CJP [ARCHIVE] on Nostr: 📅 Original date posted:2018-02-09 📝 Original message: Can you give a use case ...
📅 Original date posted:2018-02-09
📝 Original message:
Can you give a use case for this?
Usually, especially in the common case that a payment is done in
exchange for some non-cryptographic asset (e.g. physical goods), there
already is some kind of trust between payer and payee. So, if a payment
is split non-atomically into smaller transactions, and only a part
succeeds, presumably they can cooperatively figure out some way to
settle the situation.
I spoke to people of the "interledger" project, and what they are
planning to do is to non-atomically split *every* transaction into lots
of micro-payments. In fact, they consider it unnecessary to enforce
HTLCs with scripts, because their amounts are so small(*). If one
micro-payment fails, that just makes them learn that a certain channel
is unreliable, and they'll send further payments (and even the remaining
part of the same payment) through a different route.
CJP
(*) not worth the extra on-blockchain fee due to the increased tx size.
Olaoluwa Osuntokun schreef op di 06-02-2018 om 05:26 [+0000]:
> Hi Y'all,
>
>
> A common question I've seen concerning Lightning is: "I have five $2
> channels, is it possible for me to *atomically* send $6 to fulfill a
> payment?". The answer to this question is "yes", provided that the
> receiver
> waits to pull all HTLC's until the sum matches their invoice.
> Typically, one
> assumes that the receiver will supply a payment hash, and the sender
> will
> re-use the payment hash for all streams. This has the downside of
> payment
> hash re-use across *multiple* payments (which can already easily be
> correlated), and also has a failure mode where if the sender fails to
> actually satisfy all the payment flows, then the receiver can still
> just
> pull the monies (and possibly not disperse a service, or w/e).
>
>
> Conner Fromknecht and I have come up with a way to achieve this over
> Lightning while (1) not re-using any payment hashes across all payment
> flows, and (2) adding a *strong* guarantee that the receiver won't be
> paid
> until *all* partial payment flows are extended. We call this scheme
> AMP
> (Atomic Multi-path Payments). It can be experimented with on Lightning
> *today* with the addition of a new feature bit to gate this new
> feature. The beauty of the scheme is that it requires no fundamental
> changes
> to the protocol as is now, as the negotiation is strictly *end-to-end*
> between sender and receiver.
>
>
> TL;DR: we repurpose some unused space in the onion per-hop payload of
> the
> onion blob to signal our protocol (and deliver some protocol-specific
> data),
> then use additive secret sharing to ensure that the receiver can't
> pull the
> payment until they have enough shares to reconstruct the original
> pre-image.
>
>
>
>
> Protocol Goals
> ==============
> 1. Atomicity: The logical transaction should either succeed or fail in
> entirety. Naturally, this implies that the receiver should not be
> unable to
> settle *any* of the partial payments, until all of them have arrived.
>
>
> 2. Avoid Payment Hash Reuse: The payment preimages validated by the
> consensus layer should be distinct for each partial payment.
> Primarily,
> this helps avoid correlation of the partial payments, and ensures that
> malicious intermediaries straddling partial payments cannot steal
> funds.
>
>
> 3. Order Invariance: The protocol should be forgiving to the order in
> which
> partial payments arrive at the destination, adding robustness in the
> face of
> delays or routing failures.
>
>
> 4. Non-interactive Setup: It should be possible for the sender to
> perform an
> AMP without directly coordinating with the receiving node.
> Predominantly,
> this means that the *sender* is able to determine the number of
> partial
> payments to use for a particular AMP, which makes sense since they
> will be
> the one fronting the fees for the cost of this parameter. Plus, we can
> always turn a non-interactive protocol into an interactive one for the
> purposes of invoicing.
>
>
>
>
> Protocol Benefits
> =================
>
>
> Sending pay payments predominantly over an AMP-like protocol has
> several
> clear benefits:
>
>
> - Eliminates the constraint that a single path from sender to
> receiver
> with sufficient directional capacity. This reduces the pressure to
> have
> larger channels in order to support larger payment flows. As a
> result,
> the payment graph be very diffused, without sacrificing payment
> utility
>
>
> - Reduces strain from larger payments on individual paths, and
> allows the
> liquidity imbalances to be more diffuse. We expect this to have a
> non-negligible impact on channel longevity. This is due to the
> fact that
> with usage of AMP, payment flows are typically *smaller* meaning
> that
> each payment will unbalance a channel to a lesser degree that
> with one giant flow.
