layout Plain Layout Note: this diagram has been corrected since: Commitment Close Tx 1A (CC1b) -- should be CC1a, and vice-versa \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename ln-draft-fig1.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Figure 1 from the Lightning Network Draft 0.5 \begin_inset CommandInset label LatexCommand label name "fig:Figure-1-from" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard To update the commitment, A sends B a signature for B's new commitment transacti on, and B sends A a signature for A's new commitment transaction. \end_layout \begin_layout Standard As before, each commitment transaction contains two outputs, one for A and one for B; but A's commitment transaction output to itself is encumbered by an additional restriction (as is B's output to itself). Instead of paying A directly, A's output needs both A and B's signature. B provides such a signature, but on a \begin_inset Quotes eld \end_inset commitment refund \begin_inset Quotes erd \end_inset transaction which can only be spent after a delay (40 days in the paper). Thus if A closes the channel by signing and broadcasting its commitment transaction, B can collect its output immediately, but A must wait 40 days. \end_layout \begin_layout Standard This delay encumbering the output is what makes the commitment transaction \emph on revocable; \emph default once an updated commitment transaction is agreed upon, the previous commitment transaction pair is revoked by sharing the private keys needed to redeem those encumbered outputs. Thus, A shares its (throwaway) private key, and B shares its throwaway private key. If A were to sign and broadcast a revoked commitment transaction, B could not only immediately spend its own output, but it has both A's key and its own to generate a transaction which can spend the output which would normally go to A after a delay. \end_layout \begin_layout Subsection Hashed Timelock Contracts (HTLCs) \end_layout \begin_layout Standard The Lightning Network paper used a set of 4 transactions to implement a \emph on hashed timelock contract, \emph default which guarantees payment of a given amount on presentation of a secret value \emph on R \emph default within a certain timespan. Any number of these could be active within a generalized channel, and this is what allows a network to form: Node A offers node B $1 for the secret within 2 days, node B offers node C 99c for the secret within 1 day, etc. \end_layout \begin_layout Standard This arrangement for one side of a single node is shown in figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Figure-2-from" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename ln-draft-fig2.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Figure 2 from the Lightning Network Draft 0.5 \begin_inset CommandInset label LatexCommand label name "fig:Figure-2-from" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Section Enhancements To Lightning \end_layout \begin_layout Standard This paper proposes various modifications. \end_layout \begin_layout Subsection Poon-Dryja Generalized Payment Channel Modifications \end_layout \begin_layout Standard This paper proposes three changes to the commitment transactions. \end_layout \begin_layout Subsubsection Placing Timeout in Output Script \end_layout \begin_layout Standard Rather than using a separate transaction to enforce the delay, BIP65 \begin_inset CommandInset citation LatexCommand cite key "BIP65" \end_inset proposes an OP_CHECKLOCKTIMEVERIFY which allows an output to specify the minimum time at which it can be spent. With this enhancement, we no longer need a separate \begin_inset Quotes eld \end_inset commitment refund \begin_inset Quotes erd \end_inset transaction. The commitment transaction to-self output script would be a little more complex: \end_layout \begin_layout Itemize A and B's signature, OR \end_layout \begin_layout Itemize A's signature and OP_CHECKLOCKTIMEVERIFY <40 days> \end_layout \begin_layout Standard As of Nov. 13, 2015, BIP65 has been deployed and is in the process of being activated. \end_layout \begin_layout Subsubsection Using Relative Locktime \end_layout \begin_layout Standard The Poon-Dryja channel uses a 40 day locktime, because transaction locktime is absolute. Before 40 days the channel must be closed, otherwise spending a revoked transaction and immediately following it with the commit refund transaction is possible. \end_layout \begin_layout Standard BIP112[#BIP112] proposes OP_CHECKSEQUENCEVERIFY, an opcode which allows an output to specify a minimum \emph on relative \emph default time before the output can be spent \begin_inset CommandInset citation LatexCommand cite key "friedenbach_bitcoin-development_2015,BIP112" \end_inset can reduce this timeout (say, to 1 day) and avoid placing a lifetime limit on the channel, like so: \end_layout \begin_layout Itemize A and B's signature, OR \end_layout \begin_layout Itemize A's signature