We know how to do this, but it would require a discrete log equality proof, and the
+most efficient way to do this would be to do RedDSA and this at the same time, which
+means more work for e.g. hardware wallets.
Provisional proposal: exactly the same key structure as Sapling.
+
Group hashing uses the isogeny.
+
+
nsk goes away; nk is now a field element
+
TODO: ak / nk split enables splitting the security argument, but could consider merging.
+Merging would help with ivk derivation perf (though as a commitment now it's pretty cheap)
For Sapling, we have encountered multiple places where the specification uses typed
+variables to define the consensus rules, but the C++ implementation in zcashd relied on
+byte encodings to implement them. This resulted in subtly-different consensus rules being
+deployed than were intended, for example where a particular type was not round-trip
+encodable.
+
In Orchard, we avoid this by defining the consensus rules in terms of the byte encodings
+of all variables, and being explicit about any types that are not round-trip encodable.
+This makes consensus compatibility between strongly-typed implementations (such as this
+crate) and byte-oriented implementations easier to achieve.
In Sprout, we had a single proof that represented two spent notes and two new notes. This
+was necessary in order to faciliate spending multiple notes in a single transaction (to
+balance value, an output of one JoinSplit could be spent in the next one), but also
+provided a minimal level of arity-hiding: single-JoinSplit transactions all looked like
+2-in 2-out transactions, and in multi-JoinSplit transactions each JoinSplit looked like a
+1-in 1-out.
+
In Sapling, we switched to using value commitments to balance the transaction, removing
+the min-2 arity requirement. We opted for one proof per spent note and one (much simpler)
+proof per output note, which greatly improved the performance of generating outputs, but
+removed any arity-hiding from the proofs (instead having the transaction builder pad
+transactions to 1-in, 2-out).
+
For Orchard, we take a combined approach: we define an Orchard transaction as containing a
+bundle of actions, where each action is both a spend and an output. This provides the same
+inherent arity-hiding as multi-JoinSplit Sprout, but using Sapling value commitments to
+balance the transaction without doubling its size.
+
TODO: Depending on the circuit cost, we may switch to having an action internally
+represent either a spend or an output. Externally spends and outputs would still be
+indistinguishable, but the transaction would be larger.
One of the things we learned from Sapling is that having a single global commitment tree
+makes life hard for light client wallets. When a new note is received, the wallet derives
+its incremental witness from the state of the global tree at the point when the note's
+commitment is appended; this incremental state then needs to be updated with every
+subsequent commitment in the block in-order. It isn't efficient for a server to
+pre-compute and send over the necessary incremental updates for every new note in a block,
+and if a wallet requested a specific update from the server it would leak the specific
+note that was received.
+
Orchard addresses this by splitting the commitment tree into several sub-trees:
+
+
Bundle tree, that accumulates the commitments within a single bundle (and thus a single
+transaction).
+
Block tree, that accumulates the bundle tree roots within a single block.
+
Global tree, that accumulates the block tree roots.
+
+
Each of these trees has a fixed depth (necessary for being able to create proofs).
+
Chains that integrate Orchard can decouple the limits on commitments-per-subtree from
+higher-layer constraints like block size, by enabling their blocks and transactions to be
+structured internally as a series of Orchard blocks or txs (e.g. a Zcash block would
+contain a Vec<BlockTreeRoot>, that each get appended in-order).
+
Zcash level: we also bind these roots into the FlyClient history leaves, so that light
+clients can assert they are valid independently of the full block.
+
TODO: Sean is pretty sure we can just improve the Incremental Merkle Tree implementation
+to work around this, without domain-separating the tree. If we can do that instead, it may
+be simpler.
As in Sapling, we require two kinds of commitment schemes in Pollard:
+
+
HomomorphicCommit is a linearly homomorphic commitment scheme with perfect hiding, and
+strong binding reducible to DL.
+
Commit and ShortCommit are commitment schemes with perfect hiding, and strong
+binding reducible to DL.
+
+
By "strong binding" we mean that the scheme is collision resistant on the input and
+randomness.
+
We instantiate HomomorphicCommit with a Pedersen commitment, and use it for value
+commitments:
+
cv=HomomorphicCommitrcvcv(v)
+
We instantiate Commit and ShortCommit with Sinsemilla, and use them for all other
+commitments:
+
ivk=ShortCommitrivkivk(nk,ak)
+cm=Commitrcmcm(rest of note)
+
This is the same split (and rationale) as in Sapling, but using the more PLONK-efficient
+Sinsemilla instead of Bowe-Hopwood Pedersen hashes.