>
>
> - Potential fee savings for larger payments, contingent on there
> being a
> super-linear component to routed fees. It's possible that with
> modifications to the fee schedule, it's actually *cheaper* to send
> payments over multiple flows rather than one giant flow.
>
>
> - Allows for logical payments larger than the current maximum value
> of an
> individual payment. Atm we have a (temporarily) limit on the max
> payment
> size. With AMP, this can be side stepped as each flow can be up
> the max
> size, with the sum of all flows exceeding the max.
>
>
> - Given sufficient path diversity, AMPs may improve the privacy of
> LN
> Intermediaries are now unaware to how much of the total payment
> they are
> forwarding, or even if they are forwarding a partial payment at
> all.
>
>
> - Using smaller payments increases the set of possible paths a
> partial
> payment could have taken, which reduces the effectiveness of
> static
> analysis techniques involving channel capacities and the plaintext
> values being forwarded.
>
>
>
>
> Protocol Overview
> ==================
> This design can be seen as a generalization of the single,
> non-interactive
> payment scheme, that uses decoding of extra onion blobs (EOBs?) to
> encode
> extra data for the receiver. In that design, the extra data includes a
> payment preimage that the receiver can use to settle back the payment.
> EOBs
> and some method of parsing them are really the only requirement for
> this
> protocol to work. Thus, only the sender and receiver need to implement
> this
> feature in order for it to function, which can be announced using a
> feature
> bit.
>
>
> First, let's review the current format of the per-hop payload for each
> node
> described in BOLT-0004.
>
>
> ┌───────────────┬───────────────────┬────────────────┬───────────────────────┬─────────────────┬─────────────────┐
> │Realm (1 byte) │Next Addr (8 bytes)│Amount (8 bytes)│Outgoing CLTV (4
> bytes)│Unused (12 bytes)│ HMAC (32 bytes) │
> └───────────────┴───────────────────┴────────────────┴───────────────────────┴─────────────────┴─────────────────┘
> ■────────────────────────────────────────────────────────────────────────────────────────────────────────────────■
> ┌─────────────────┐
> │65 Bytes Per Hop │
> └─────────────────┘
>
>
> Currently, *each* node gets a 65-byte payload. We use this payload to
> give
> each node instructions on *how* to forward a payment. We tell each
> node: the
> realm (or chain to forward on), then next node to forward to, the
> amount to
> forward (this is where fees are extracted by forwarding out less than
> in),
> the outgoing CLTV (allows verification that the prior node didn't
> modify any
> values), and finally an HMAC over the entire thing.
>
>
> Two important points:
> 1. We have 12 bytes for each hop that are currently unpurposed and
> can be
> used by application protocols to signal new interpretation of bytes
> and
> also deliver additional encrypted+authenticated data to *each* hop.
>
>
> 2. The protocol currently has a hard limit of 20-hops. With this
> feature
> we ensure that the packet stays fixed sized during processing in
> order to
> avoid leaking positional information. Typically most payments won't
> use
> all 20 hops, as a result, we can use the remaining hops to stuff in
> *even
> more* data.
>
>
>
>
> Protocol Description
> ====================
> The solution we propose is Atomic Multi-path Payments (AMPs). At a
> high
> level, this leverages EOBs to deliver additive shares of a base
> preimage,
> from which the payment preimages of partial payments can be derived.
> The
> receiver can only construct this value after having received all of
> the
> partial payments, satisfying the atomicity constraint.
>
>
> The basic protocol:
>
>
> Primitives
> ==========
> Let H be a CRH function.
> Let || denote concatenation.
> Let ^ denote xor.
>
>
>
>
> Sender Requirements
> ===================
> The parameters to the sending procedure are a random identifier ID,
> the
> number of partial payments n, and the total payment value V. Assume
> the
> sender has some way of dividing V such that V = v_1 + … + v_n.
>
>
> To begin, the sender builds the base preimage BP, from which n partial
> preimages will be derived. Next, the sender samples n additive shares
> s_1,
> …, s_n, and takes the sum to compute BP = s_1 ^ … ^ s_n.
>
>
> With the base preimage created, the sender now moves on to
> constructing the
> n partial payments. For each i in [1,n], the sender deterministically
> computes the partial preimage r_i = H(BP || i), by concatenating the
> sequence number i to the base preimage and hashing the result.
> Afterwards,
> it applies H to determine the payment hash to use in the i’th partial
> payment as h_i = H(r_i). Note that that with this preimage derivation
> scheme, once the payments are pulled each pre-image is distinct and
> indistinguishable from any other.