and OP_CHECKSEQUENCEVERIFY <1 day> \end_layout \begin_layout Standard As of Nov. 13, 2015, BIP112 has not been deployed. \end_layout \begin_layout Subsubsection Using Revocation Preimages Instead of Private Keys \end_layout \begin_layout Standard There's a slightly more intuitive and more efficient method than exchanging private keys, which is to reuse a technique of hash preimages which is already needed for HTLCs (as we see later). \end_layout \begin_layout Standard Instead of using a private key, B uses knowledge of a hash preimage as well as its signature to steal funds from a revoked commitment transaction. Thus, to create a commitment transaction each side provides a hash value; to revoke a commitment transaction it provides the prehash image. \end_layout \begin_layout Standard The resulting commitment transaction to-self output now looks like: \end_layout \begin_layout Itemize B's signature and a preimage which hashes to , OR \end_layout \begin_layout Itemize A's signature and OP_CHECKSEQUENCEVERIFY <1 day> \end_layout \begin_layout Standard This can be expressed fairly easily in bitcoin's script-based scripting language, as annotated in \begin_inset CommandInset ref LatexCommand nameref reference "sub:Commitment-Outputs-For" \end_inset . The final pair of commitment transaction outputs is shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Commitment-Transaction-Outputs" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename commit-tx.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Commitment Transaction Outputs \begin_inset CommandInset label LatexCommand label name "fig:Commitment-Transaction-Outputs" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Channel Opening Modifications \end_layout \begin_layout Standard The method of creating the first commitment transaction before signing the anchor transaction (as proposed in the paper) presents two problems in practice: \end_layout \begin_layout Enumerate The anchor transaction id required for the commitment input will only be known once the anchor is signed, and \end_layout \begin_layout Enumerate The anchor transaction can be malleated by either party before entering the blockchain, rendering the commitment input unusable. \end_layout \begin_layout Standard The last of these is particularly pernicious, as BIP62 doesn't solve it: signatories can always re-sign a transaction, hence altering its transaction ID. The paper proposes new SIGHASH flags which mitigate this problem, but we are attempting to avoid that. \end_layout \begin_layout Standard Our approach is to only have one-sided anchors. These can be later balanced by the lightning network itself, or an atomic-swap to an on-chain bitcoin transaction \begin_inset CommandInset citation LatexCommand cite key "go1111111_single_anchor" \end_inset . Any bitcoin transaction fees are initially funded by that anchor, but the implementation splits fees where possible and never allows either side to spend funds in the channel if they would no longer be able to pay their share. \end_layout \begin_layout Subsection Hashed Timelock Contract (HTLC) Modification \end_layout \begin_layout Standard Using the same techniques used above, we can condense each HTLC into a single output script on the commitment transaction. This output is spendable under three conditions: \end_layout \begin_layout Enumerate Recipient knows the R value (funds go to recipient), or \end_layout \begin_layout Enumerate The HTLC has timed out (funds return to sender), or \end_layout \begin_layout Enumerate The Commit transaction has been revoked (funds go to other side). \end_layout \begin_layout Standard Unlike the original paper, we use revocation preimages instead of sharing temporary private keys. If we also use OP_CHECKLOCKTIMEVERIFY and OP_CHECKSEQUENCEVERIFY it is fairly simple to express these conditions in a single output script. \end_layout \begin_layout Standard For each direction the HTLC could transfer funds, there are two scripts required; one for A's commitment transaction and one for B's commitment transaction. It's also a requirement that the conditions which allow payment to oneself be delayed, to give the other side an opportunity to take the funds in case of revocation. This is shown (omitting the HTLC to-self delays, which depend on the orientatio n of payer/payee with respect to A and B) in figure \begin_inset CommandInset ref LatexCommand ref reference "fig:HTLC-Using-Revocation" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename htlc.