+
Note that we also deviate from Sapling by using ShortCommit to deriving ivk
+instead of a full PRF. This removes an unnecessary (large) PRF primitive from the circuit,
+at the cost of requiring rivk to be part of the full viewing key.
Hash is a keyed circuit-efficient hash (such as Rescue).
+
ρ is unique to this output. As with hSig in Sprout, ρ includes
+the nullifiers of any Orchard notes being spent.
+
+
If spends and outputs are merged / combined, then we always have a nullifier
+(internally derived from a real or dummy note), and can rely on the nullifier
+derivation process to prevent an adversary from choosing dummy nullifiers arbitrarily.
+
If spends and outputs are not merged, then ρ should probably also include
+unique information from other parts of the transaction as well.
+
TODO: Decide which of the above two cases will be used, and update this.
+
+
+
ψ is sender-controlled randomness. It is not required to be unique, and in practice
+is derived from a sender-selected random value rseed.
+
G is an fixed independent base.
+
+
This gives a note structure of
+
(addr,v,ρ,ψ,rcm).
+
The nullifier commits to the note value via cm in order to domain-separate
+nullifiers for zero-valued notes from other notes.
We care about several security properties for our nullifiers:
+
+
+
Balance: can I forge money?
+
+
+
Note Privacy: can I gain information about notes only from the public block chain?
+
+
This describes notes sent in-band.
+
+
+
+
Note Privacy (OOB): can I gain information about notes sent out-of-band, only from
+the public block chain?
+
+
In this case, we assume privacy of the channel over which the note is sent, and that
+the adversary does not have access to any notes sent to the same address which are
+then spent (so that the nullifier is on the block chain somewhere).
+
+
+
+
Spend Unlinkability: given the incoming viewing key for an address, and not the full
+viewing key, can I (possibly the sender) detect spends of any notes sent to that address?
+
+
We're giving ivk to the attacker and allowing it to be the sender in order to make
+this property as strong as possible: they will have all the notes sent to that
+address.
+
+
+
+
Faerie Resistance: can I perform a Faerie Gold attack (i.e. cause notes to be
+accepted that are unspendable)?
+
+
+
We assume (and instantiate elsewhere) the following primitives:
+
+
GH is a cryptographic hash into the group (such as BLAKE2s with simplified SWU), used
+to derive all fixed independent bases.
+
E is an elliptic curve (such as Pallas).
+
KDF is the note encryption key derivation function.
+
+
For our chosen design, our desired security properties rely on the following assumptions:
HashDHEF is computational Diffie-Hellman using F for the key derivation, with
+one-time ephemeral keys. This assumption is heuristically weaker than DDHE but stronger
+than DLE.
+
We omit ROGH as a security assumption because we only rely on the random oracle
+applied to fixed inputs defined by the protocol, i.e. to generate the fixed base
+G, not to attacker-specified inputs.
+
+
† We additionally assume that for any input x, {Hashnk(x):>nk∈E} gives a scalar in an adequate range for DDHE. (Otherwise, Hash
+could be trivial, e.g. independent of nk.)
⚠ Caution: be skeptical of the claims in this table about what
+problem(s) each security property depends on. They may not be accurate and are definitely
+not fully rigorous.
H is calculated by the sender as H=GH(ρ), and would be provided in the action.
+
I is an fixed independent base, independent of G and any others
+returned by GH.
+
+
For the options that use H, when spending a note,
+
+
if it's a real note, then H is as computed for that note, so it is a unique RO output;
+
if it's a dummy note, we enforce that it is some fixed base independent of other bases.
+
+
The Commitnf variants enabled nullifier domain separation based on note
+value, without directly depending on cm (which in its native type is a base
+field element, not a group element). We decided instead to follow Sapling by defining an
+intermediate representation of cm as a group element, that is only used in
+nullifier computation.
@@ -182,14 +183,263 @@ Public Licence, version 1.0.
while ensuring that all improvements are eventually open source. See
here for why the TGPPL exists,
graphically illustrated on three slides.
+
We know how to do this, but it would require a discrete log equality proof, and the
+most efficient way to do this would be to do RedDSA and this at the same time, which
+means more work for e.g. hardware wallets.