>
>
> With all of the pieces in place, the sender initiates the i’th payment
> by
> constructing a route to the destination with value v_i and payment
> hash h_i.
> The tuple (ID, n, s_i) is included in the EOB to be opened by the
> receiver.
>
>
> In order to include the three tuple within the per-hop payload for the
> final
> destination, we repurpose the _first_ byte of the un-used padding
> bytes in
> the payload to signal version 0x01 of the AMP protocol (note this is a
> PoC
> outline, we would need to standardize signalling of these 12 bytes to
> support other protocols). Typically this byte isn't set, so the
> existence of
> this means that we're (1) using AMP, and (2) the receiver should
> consume the
> _next_ hop as well. So if the payment length is actually 5, the sender
> tacks
> on an additional dummy 6th hop, encrypted with the _same_ shared
> secret for
> that hop to deliver the e2e encrypted data.
>
>
> Note, the sender can retry partial payments just as they would normal
> payments, since they are order invariant, and would be
> indistinguishable
> from regular payments to intermediaries in the network.
>
>
>
>
> Receiver
Requirements
> =====================
>
>
> Upon the arrival of each partial payment, the receiver will
> iteratively
> reconstruct BP, and do some bookkeeping to figure out when to settle
> the
> partial payments. During this reconstruction process, the receiver
> does not
> need to be aware of the order in which the payments were sent, and in
> fact
> nothing about the incoming partial payments reveals this information
> to the
> receiver, though this can be learned after reconstructing BP.
>
>
> Each EOB is decoded to retrieve (ID, n, s_i), where i is the unique
> but
> unknown index of the incoming partial payment. The receiver has access
> to
> persistent key-value store DB that maps ID to (n, c*, BP*), where c*
> represents the number of partial payments received, BP* is the sum of
> the
> received additive shares, and the superscript * denotes that the value
> is
> being updated iteratively. c* and BP* both have initial values of 0.
>
>
> In the basic protocol, the receiver cache’s the first n it sees, and
> verifies that all incoming partial payments have the same n. The
> receiver
> should reject all partial payments if any EOB deviates. Next, the we
> update
> our persistent store with DB[ID] = (n, c* + 1, BP* ^ s_i), advancing
> the
> reconstruction by one step.
>
>
> If c* + 1 < n, there are still more packets in flight, so we sit
> tight.
> Otherwise, the receiver assumes all partial payments have arrived, and
> can
> being settling them back. Using the base preimage BP = BP* ^ s_i from
> our
> final iteration, the receiver can re-derive all n partial preimages
> and
> payment hashes, using r_i = H(BP || i) and h_i = H(r_i) simply through
> knowledge of n and BP.
>
>
> Finally, the receiver settles back any outstanding payments that
> include
> payment hash h_i using the partial preimage r_i. Each r_i will appear
> random
> due to the nature of H, as will it’s corresponding h_i. Thus, each
> partial
> payment should appear uncorrelated, and does not reveal that it is
> part of
> an AMP nor the number of partial payments used.
>
>
> Non-interactive to Interactive AMPs
> ===================================
>
>
> Sender simply receives an ID and amount from the receiver in an
> invoice
> before initiating the protocol. The receiver should only consider the
> invoice settled if the total amount received in partial payments
> containing
> ID matches or exceeds the amount specified in the invoice. With this
> variant, the receiver is able to map all partial payments to a
> pre-generated
> invoice statement.
>
>
>
>
> Additive Shares vs Threshold-Shares
> ===================================
>
>
> The biggest reason to use additive shares seems to be atomicity.
> Threshold
> shares open the door to some partial payments being settled, even if
> others
> are left in flight. Haven’t yet come up with a good reason for using
> threshold schemes, but there seem to be plenty against it.
>
>
> Reconstruction of additive shares can be done iteratively, and is win
> for
> the storage and computation requirements on the receiving end. If the
> sender
> decides to use fewer than n partial payments, the remaining shares
> could be
> included in the EOB of the final partial payment to allow the sender
> to
> reconstruct sooner. Sender could also optimistically do partial
> reconstruction on this last aggregate value.
>
>
>
>
> Adaptive AMPs
> =============
>
>
> The sender may not always be aware of how many partial payments they
> wish to
> send at the time of the first partial payment, at which point the
> simplified
> protocol would require n to be chosen. To accommodate, the above
> scheme can
> be adapted to handle a dynamically chosen n by iteratively
> constructing the
> shared secrets as follows.