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout HTLC Using Revocation Preimages, OP_CLTV and OP_CSV (simplified) \begin_inset CommandInset label LatexCommand label name "fig:HTLC-Using-Revocation" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard The scripts for this can be found in \begin_inset CommandInset ref LatexCommand nameref reference "sec:Appendix-A:-Scripts" \end_inset . \end_layout \begin_layout Section Conclusions \end_layout \begin_layout Standard Secret preimages can replace exposure of temporary private keys in the Lightning Network constructs with no loss of generality, and a slight gain in simplicity. \end_layout \begin_layout Standard The use of script conditionals to enforce timeouts instead of using separate pre-signed transactions reduces an HTLC from a set of four dual-signed transactions to a single (more complex) output script, and additionally avoids any requirement for new CHECKSIG flags for HTLCs. \end_layout \begin_layout Standard By using a rebalanced single anchor, channel establishment can also avoid new CHECKSIG flags, though it loses the important ability to outsource the enforcement of channel contract terms. \end_layout \begin_layout Section* Acknowlegments \end_layout \begin_layout Standard Thanks to mmeijeri on Reddit's r/Bitcoin for pointing out a flaw in escape transactions reusing the same A and B keys as the commitment transaction in \begin_inset CommandInset ref LatexCommand nameref reference "sec:Appendix-B:-Dual" \end_inset \begin_inset Foot status open \begin_layout Plain Layout https://www.reddit.com/r/Bitcoin/comments/3dlxw4/reaching_the_ground_with_lightnin g_lightning/ct80xpp \end_layout \end_inset . Thanks to John Newbery for multiple formatting and typing corrections. \end_layout \begin_layout Standard Thanks to Joseph Poon for designing the escape/fast-escape dual-anchor method, as well as finding a flaw in my original formulation of the dual anchor construct and reviewing an earlier draft of this paper. Also thanks to him and Thaddeus Dryja for the initial eye-opening Lightning Network paper. \end_layout \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex bibfiles "bitcoin" options "bibtotoc,plain" \end_inset \end_layout \begin_layout Section* Appendix A: Transaction Scripts \begin_inset CommandInset label LatexCommand label name "sec:Appendix-A:-Scripts" \end_inset \end_layout \begin_layout Standard All outputs are expressed as pay-to-scripthash outputs, where the redeeming input provides the redeemscript. Where a redeem-hash value is optional, it is generally supplied: for example, if we want to pay to A if a preimage is supplied and B if no preimage is supplied, we expect the input scriptsig to provide two arguments in both cases (generally a zero in the second case). This saves an extra test (of form \begin_inset Quotes eld \end_inset OP_DEPTH OP_EQUAL \begin_inset Quotes erd \end_inset ), at cost of a single byte in the input script. \end_layout \begin_layout Subsection* Anchor Transaction \end_layout \begin_layout Standard The anchor inputs are whatever the node chooses. \end_layout \begin_layout Subsubsection* Anchor Output Redeemscript \end_layout \begin_layout Standard The anchor output is a pay to script hash, with a redeemscript as follows: \end_layout \begin_layout Description OP_HASH \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset OP_EQUAL If the secret is supplied, \end_layout \begin_layout Description OP_IF \end_layout \begin_deeper \begin_layout Description Should be signed by B's escape key. \end_layout \end_deeper \begin_layout Description OP_ELSE \end_layout \begin_deeper \begin_layout Description Should be signed by B's commitment key. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description 2 \begin_inset space ~ \end_inset OP_SWAP Put 2 before B's key on the stack. \end_layout \begin_layout Description \begin_inset space ~ \end_inset 2 \begin_inset space ~ \end_inset OP_CHECKMULTISIG Make sure A and B have signed. \end_layout \begin_layout Subsection* Commitment Transactions For Generalized Channels \begin_inset CommandInset label LatexCommand label name "sub:Commitment-Outputs-For" \end_inset \end_layout \begin_layout Standard These examples are for A's Commitment Transaction; switch A and B to get B's commitment transaction. \end_layout \begin_layout Subsubsection* Commitment Input Script \end_layout \begin_layout Standard The commitment transaction has two inputs; one which spends each anchor output. The zero after the signature indicates it is not revealing the secret: \end_layout \begin_layout Description 0 \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset 0 \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsubsection* Commitment Transaction Output Redeemscripts \end_layout \begin_layout Standard One output pays B's funds to B as normal (eg. pay to scripthash \begin_inset Quotes eld \end_inset OP_CHECKSIG \begin_inset Quotes erd \end_inset ). The other output pays A's funds: either to B if they supply the revocation preimage, or to A after a delay. This is the redeemscript: \end_layout \begin_layout Description OP_HASH160 \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset OP_EQUAL Did they supply revocation preimage? \end_layout \begin_layout Description OP_IF \end_layout \begin_deeper \begin_layout Description To B. \end_layout \end_deeper \begin_layout Description OP_ELSE \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKSEQUENCEVERIFY \begin_inset space ~ \end_inset OP_DROP Spending transaction must be after timeout \end_layout \begin_layout Description To A. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description OP_CHECKSIG Signature must be correct. \end_layout \begin_layout Subsubsection* Spending Commitment Output \end_layout \begin_layout Standard Either B using a revocation preimage: \end_layout \begin_layout Description \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Standard Or A using after a timeout: \end_layout \begin_layout Description \begin_inset space ~ \end_inset 0 \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsection* Hash Locked Transaction Commitments \end_layout \begin_layout Standard There are two styles of commitment transaction outputs for HTLCs: a \begin_inset Quotes eld \end_inset sender \begin_inset Quotes erd \end_inset and \begin_inset Quotes eld \end_inset receiver \begin_inset Quotes erd \end_inset case. The output is a pay-to-script-hash, so the redeemscripts are shown below. \end_layout \begin_layout Standard These scripts show A as the sender, and B as the receiver: exchange A and B for the reverse. \end_layout \begin_layout Subsubsection* HTLC Sender Redeemscript \end_layout \begin_layout Description OP_HASH160 \begin_inset space ~ \end_inset OP_DUP Replace top element with two copies of its hash \end_layout \begin_layout Description \begin_inset space ~ \end_inset OP_EQUAL Test if they supplied the HTLC R value \end_layout \begin_layout Description OP_SWAP \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset OP_EQUAL \begin_inset space ~ \end_inset OP_ADD Or the commitment revocation hash \end_layout \begin_layout Description OP_IF If any hash matched. \end_layout \begin_deeper \begin_layout Description Pay to B. \end_layout \end_deeper \begin_layout Description OP_ELSE Must be A, after HTLC has timed out. \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKLOCKTIMEVERIFY Ensure (absolute) time has passed. \end_layout \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKSEQUENCEVERIFY Delay gives B enough time to use revocation if it has it. \end_layout \begin_layout Description OP_2DROP Drop the delay and htlc-timeout from the stack. \end_layout \begin_layout Description Pay to A. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description OP_CHECKSIG Verify A or B's signature is correct. \end_layout \begin_layout Subsubsection* HTLC Receiver Redeemscript \end_layout \begin_layout Description OP_HASH160 \begin_inset space ~ \end_inset OP_DUP Replace top element with two copies of its hash \end_layout \begin_layout Description \begin_inset space ~ \end_inset OP_EQUAL B redeeming the contract, using R preimage? \end_layout \begin_layout Description OP_IF \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKSEQUENCEVERIFY Delay gives A enough time to use revocation if it has it. \end_layout \begin_layout Description OP_2DROP Drop extra hash and delay from the stack \end_layout \begin_layout Description Pay to B \end_layout \end_deeper \begin_layout Description OP_ELSE \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_EQUAL If the commit has been revoked. \end_layout \begin_layout Description OP_NOTIF If not, you need to wait for timeout. \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKLOCKTIMEVERIFY \begin_inset space ~ \end_inset OP_DROP Ensure (absolute) time has passed. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description Pay to A \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description OP_CHECKSIG Verify A or B's signature is correct. \end_layout \begin_layout Subsubsection* Redeeming A HTLC Output \end_layout \begin_layout Standard To redeem an HTLC, the recipient one provides the preimage R, and their signature. In our example above, B can redeem the HTLC: \end_layout \begin_layout Description \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsubsection* Claiming a Timed-out HTLC \end_layout \begin_layout Standard To claim a timed-out HTLC, the sender supplies a zero value (which is nice and short, but fails to hash to any of the revocation hashes), and their signature. In our example above, A can claim the timed-out HTLC: \end_layout \begin_layout Description \begin_inset space ~ \end_inset 0 \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsubsection* Claiming A HTLC Output For A Revoked Commitment Transaction \end_layout \begin_layout Standard If either side publishes a commitment transaction which has been revoked, we can use the revocation preimage they supplied to spend all the outputs. This example shows A claiming the HTLC output if B broadcasts a revoked commitment transaction: \end_layout \begin_layout Description \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Section* Appendix B: Dual Anchors With Escape Transactions \begin_inset CommandInset label LatexCommand label name "sec:Appendix-B:-Dual" \end_inset \end_layout \begin_layout Standard This