Provisional proposal: exactly the same key structure as Sapling.
+
Group hashing uses the isogeny.
+
+
nsk goes away; nk is now a field element
+
TODO: ak / nk split enables splitting the security argument, but could consider merging.
+Merging would help with ivk derivation perf (though as a commitment now it's pretty cheap)
For Sapling, we have encountered multiple places where the specification uses typed
+variables to define the consensus rules, but the C++ implementation in zcashd relied on
+byte encodings to implement them. This resulted in subtly-different consensus rules being
+deployed than were intended, for example where a particular type was not round-trip
+encodable.
+
In Orchard, we avoid this by defining the consensus rules in terms of the byte encodings
+of all variables, and being explicit about any types that are not round-trip encodable.
+This makes consensus compatibility between strongly-typed implementations (such as this
+crate) and byte-oriented implementations easier to achieve.
In Sprout, we had a single proof that represented two spent notes and two new notes. This
+was necessary in order to faciliate spending multiple notes in a single transaction (to
+balance value, an output of one JoinSplit could be spent in the next one), but also
+provided a minimal level of arity-hiding: single-JoinSplit transactions all looked like
+2-in 2-out transactions, and in multi-JoinSplit transactions each JoinSplit looked like a
+1-in 1-out.
+
In Sapling, we switched to using value commitments to balance the transaction, removing
+the min-2 arity requirement. We opted for one proof per spent note and one (much simpler)
+proof per output note, which greatly improved the performance of generating outputs, but
+removed any arity-hiding from the proofs (instead having the transaction builder pad
+transactions to 1-in, 2-out).
+
For Orchard, we take a combined approach: we define an Orchard transaction as containing a
+bundle of actions, where each action is both a spend and an output. This provides the same
+inherent arity-hiding as multi-JoinSplit Sprout, but using Sapling value commitments to
+balance the transaction without doubling its size.
+
TODO: Depending on the circuit cost, we may switch to having an action internally
+represent either a spend or an output. Externally spends and outputs would still be
+indistinguishable, but the transaction would be larger.
As in Sapling, we require two kinds of commitment schemes in Pollard:
+
+
HomomorphicCommit is a linearly homomorphic commitment scheme with perfect hiding, and
+strong binding reducible to DL.
+
Commit and ShortCommit are commitment schemes with perfect hiding, and strong
+binding reducible to DL.
+
+
By "strong binding" we mean that the scheme is collision resistant on the input and
+randomness.
+
We instantiate HomomorphicCommit with a Pedersen commitment, and use it for value
+commitments:
+
cv=HomomorphicCommitrcvcv(v)
+
We instantiate Commit and ShortCommit with Sinsemilla, and use them for all other
+commitments:
+
ivk=ShortCommitrivkivk(nk,ak)
+cm=Commitrcmcm(rest of note)
+
This is the same split (and rationale) as in Sapling, but using the more PLONK-efficient
+Sinsemilla instead of Bowe-Hopwood Pedersen hashes.
+
Note that we also deviate from Sapling by using ShortCommit to deriving ivk
+instead of a full PRF. This removes an unnecessary (large) PRF primitive from the circuit,
+at the cost of requiring rivk to be part of the full viewing key.
One of the things we learned from Sapling is that having a single global commitment tree
+makes life hard for light client wallets. When a new note is received, the wallet derives
+its incremental witness from the state of the global tree at the point when the note's
+commitment is appended; this incremental state then needs to be updated with every
+subsequent commitment in the block in-order. It isn't efficient for a server to
+pre-compute and send over the necessary incremental updates for every new note in a block,
+and if a wallet requested a specific update from the server it would leak the specific
+note that was received.
+
Orchard addresses this by splitting the commitment tree into several sub-trees:
+
+
Bundle tree, that accumulates the commitments within a single bundle (and thus a single
+transaction).
+
Block tree, that accumulates the bundle tree roots within a single block.
+
Global tree, that accumulates the block tree roots.
+
+
Each of these trees has a fixed depth (necessary for being able to create proofs).
+
Chains that integrate Orchard can decouple the limits on commitments-per-subtree from
+higher-layer constraints like block size, by enabling their blocks and transactions to be
+structured internally as a series of Orchard blocks or txs (e.g. a Zcash block would
+contain a Vec<BlockTreeRoot>, that each get appended in-order).