>
>
> Starting with a base preimage BP, the key trick is that the sender
> remember
> the difference between the base preimage and the sum of all partial
> preimages used so far. The relation is described using the following
> equations:
>
>
> X_0 = 0
> X_i = X_{i-1} ^ s_i
> X_n = BP ^ X_{n-1}
>
>
> where if n=1, X_1 = BP, implying that this is in fact a generalization
> of
> the single, non-interactive payment scheme mentioned above. For
> i=1, ...,
> n-1, the sender sends s_i in the EOB, and X_n for the n-th share.
>
>
> Iteratively reconstructing s_1 ^ …. ^ s_{n-1} ^ X_n = BP, allows the
> receiver to compute all relevant r_i = H(BP || i) and h_i = H(r_i).
> Lastly,
> the final number of partial payments n could be signaled in the final
> EOB,
> which would also serve as a sentinel value for signaling completion.
> In
> response to DOS vectors stemming from unknown values of n,
> implementations
> could consider advertising a maximum value for n, or adopting some
> sort of
> framing pattern for conveying that more partial payments are on the
> way.
>
>
> We can further modify our usage of the per-hop payloads to send
> (H(BP), s_i) to
> consume most of the EOB sent from sender to receiver. In this
> scenario, we'd
> repurpose the 11-bytes *after* our signalling byte in the unused byte
> section
> to store the payment ID (which should be unique for each payment). In
> the case
> of a non-interactive payment, this will be unused. While for
> interactive
> payments, this will be the ID within the invoice. To deliver this
> slimmer
> 2-tuple, we'll use 32-bytes for the hash of the BP, and 32-bytes for
> the
> partial pre-image share, leaving an un-used byte in the payload.
>
>
>
>
> Cross-Chain AMPs
> ================
>
>
> AMPs can be used to pay a receiver in multiple currencies
> atomically...which
> is pretty cool :D
>
>
>
>
> Open Research Questions
> =======================
>
>
> The above is a protocol sketch to achieve atomic multi-path payments
> over
> Lightning. The details concerning onion blob usage serves as a
> template that
> future protocols can draw upon in order to deliver additional data to
> *any*
> hop in the route. However, there are still a few open questions before
> something like this can be feasibly deployed.
>
>
> 1. How does the sender decide how many chunked payments to send, and
> the
> size of each payment?
>
>
> - Upon a closer examination, this seems to overlap with the task of
> congestion control within TCP. The sender may be able to utilize
> inspired heuristics to gauge: (1) how large the initial payment
> should be
> and (2) how many subsequent payments may be required. Note that if
> the
> first payment succeeds, then the exchange is over in a signal
> round.
>
>
> 2. How can AMP and HORNET be composed?
>
>
> - If we eventually integrate HORNET, then a distinct communications
> sessions can be established to allow the sender+receiver to
> exchange
> up-to-date partial payment information. This may allow the sender
> to more
> accurately size each partial payment.
>
> 3. Can the sender's initial strategy be governed by an instance of the
> Push-relabel max flow algo?
>
>
> 4. How does this mesh with the current max HTLC limit on a commitment?
>
>
> - ATM, we have a max limit on the number of active HTLC's on a
> particular
> commitment transaction. We do this, as otherwise it's possible
> that the
> transaction is too large, and exceeds standardness w.r.t
> transaction
> size. In a world where most payments use an AMP-like protocol,
> then
> overall ant any given instance there will be several pending
> HTLC's on
> commitments network wise.
>
>
> This may incentivize nodes to open more channels in order to
> support
> the increased commitment space utilization.
>
>
>
>
> Conclusion
> ==========
>
>
> We've presented a design outline of how to integrate atomic multi-path
> payments (AMP) into Lightning. The existence of such a construct
> allows a
> sender to atomically split a payment flow amongst several individual
> payment
> flows. As a result, larger channels aren't as important as it's
> possible to
> utilize one total outbound payment bandwidth to send several channels.
> Additionally, in order to support the increased load, internal routing
> nodes
> are incensed have more active channels. The existence of AMP-like
> payments
> may also increase the longevity of channels as there'll be smaller,
> more
> numerous payment flows, making it unlikely that a single payment comes
> across unbalances a channel entirely. We've also showed how one can
> utilize
> the current onion packet format to deliver additional data from a
> sender to
> receiver, that's still e2e authenticated.