appendix presents a dual-input anchor solution which doesn't require additional bitcoin signature flags. It is not being proposed currently, as it seems that a single-sided anchor is probably sufficient. \end_layout \begin_layout Subsection Separate Anchor Transactions \end_layout \begin_layout Standard To avoid the problem of needing all anchor signatures to derive the anchor transaction ID to create the commitment transaction input, we split the anchor into two transactions; thus A knows its anchor transaction ID, and B knows its anchor transaction ID as shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Simplistic-Dual-Anchor" \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename dual-anchor-diag1.eps scale 50 \end_inset \begin_inset Caption Standard \begin_layout Plain Layout Simplistic Dual Anchor Design \begin_inset CommandInset label LatexCommand label name "fig:Simplistic-Dual-Anchor" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard This form allows A and B to create commitment transactions which spends the anchors outputs by exchanging anchor transaction IDs. It has the problem that if the other party does not then broadcast its anchor transaction, we cannot spend the commitment transaction, and our own anchor funds are stuck. \end_layout \begin_layout Standard Thus we introduce an \emph on escape \emph default transaction, which lets us regain our anchor funds in that case, as shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Dual-Anchor2" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename dual-anchor-diag2.eps scale 50 \end_inset \begin_inset Caption Standard \begin_layout Plain Layout Dual Anchor With Simple Escape Transactions \begin_inset CommandInset label LatexCommand label name "fig:Dual-Anchor2" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard However, this escape transaction would let either side remove its funds from the channel at any time, which would make the channel insecure. Thus, after the commitment transactions have been established, we want to revoke the escape transactions. We can do the same way we did for the commitment transaction revocation; by placing restrictions on the \begin_inset Quotes eld \end_inset to-me \begin_inset Quotes erd \end_inset output. In particular, adding a delay if paying back to the anchor owner, and allowing it to be spent by the other party immediately if they possess the revocation preimage, as shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Anchor-revoc-escape" \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename dual-anchor-diag3.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Dual Anchors With Revocable Escape Transactions \begin_inset CommandInset label LatexCommand label name "fig:Anchor-revoc-escape" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Unfortunately, this revocation is not a complete solution; if B uses its escape transaction, A can collect B's anchor funds, but it has no way of collecting its own! The commitment transaction cannot be used, as one of its inputs has been spent by B's escape transaction. A's own escape transaction has been revoked, so B would simply steal the funds. \end_layout \begin_layout Standard Thus we need an additional construction, such that using one escape transaction immediately unlocks the other anchor funds for its owner. To do this, we ensure that the escape transaction is forced to reveal a secret, which is a fairly well-established technique \begin_inset CommandInset citation LatexCommand cite key "nolan_alt" \end_inset . The anchor transaction is modified to either require both signatures (for the commitment transaction), or both signatures and the secret (for the escape transaction), as shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Secret-Revelation-by" \end_inset . Note that this requires the other party to provide an alternate key (denoted here using A' and B'), otherwise there is no way to force the escape transactio n to provide the secret. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename dual-anchor-diag4.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Secret Revelation by Escape Transactions \begin_inset CommandInset label LatexCommand label name "fig:Secret-Revelation-by" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard That revealed secret can be used with the other alternative: the \emph on fast escape transaction. \emph default This reveals the secret just like the escape transaction, but its output is immediately usable if one knows the other side's secret. This is shown in Figure \begin_inset CommandInset ref LatexCommand ref reference "fig:Final-Dual-Anchor" \end_inset . Thus, if B broadcasts its escape transaction after it has been revoked, A can (after ensuring escape B is sufficiently deep in the block chain) broadcast its fast escape transaction and use B's secret to immediately spend the output. \end_layout \begin_layout Standard On the other hand, if B broadcasts its fast escape transaction without knowing A's secret, A can simply wait for the timeout and spend the fast escape output, then use its own fast escape transaction and B's secret to recover its own anchor funds as well. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status open \begin_layout Plain Layout \align center \begin_inset Graphics filename dual-anchor-final.eps scale 50 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption Standard \begin_layout Plain Layout Final Dual Anchor Design \begin_inset CommandInset label LatexCommand label name "fig:Final-Dual-Anchor" \end_inset \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard The final scripts are shown in \begin_inset CommandInset ref LatexCommand nameref reference "sec:Appendix-A:-Scripts" \end_inset . \end_layout \begin_layout Subsection Disadvantages of The Dual Anchor Approach \end_layout \begin_layout Standard Unlike the mutual anchor approach, use of escape transactions is not outsourcabl e: you cannot have an untrusted third party which can monitor the network for the other sides' revoked escape transaction and respond with your own escape transaction. If you were to provide a third party with your fast escape transaction, you would necessarily provide it with the secret, which it could give to B. \end_layout \begin_layout Subsection Script Definitions for Escape Transactions \end_layout \begin_layout Subsection* Escape Transaction \end_layout \begin_layout Standard The escape transaction for A spends A's anchor output and reveals A's secret. Similarly for B. \end_layout \begin_layout Subsubsection* Escape Input Script \end_layout \begin_layout Standard The extra 0 at the start is due to the OP_CHECKMULTISIG out-by-one-bug. \end_layout \begin_layout Description 0 \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsubsection* Escape Output Redeemscript \end_layout \begin_layout Standard This allows two paths: one for the other side to use the revocation image, and one for this side to get their funds back after a delay. This show's A's script, but B's is the same with A and B exchanged. \end_layout \begin_layout Description OP_HASH160 \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset OP_EQUAL Check if the top of the stack contains the revocation image. \end_layout \begin_layout Description OP_IF \end_layout \begin_deeper \begin_layout Description Funds for B. \end_layout \end_deeper \begin_layout Description OP_ELSE It's A getting their funds back \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKSEQUENCEVERIFY \begin_inset space ~ \end_inset OP_DROP Ensure delay. \end_layout \begin_layout Description Needs to be signed by A. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description OP_CHECKSIG Make sure it's signed correctly. \end_layout \begin_layout Subsubsection* Spending The Escape Output \end_layout \begin_layout Standard Either B using a revocation preimage: \end_layout \begin_layout Description \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Standard Or A using after a timeout: \end_layout \begin_layout Description \begin_inset space ~ \end_inset 0 \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsection* Fast-Escape Transaction \end_layout \begin_layout Subsubsection* Fast-Escape Input Script \end_layout \begin_layout Standard This is identical to the normal escape input script. \end_layout \begin_layout Description 0 \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Subsubsection* Fast-Escape Output Redeemscript \end_layout \begin_layout Standard This allows two paths: one for this side to use the other side's secret (revealed by them using an escape transaction), and one for the other side to claim this side's anchor funds after a delay. This shows A's script, but B's is the same with A and B exchanged. \end_layout \begin_layout Description OP_HASH \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset OP_EQUAL If top argument is B's secret \end_layout \begin_layout Description OP_IF \end_layout \begin_deeper \begin_layout Description For A \end_layout \end_deeper \begin_layout Description OP_ELSE B gets it if A doesn't know the secret. \end_layout \begin_deeper \begin_layout Description \begin_inset space ~ \end_inset OP_CHECKSEQUENCEVERIFY \begin_inset space ~ \end_inset OP_DROP Ensure delay. \end_layout \begin_layout Description Needs to be signed by B. \end_layout \end_deeper \begin_layout Description OP_ENDIF \end_layout \begin_layout Description OP_CHECKSIG Make sure it's signed correctly. \end_layout \begin_layout Subsubsection* Spending The Fast-Escape Output \end_layout \begin_layout Standard Either A using B's secret revealed by B using its own escape transaction: \end_layout \begin_layout Description \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset {} \end_layout \begin_layout Standard Or B using after a timeout: \end_layout \begin_layout Description \begin_inset space ~ \end_inset 0 \begin_inset space ~ \end_inset {} \end_layout \end_body \end_document