+
Zcash level: we also bind these roots into the FlyClient history leaves, so that light
+clients can assert they are valid independently of the full block.
+
TODO: Sean is pretty sure we can just improve the Incremental Merkle Tree implementation
+to work around this, without domain-separating the tree. If we can do that instead, it may
+be simpler.
Hash is a keyed circuit-efficient hash (such as Rescue).
+
ρ is unique to this output. As with hSig in Sprout, ρ includes
+the nullifiers of any Orchard notes being spent.
+
+
If spends and outputs are merged / combined, then we always have a nullifier
+(internally derived from a real or dummy note), and can rely on the nullifier
+derivation process to prevent an adversary from choosing dummy nullifiers arbitrarily.
+
If spends and outputs are not merged, then ρ should probably also include
+unique information from other parts of the transaction as well.
+
TODO: Decide which of the above two cases will be used, and update this.
+
+
+
ψ is sender-controlled randomness. It is not required to be unique, and in practice
+is derived from a sender-selected random value rseed.
+
G is an fixed independent base.
+
+
This gives a note structure of
+
(addr,v,ρ,ψ,rcm).
+
The nullifier commits to the note value via cm in order to domain-separate
+nullifiers for zero-valued notes from other notes.
We care about several security properties for our nullifiers:
+
+
+
Balance: can I forge money?
+
+
+
Note Privacy: can I gain information about notes only from the public block chain?
+
+
This describes notes sent in-band.
+
+
+
+
Note Privacy (OOB): can I gain information about notes sent out-of-band, only from
+the public block chain?
+
+
In this case, we assume privacy of the channel over which the note is sent, and that
+the adversary does not have access to any notes sent to the same address which are
+then spent (so that the nullifier is on the block chain somewhere).
+
+
+
+
Spend Unlinkability: given the incoming viewing key for an address, and not the full
+viewing key, can I (possibly the sender) detect spends of any notes sent to that address?
+
+
We're giving ivk to the attacker and allowing it to be the sender in order to make
+this property as strong as possible: they will have all the notes sent to that
+address.
+
+
+
+
Faerie Resistance: can I perform a Faerie Gold attack (i.e. cause notes to be
+accepted that are unspendable)?
+
+
+
We assume (and instantiate elsewhere) the following primitives:
+
+
GH is a cryptographic hash into the group (such as BLAKE2s with simplified SWU), used
+to derive all fixed independent bases.
+
E is an elliptic curve (such as Pallas).
+
KDF is the note encryption key derivation function.
+
+
For our chosen design, our desired security properties rely on the following assumptions:
HashDHEF is computational Diffie-Hellman using F for the key derivation, with
+one-time ephemeral keys. This assumption is heuristically weaker than DDHE but stronger
+than DLE.
+
We omit ROGH as a security assumption because we only rely on the random oracle
+applied to fixed inputs defined by the protocol, i.e. to generate the fixed base
+G, not to attacker-specified inputs.
+
+
† We additionally assume that for any input x, {Hashnk(x):>nk∈E} gives a scalar in an adequate range for DDHE. (Otherwise, Hash
+could be trivial, e.g. independent of nk.)
⚠ Caution: be skeptical of the claims in this table about what
+problem(s) each security property depends on. They may not be accurate and are definitely
+not fully rigorous.
H is calculated by the sender as H=GH(ρ), and would be provided in the action.
+
I is an fixed independent base, independent of G and any others
+returned by GH.
+
+
For the options that use H, when spending a note,
+
+
if it's a real note, then H is as computed for that note, so it is a unique RO output;
+
if it's a dummy note, we enforce that it is some fixed base independent of other bases.
+
+
The Commitnf variants enabled nullifier domain separation based on note
+value, without directly depending on cm (which in its native type is a base
+field element, not a group element). We decided instead to follow Sapling by defining an
+intermediate representation of cm as a group element, that is only used in
+nullifier computation.