>
>
>
>
> -- Conner && Laolu
>
>
> _______________________________________________
> Lightning-dev mailing list
> Lightning-dev at lists.linuxfoundation.org
> https://lists.linuxfoundation.org/mailman/listinfo/lightning-dev
📝 Original message:
Can you give a use case for this?
Usually, especially in the common case that a payment is done in
exchange for some non-cryptographic asset (e.g. physical goods), there
already is some kind of trust between payer and payee. So, if a payment
is split non-atomically into smaller transactions, and only a part
succeeds, presumably they can cooperatively figure out some way to
settle the situation.
I spoke to people of the "interledger" project, and what they are
planning to do is to non-atomically split *every* transaction into lots
of micro-payments. In fact, they consider it unnecessary to enforce
HTLCs with scripts, because their amounts are so small(*). If one
micro-payment fails, that just makes them learn that a certain channel
is unreliable, and they'll send further payments (and even the remaining
part of the same payment) through a different route.
CJP
(*) not worth the extra on-blockchain fee due to the increased tx size.
Olaoluwa Osuntokun schreef op di 06-02-2018 om 05:26 [+0000]:
> Hi Y'all,
>
>
> A common question I've seen concerning Lightning is: "I have five $2
> channels, is it possible for me to *atomically* send $6 to fulfill a
> payment?". The answer to this question is "yes", provided that the
> receiver
> waits to pull all HTLC's until the sum matches their invoice.
> Typically, one
> assumes that the receiver will supply a payment hash, and the sender
> will
> re-use the payment hash for all streams. This has the downside of
> payment
> hash re-use across *multiple* payments (which can already easily be
> correlated), and also has a failure mode where if the sender fails to
> actually satisfy all the payment flows, then the receiver can still
> just
> pull the monies (and possibly not disperse a service, or w/e).
>
>
> Conner Fromknecht and I have come up with a way to achieve this over
> Lightning while (1) not re-using any payment hashes across all payment
> flows, and (2) adding a *strong* guarantee that the receiver won't be
> paid
> until *all* partial payment flows are extended. We call this scheme
> AMP
> (Atomic Multi-path Payments). It can be experimented with on Lightning
> *today* with the addition of a new feature bit to gate this new
> feature. The beauty of the scheme is that it requires no fundamental
> changes
> to the protocol as is now, as the negotiation is strictly *end-to-end*
> between sender and receiver.
>
>
> TL;DR: we repurpose some unused space in the onion per-hop payload of
> the
> onion blob to signal our protocol (and deliver some protocol-specific
> data),
> then use additive secret sharing to ensure that the receiver can't
> pull the
> payment until they have enough shares to reconstruct the original
> pre-image.
>
>
>
>
> Protocol Goals
> ==============
> 1. Atomicity: The logical transaction should either succeed or fail in
> entirety. Naturally, this implies that the receiver should not be
> unable to
> settle *any* of the partial payments, until all of them have arrived.
>
>
> 2. Avoid Payment Hash Reuse: The payment preimages validated by the
> consensus layer should be distinct for each partial payment.
> Primarily,
> this helps avoid correlation of the partial payments, and ensures that
> malicious intermediaries straddling partial payments cannot steal
> funds.
>
>
> 3. Order Invariance: The protocol should be forgiving to the order in
> which
> partial payments arrive at the destination, adding robustness in the
> face of
> delays or routing failures.
>
>
> 4. Non-interactive Setup: It should be possible for the sender to
> perform an
> AMP without directly coordinating with the receiving node.
> Predominantly,
> this means that the *sender* is able to determine the number of
> partial
> payments to use for a particular AMP, which makes sense since they
> will be
> the one fronting the fees for the cost of this parameter. Plus, we can
> always turn a non-interactive protocol into an interactive one for the
> purposes of invoicing.
>
>
>
>
> Protocol Benefits
> =================
>
>
> Sending pay payments predominantly over an AMP-like protocol has
> several
> clear benefits:
>
>
> - Eliminates the constraint that a single path from sender to
> receiver
> with sufficient directional capacity. This reduces the pressure to
> have
> larger channels in order to support larger payment flows. As a
> result,
> the payment graph be very diffused, without sacrificing payment
> utility
>
>
> - Reduces strain from larger payments on individual paths, and
> allows the
> liquidity imbalances to be more diffuse. We expect this to have a
> non-negligible impact on channel longevity. This is due to the
> fact that
> with usage of AMP, payment flows are typically *smaller* meaning
> that
> each payment will unbalance a channel to a lesser degree that
> with one giant flow.
>
>
> - Potential fee savings for larger payments, contingent on there
> being a
> super-linear component to routed fees. It's possible that with
> modifications to the fee schedule, it's actually *cheaper* to send
> payments over multiple flows rather than one giant flow.
>
>
> - Allows for logical payments larger than the current maximum value
> of an
> individual payment. Atm we have a (temporarily) limit on the max
> payment
> size. With AMP, this can be side stepped as each flow can be up
> the max
> size, with the sum of all flows exceeding the max.
>
>
> - Given sufficient path diversity, AMPs may improve the privacy of
> LN
> Intermediaries are now unaware to how much of the total payment
> they are
> forwarding, or even if they are forwarding a partial payment at
> all.
>
>
> - Using smaller payments increases the set of possible paths a
> partial
> payment could have taken, which reduces the effectiveness of
> static
> analysis techniques involving channel capacities and the plaintext
> values being forwarded.
>
>
>
>
> Protocol Overview
> ==================
> This design can be seen as a generalization of the single,
> non-interactive
> payment scheme, that uses decoding of extra onion blobs (EOBs?) to
> encode
> extra data for the receiver. In that design, the extra data includes a
> payment preimage that the receiver can use to settle back the payment.
> EOBs
> and some method of parsing them are really the only requirement for
> this
> protocol to work. Thus, only the sender and receiver need to implement
> this
> feature in order for it to function, which can be announced using a
> feature
> bit.
>
>
> First, let's review the current format of the per-hop payload for each
> node
> described in BOLT-0004.
>
>
> ┌───────────────┬───────────────────┬────────────────┬───────────────────────┬─────────────────┬─────────────────┐
> │Realm (1 byte) │Next Addr (8 bytes)│Amount (8 bytes)│Outgoing CLTV (4
> bytes)│Unused (12 bytes)│ HMAC (32 bytes) │
> └───────────────┴───────────────────┴────────────────┴───────────────────────┴─────────────────┴─────────────────┘
> ■────────────────────────────────────────────────────────────────────────────────────────────────────────────────■
> ┌─────────────────┐
> │65 Bytes Per Hop │
> └─────────────────┘
>
>
> Currently, *each* node gets a 65-byte payload. We use this payload to
> give
> each node instructions on *how* to forward a payment. We tell each
> node: the
> realm (or chain to forward on), then next node to forward to, the
> amount to
> forward (this is where fees are extracted by forwarding out less than
> in),
> the outgoing CLTV (allows verification that the prior node didn't
> modify any
> values), and finally an HMAC over the entire thing.
>
>
> Two important points:
> 1. We have 12 bytes for each hop that are currently unpurposed and
> can be
> used by application protocols to signal new interpretation of bytes
> and
> also deliver additional encrypted+authenticated data to *each* hop.
>
>
> 2. The protocol currently has a hard limit of 20-hops. With this
> feature
> we ensure that the packet stays fixed sized during processing in
> order to
> avoid leaking positional information. Typically most payments won't
> use
> all 20 hops, as a result, we can use the remaining hops to stuff in
> *even
> more* data.
>
>
>
>
> Protocol Description
> ====================
> The solution we propose is Atomic Multi-path Payments (AMPs). At a
> high
> level, this leverages EOBs to deliver additive shares of a base
> preimage,
> from which the payment preimages of partial payments can be derived.
> The
> receiver can only construct this value after having received all of
> the
> partial payments, satisfying the atomicity constraint.
>
>
> The basic protocol:
>
>
> Primitives
> ==========
> Let H be a CRH function.
> Let || denote concatenation.
> Let ^ denote xor.
>
>
>
>
> Sender Requirements
> ===================
> The parameters to the sending procedure are a random identifier ID,
> the
> number of partial payments n, and the total payment value V. Assume
> the
> sender has some way of dividing V such that V = v_1 + … + v_n.
>
>
> To begin, the sender builds the base preimage BP, from which n partial
> preimages will be derived. Next, the sender samples n additive shares
> s_1,
> …, s_n, and takes the sum to compute BP = s_1 ^ … ^ s_n.
>
>
> With the base preimage created, the sender now moves on to
> constructing the
> n partial payments. For each i in [1,n], the sender deterministically
> computes the partial preimage r_i = H(BP || i), by concatenating the
> sequence number i to the base preimage and hashing the result.
> Afterwards,
> it applies H to determine the payment hash to use in the i’th partial
> payment as h_i = H(r_i). Note that that with this preimage derivation
> scheme, once the payments are pulled each pre-image is distinct and
> indistinguishable from any other.