diff --git a/searchindex.js b/searchindex.js
index 343ded02..b42e63f3 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Object.assign(window.search, {"doc_urls":["index.html#orchard---cratesio","index.html#documentation","index.html#license","concepts.html#concepts","concepts/preliminaries.html#preliminaries","user.html#user-documentation","user/keys.html#creating-keys-and-addresses","user/creating-notes.html#creating-notes","user/spending-notes.html#spending-notes","user/integration.html#integration-into-an-existing-chain","design.html#design"],"index":{"documentStore":{"docInfo":{"0":{"body":8,"breadcrumbs":2,"title":2},"1":{"body":4,"breadcrumbs":1,"title":1},"10":{"body":0,"breadcrumbs":1,"title":1},"2":{"body":49,"breadcrumbs":1,"title":1},"3":{"body":0,"breadcrumbs":1,"title":1},"4":{"body":0,"breadcrumbs":2,"title":1},"5":{"body":0,"breadcrumbs":2,"title":2},"6":{"body":0,"breadcrumbs":5,"title":3},"7":{"body":0,"breadcrumbs":4,"title":2},"8":{"body":0,"breadcrumbs":4,"title":2},"9":{"body":0,"breadcrumbs":5,"title":3}},"docs":{"0":{"body":"IMPORTANT : This library is being actively developed and should not be used in production software.","breadcrumbs":"orchard Crates.io","id":"0","title":"orchard Crates.io"},"1":{"body":"The Orchard Book Crate documentation","breadcrumbs":"Documentation","id":"1","title":"Documentation"},"10":{"body":"","breadcrumbs":"Design","id":"10","title":"Design"},"2":{"body":"Copyright 2020 The Electric Coin Company. 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Note that we also deviate from Sapling by using ShortCommit to deriving ivk instead of a full PRF. This removes an unnecessary (large) PRF primitive from the circuit, at the cost of requiring rivk to be part of the full viewing key.","breadcrumbs":"Design » Commitments","id":"20","title":"Commitments"},"21":{"body":"One of the things we learned from Sapling is that having a single global commitment tree makes life hard for light client wallets. When a new note is received, the wallet derives its incremental witness from the state of the global tree at the point when the note's commitment is appended; this incremental state then needs to be updated with every subsequent commitment in the block in-order. It isn't efficient for a server to pre-compute and send over the necessary incremental updates for every new note in a block, and if a wallet requested a specific update from the server it would leak the specific note that was received. Orchard addresses this by splitting the commitment tree into several sub-trees: Bundle tree, that accumulates the commitments within a single bundle (and thus a single transaction). Block tree, that accumulates the bundle tree roots within a single block. Global tree, that accumulates the block tree roots. Each of these trees has a fixed depth (necessary for being able to create proofs). Chains that integrate Orchard can decouple the limits on commitments-per-subtree from higher-layer constraints like block size, by enabling their blocks and transactions to be structured internally as a series of Orchard blocks or txs (e.g. a Zcash block would contain a Vec, that each get appended in-order). Zcash level: we also bind these roots into the FlyClient history leaves, so that light clients can assert they are valid independently of the full block. TODO: Sean is pretty sure we can just improve the Incremental Merkle Tree implementation to work around this, without domain-separating the tree. If we can do that instead, it may be simpler.","breadcrumbs":"Design » Commitment tree","id":"21","title":"Commitment tree"},"22":{"body":"The nullifier design we use for Orchard is nf=[Hashnk(ρ)+ψ(modp)]G+cm, where: Hash is a keyed circuit-efficient hash (such as Rescue). ρ is unique to this output. As with hSig in Sprout, ρ includes the nullifiers of any Orchard notes being spent. If spends and outputs are merged / combined, then we always have a nullifier (internally derived from a real or dummy note), and can rely on the nullifier derivation process to prevent an adversary from choosing dummy nullifiers arbitrarily. If spends and outputs are not merged, then ρ should probably also include unique information from other parts of the transaction as well. TODO: Decide which of the above two cases will be used, and update this. ψ is sender-controlled randomness. It is not required to be unique, and in practice is derived from a sender-selected random value rseed. G is an fixed independent base. This gives a note structure of (addr,v,ρ,ψ,rcm). The nullifier commits to the note value via cm in order to domain-separate nullifiers for zero-valued notes from other