>
>
> With all of the pieces in place, the sender initiates the i’th payment
> by
> constructing a route to the destination with value v_i and payment
> hash h_i.
> The tuple (ID, n, s_i) is included in the EOB to be opened by the
> receiver.
>
>
> In order to include the three tuple within the per-hop payload for the
> final
> destination, we repurpose the _first_ byte of the un-used padding
> bytes in
> the payload to signal version 0x01 of the AMP protocol (note this is a
> PoC
> outline, we would need to standardize signalling of these 12 bytes to
> support other protocols). Typically this byte isn't set, so the
> existence of
> this means that we're (1) using AMP, and (2) the receiver should
> consume the
> _next_ hop as well. So if the payment length is actually 5, the sender
> tacks
> on an additional dummy 6th hop, encrypted with the _same_ shared
> secret for
> that hop to deliver the e2e encrypted data.
>
>
> Note, the sender can retry partial payments just as they would normal
> payments, since they are order invariant, and would be
> indistinguishable
> from regular payments to intermediaries in the network.
>
>
>
>
> Receiver
Requirements
> =====================
>
>
> Upon the arrival of each partial payment, the receiver will
> iteratively
> reconstruct BP, and do some bookkeeping to figure out when to settle
> the
> partial payments. During this reconstruction process, the receiver
> does not
> need to be aware of the order in which the payments were sent, and in
> fact
> nothing about the incoming partial payments reveals this information
> to the
> receiver, though this can be learned after reconstructing BP.
>
>
> Each EOB is decoded to retrieve (ID, n, s_i), where i is the unique
> but
> unknown index of the incoming partial payment. The receiver has access
> to
> persistent key-value store DB that maps ID to (n, c*, BP*), where c*
> represents the number of partial payments received, BP* is the sum of
> the
> received additive shares, and the superscript * denotes that the value
> is
> being updated iteratively. c* and BP* both have initial values of 0.
>
>
> In the basic protocol, the receiver cache’s the first n it sees, and
> verifies that all incoming partial payments have the same n. The
> receiver
> should reject all partial payments if any EOB deviates. Next, the we
> update
> our persistent store with DB[ID] = (n, c* + 1, BP* ^ s_i), advancing
> the
> reconstruction by one step.
>
>
> If c* + 1 < n, there are still more packets in flight, so we sit
> tight.
> Otherwise, the receiver assumes all partial payments have arrived, and
> can
> being settling them back. Using the base preimage BP = BP* ^ s_i from
> our
> final iteration, the receiver can re-derive all n partial preimages
> and
> payment hashes, using r_i = H(BP || i) and h_i = H(r_i) simply through
> knowledge of n and BP.
>
>
> Finally, the receiver settles back any outstanding payments that
> include
> payment hash h_i using the partial preimage r_i. Each r_i will appear
> random
> due to the nature of H, as will it’s corresponding h_i. Thus, each
> partial
> payment should appear uncorrelated, and does not reveal that it is
> part of
> an AMP nor the number of partial payments used.
>
>
> Non-interactive to Interactive AMPs
> ===================================
>
>
> Sender simply receives an ID and amount from the receiver in an
> invoice
> before initiating the protocol. The receiver should only consider the
> invoice settled if the total amount received in partial payments
> containing
> ID matches or exceeds the amount specified in the invoice. With this
> variant, the receiver is able to map all partial payments to a
> pre-generated
> invoice statement.
>
>
>
>
> Additive Shares vs Threshold-Shares
> ===================================
>
>
> The biggest reason to use additive shares seems to be atomicity.
> Threshold
> shares open the door to some partial payments being settled, even if
> others
> are left in flight. Haven’t yet come up with a good reason for using
> threshold schemes, but there seem to be plenty against it.
>
>
> Reconstruction of additive shares can be done iteratively, and is win
> for
> the storage and computation requirements on the receiving end. If the
> sender
> decides to use fewer than n partial payments, the remaining shares
> could be
> included in the EOB of the final partial payment to allow the sender
> to
> reconstruct sooner. Sender could also optimistically do partial
> reconstruction on this last aggregate value.
>
>
>
>
> Adaptive AMPs
> =============
>
>
> The sender may not always be aware of how many partial payments they
> wish to
> send at the time of the first partial payment, at which point the
> simplified
> protocol would require n to be chosen. To accommodate, the above
> scheme can
> be adapted to handle a dynamically chosen n by iteratively
> constructing the
> shared secrets as follows.
>
>
> Starting with a base preimage BP, the key trick is that the sender
> remember
> the difference between the base preimage and the sum of all partial
> preimages used so far. The relation is described using the following
> equations:
>
>
> X_0 = 0
> X_i = X_{i-1} ^ s_i
> X_n = BP ^ X_{n-1}
>
>
> where if n=1, X_1 = BP, implying that this is in fact a generalization
> of
> the single, non-interactive payment scheme mentioned above. For
> i=1, ...,
> n-1, the sender sends s_i in the EOB, and X_n for the n-th share.
>
>
> Iteratively reconstructing s_1 ^ …. ^ s_{n-1} ^ X_n = BP, allows the
> receiver to compute all relevant r_i = H(BP || i) and h_i = H(r_i).
> Lastly,
> the final number of partial payments n could be signaled in the final
> EOB,
> which would also serve as a sentinel value for signaling completion.
> In
> response to DOS vectors stemming from unknown values of n,
> implementations
> could consider advertising a maximum value for n, or adopting some
> sort of
> framing pattern for conveying that more partial payments are on the
> way.
>
>
> We can further modify our usage of the per-hop payloads to send
> (H(BP), s_i) to
> consume most of the EOB sent from sender to receiver. In this
> scenario, we'd
> repurpose the 11-bytes *after* our signalling byte in the unused byte
> section
> to store the payment ID (which should be unique for each payment). In
> the case
> of a non-interactive payment, this will be unused. While for
> interactive
> payments, this will be the ID within the invoice. To deliver this
> slimmer
> 2-tuple, we'll use 32-bytes for the hash of the BP, and 32-bytes for
> the
> partial pre-image share, leaving an un-used byte in the payload.
>
>
>
>
> Cross-Chain AMPs
> ================
>
>
> AMPs can be used to pay a receiver in multiple currencies
> atomically...which
> is pretty cool :D
>
>
>
>
> Open Research Questions
> =======================
>
>
> The above is a protocol sketch to achieve atomic multi-path payments
> over
> Lightning. The details concerning onion blob usage serves as a
> template that
> future protocols can draw upon in order to deliver additional data to
> *any*
> hop in the route. However, there are still a few open questions before
> something like this can be feasibly deployed.
>
>
> 1. How does the sender decide how many chunked payments to send, and
> the
> size of each payment?
>
>
> - Upon a closer examination, this seems to overlap with the task of
> congestion control within TCP. The sender may be able to utilize
> inspired heuristics to gauge: (1) how large the initial payment
> should be
> and (2) how many subsequent payments may be required. Note that if
> the
> first payment succeeds, then the exchange is over in a signal
> round.
>
>
> 2. How can AMP and HORNET be composed?
>
>
> - If we eventually integrate HORNET, then a distinct communications
> sessions can be established to allow the sender+receiver to
> exchange
> up-to-date partial payment information. This may allow the sender
> to more
> accurately size each partial payment.
>
> 3. Can the sender's initial strategy be governed by an instance of the
> Push-relabel max flow algo?
>
>
> 4. How does this mesh with the current max HTLC limit on a commitment?
>
>
> - ATM, we have a max limit on the number of active HTLC's on a
> particular
> commitment transaction. We do this, as otherwise it's possible
> that the
> transaction is too large, and exceeds standardness w.r.t
> transaction
> size. In a world where most payments use an AMP-like protocol,
> then
> overall ant any given instance there will be several pending
> HTLC's on
> commitments network wise.
>
>
> This may incentivize nodes to open more channels in order to
> support
> the increased commitment space utilization.
>
>
>
>
> Conclusion
> ==========
>
>
> We've presented a design outline of how to integrate atomic multi-path
> payments (AMP) into Lightning. The existence of such a construct
> allows a
> sender to atomically split a payment flow amongst several individual
> payment
> flows. As a result, larger channels aren't as important as it's
> possible to
> utilize one total outbound payment bandwidth to send several channels.
> Additionally, in order to support the increased load, internal routing
> nodes
> are incensed have more active channels. The existence of AMP-like
> payments
> may also increase the longevity of channels as there'll be smaller,
> more
> numerous payment flows, making it unlikely that a single payment comes
> across unbalances a channel entirely. We've also showed how one can
> utilize
> the current onion packet format to deliver additional data from a
> sender to
> receiver, that's still e2e authenticated.
>
>
>
>
> -- Conner && Laolu
>
>
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