notes.","breadcrumbs":"Design » Nullifiers","id":"22","title":"Nullifiers"},"23":{"body":"We care about several security properties for our nullifiers: Balance: can I forge money? Note Privacy: can I gain information about notes only from the public block chain? This describes notes sent in-band. Note Privacy (OOB): can I gain information about notes sent out-of-band, only from the public block chain? In this case, we assume privacy of the channel over which the note is sent, and that the adversary does not have access to any notes sent to the same address which are then spent (so that the nullifier is on the block chain somewhere). Spend Unlinkability: given the incoming viewing key for an address, and not the full viewing key, can I (possibly the sender) detect spends of any notes sent to that address? We're giving ivk to the attacker and allowing it to be the sender in order to make this property as strong as possible: they will have all the notes sent to that address. Faerie Resistance: can I perform a Faerie Gold attack (i.e. cause notes to be accepted that are unspendable)? We assume (and instantiate elsewhere) the following primitives: GH is a cryptographic hash into the group (such as BLAKE2s with simplified SWU), used to derive all fixed independent bases. E is an elliptic curve (such as Pallas). KDF is the note encryption key derivation function. For our chosen design, our desired security properties rely on the following assumptions: BalanceNote PrivacyNote Privacy (OOB)Spend UnlinkabilityFaerie ResistanceDLEHashDHEKDFNear perfect‡DDHE†∨PRFHashDLE HashDHEF is computational Diffie-Hellman using F for the key derivation, with one-time ephemeral keys. This assumption is heuristically weaker than DDHE but stronger than DLE. We omit ROGH as a security assumption because we only rely on the random oracle applied to fixed inputs defined by the protocol, i.e. to generate the fixed base G, not to attacker-specified inputs. † We additionally assume that for any input x, {Hashnk(x):>nk∈E} gives a scalar in an adequate range for DDHE. (Otherwise, Hash could be trivial, e.g. independent of nk.) ‡ Statistical distance <2−167.8 from perfect.","breadcrumbs":"Design » Security properties","id":"23","title":"Security properties"},"24":{"body":"⚠ Caution: be skeptical of the claims in this table about what problem(s) each security property depends on. They may not be accurate and are definitely not fully rigorous. nf[nk][θ]H[nk]H+[rnf]IHash([nk][θ]H)Hash([nk]H+[rnf]I)[Hashnk(ψ)][θ]H[Hashnk(ψ)]H+[rnf]I[Hashnk(ψ)]G+[θ]H[Hashnk(ψ)]H+cm[Hashnk(ρ,ψ)]G+cm[Hashnk(ρ)]G+cm[Hashnk(ρ,ψ)]G+Commitrnfnf(v,ρ)[Hashnk(ρ)]G+Commitrnfnf(v,ρ)[Hashnk(ρ,ψ)]G+[rnf]I+cm[Hashnk(ρ)]G+[rnf]I+cmNote(addr,v,H,θ,rcm)(addr,v,H,rnf,rcm)(addr,v,H,θ,rcm)(addr,v,H,rnf,rcm)(addr,v,H,θ,ψ,rcm)(addr,v,H,rnf,ψ,rcm)(addr,v,H,θ,ψ,rcm)(addr,v,H,ψ,rcm)(addr,v,ρ,ψ,rcm)(addr,v,ρ,rcm)(addr,v,ρ,rnf,ψ,rcm)(addr,v,ρ,rnf,rcm)(addr,v,ρ,rnf,ψ,rcm)(addr,v,ρ,rnf,rcm)BalanceDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLENote PrivacyHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFNote Privacy (OOB)PerfectPerfectPerfectPerfectPerfectPerfectPerfectPRFHashPRFHashPRFHashPerfectPerfectPerfectPerfectSpend UnlinkabilityDDHEDDHEDDHE∨PreHashDDHE∨PreHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashFaerie ResistanceROGH∧DLEROGH∧DLECollHash∧ROGH∧DLECollHash∧ROGH∧DLEROGH∧DLEROGH∧DLEROGH∧DLEDLEDLEDLEDLEDLEDLEDLE In the above alternatives: H is calculated by the sender as H=GH(ρ), and would be provided in the action. I is an fixed independent base, independent of G and any others returned by GH. For the options that use H, when spending a note, if it's a real note, then H is as computed for that note, so it is a unique RO output; if it's a dummy note, we enforce that it is some fixed base independent of other bases. The Commitnf variants enabled nullifier domain separation based on note value, without directly depending on cm (which in its native type is a base field element, not a group element). We decided instead to follow Sapling by defining an intermediate representation of cm as a group element, that is only used in nullifier computation.","breadcrumbs":"Design » Considered alternatives","id":"24","title":"Considered alternatives"},"25":{"body":"Orchard signatures are an instantiation of RedDSA with a cofactor of 1. TODO: Should it be possible to sign partial transactions? If we're going to merge down all the signatures into a single one, and also want this, we need to ensure there's a feasible MPC.","breadcrumbs":"Design » Signatures","id":"25","title":"Signatures"},"26":{"body":"","breadcrumbs":"Design » Circuit","id":"26","title":"Circuit"},"3":{"body":"","breadcrumbs":"Concepts","id":"3","title":"Concepts"},"4":{"body":"","breadcrumbs":"Concepts » Preliminaries","id":"4","title":"Preliminaries"},"5":{"body":"","breadcrumbs":"User Documentation","id":"5","title":"User Documentation"},"6":{"body":"","breadcrumbs":"User Documentation » Creating keys and addresses","id":"6","title":"Creating keys and addresses"},"7":{"body":"","breadcrumbs":"User Documentation » Creating notes","id":"7","title":"Creating notes"},"8":{"body":"","breadcrumbs":"User Documentation » Spending notes","id":"8","title":"Spending notes"},"9":{"body":"","breadcrumbs":"User Documentation » Integration into an existing chain","id":"9","title":"Integration into an existing 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We know how to do this, but it would require a discrete log equality proof, and the most efficient way to do this would be to do RedDSA and this at the same time, which means more work for e.g. hardware wallets.","breadcrumbs":"Non-requirements","id":"13","title":"Non-requirements"},"14":{"body":"Should we have one memo per output, or one memo per transaction, or 0..n memos? Variable, or (1 or n), is a potential privacy leak. Need to consider the privacy issue related to light clients requesting individual memos vs being able to fetch all memos.","breadcrumbs":"Open issues","id":"14","title":"Open issues"},"15":{"body":"Provisional proposal: exactly the same key structure as Sapling. Group hashing uses the isogeny. nsk goes away; nk is now a field element TODO: ak / nk split enables splitting the security argument, but could consider merging. Merging would help with ivk derivation perf (though as a commitment now it's pretty cheap) TODO: nullifier computation ZIP 32 integration Use same Sapling design? Simpler \"hardened-only\" derivation structure? Improve diversifier integration / documentation","breadcrumbs":"Key structure","id":"15","title":"Key structure"},"16":{"body":"TODO: UDAs: arbitrary vs whitelisted","breadcrumbs":"Note structure","id":"16","title":"Note structure"},"17":{"body":"For Sapling, we have encountered multiple places where the specification uses typed variables to define the consensus rules, but the C++ implementation in zcashd relied on byte encodings to implement them. This resulted in subtly-different consensus rules being deployed than were intended, for example where a particular type was not round-trip encodable. In Orchard, we avoid this by defining the consensus rules in terms of the byte encodings of all variables, and being explicit about any types that are not round-trip encodable. 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See here for why the TGPPL exists, graphically illustrated on three slides.","breadcrumbs":"License","id":"2","title":"License"},"20":{"body":"As in Sapling, we require two kinds of commitment schemes in Pollard: HomomorphicCommit is a linearly homomorphic commitment scheme with perfect hiding, and strong binding reducible to DL. Commit and ShortCommit are commitment schemes with perfect hiding, and strong binding reducible to DL. By \"strong binding\" we mean that the scheme is collision resistant on the input and randomness. We instantiate HomomorphicCommit with a Pedersen commitment, and use it for value commitments: cv=HomomorphicCommitrcvcv(v) We instantiate Commit and ShortCommit with Sinsemilla, and use them for all other commitments: ivk=ShortCommitrivkivk(nk,ak) cm=Commitrcmcm(rest of note) This is the same split (and rationale) as in Sapling, but using the more PLONK-efficient Sinsemilla instead of Bowe-Hopwood Pedersen hashes. Note that we also deviate from Sapling by using ShortCommit to deriving ivk instead of a full PRF. This removes an unnecessary (large) PRF primitive from the circuit, at the cost of requiring rivk to be part of the full viewing key.","breadcrumbs":"Design » Commitments","id":"20","title":"Commitments"},"21":{"body":"One of the things we learned from Sapling is that having a single global commitment tree makes life hard for light client wallets. When a new note is received, the wallet derives its incremental witness from the state of the global tree at the point when the note's commitment is appended; this incremental state then needs to be updated with every subsequent commitment in the block in-order. It isn't efficient for a server to pre-compute and send over the necessary incremental updates for every new note in a block, and if a wallet requested a specific update from the server it would leak the specific note that was received. Orchard addresses this by splitting the commitment tree into several sub-trees: Bundle tree, that accumulates the commitments within a single bundle (and thus a single transaction). Block tree, that accumulates the bundle tree roots within a single block. Global tree, that accumulates the block tree roots. Each of these trees has a fixed depth (necessary for being able to create proofs). Chains that integrate Orchard can decouple the limits on commitments-per-subtree from higher-layer constraints like block size, by enabling their blocks and transactions to be structured internally as a series of Orchard blocks or txs (e.g. a Zcash block would contain a Vec, that each get appended in-order). Zcash level: we also bind these roots into the FlyClient history leaves, so that light clients can assert they are valid independently of the full block. TODO: Sean is pretty sure we can just improve the Incremental Merkle Tree implementation to work around this, without domain-separating the tree. If we can do that instead, it may be simpler.","breadcrumbs":"Design » Commitment tree","id":"21","title":"Commitment tree"},"22":{"body":"The nullifier design we use for Orchard is nf=[Hashnk(ρ)+ψ(modp)]G+cm, where: Hash is a keyed circuit-efficient hash (such as Rescue). ρ is unique to this output. As with hSig in Sprout, ρ includes the nullifiers of any Orchard notes being spent. If spends and outputs are merged / combined, then we always have a nullifier (internally derived from a real or dummy note), and can rely on the nullifier derivation process to prevent an adversary from choosing dummy nullifiers arbitrarily. If spends and outputs are not merged, then ρ should probably also include unique information from other parts of the transaction as well. TODO: Decide which of the above two cases will be used, and update this. ψ is sender-controlled randomness. It is not required to be unique, and in practice is derived from a sender-selected random value rseed. G is an fixed independent base. This gives a note structure of (addr,v,ρ,ψ,rcm). The nullifier commits to the note value via cm in order to domain-separate nullifiers for zero-valued notes from other notes.","breadcrumbs":"Design » Nullifiers","id":"22","title":"Nullifiers"},"23":{"body":"We care about several security properties for our nullifiers: Balance: can I forge money? Note Privacy: can I gain information about notes only from the public block chain? This describes notes sent in-band. Note Privacy (OOB): can I gain information about notes sent out-of-band, only from the public block chain? In this case, we assume privacy of the channel over which the note is sent, and that the adversary does not have access to any notes sent to the same address which are then spent (so that the nullifier is on the block chain somewhere). Spend Unlinkability: given the incoming viewing key for an address, and not the full viewing key, can I (possibly the sender) detect spends of any notes sent to that address? We're giving ivk to the attacker and allowing it to be the sender in order to make this property as strong as possible: they will have all the notes sent to that address. Faerie Resistance: can I perform a Faerie Gold attack (i.e. cause notes to be accepted that are unspendable)? We assume (and instantiate elsewhere) the following primitives: GH is a cryptographic hash into the group (such as BLAKE2s with simplified SWU), used to derive all fixed independent bases. E is an elliptic curve (such as Pallas). KDF is the note encryption key derivation function. For our chosen design, our desired security properties rely on the following assumptions: BalanceNote PrivacyNote Privacy (OOB)Spend UnlinkabilityFaerie ResistanceDLEHashDHEKDFNear perfect‡DDHE†∨PRFHashDLE HashDHEF is computational Diffie-Hellman using F for the key derivation, with one-time ephemeral keys. This assumption is heuristically weaker than DDHE but stronger than DLE. We omit ROGH as a security assumption because we only rely on the random oracle applied to fixed inputs defined by the protocol, i.e. to generate the fixed base G, not to attacker-specified inputs. † We additionally assume that for any input x, {Hashnk(x):>nk∈E} gives a scalar in an adequate range for DDHE. (Otherwise, Hash could be trivial, e.g. independent of nk.) ‡ Statistical distance <2−167.8 from perfect.","breadcrumbs":"Design » Security properties","id":"23","title":"Security properties"},"24":{"body":"⚠ Caution: be skeptical of the claims in this table about what problem(s) each security property depends on. They may not be accurate and are definitely not fully rigorous. nf[nk][θ]H[nk]H+[rnf]IHash([nk][θ]H)Hash([nk]H+[rnf]I)[Hashnk(ψ)][θ]H[Hashnk(ψ)]H+[rnf]I[Hashnk(ψ)]G+[θ]H[Hashnk(ψ)]H+cm[Hashnk(ρ,ψ)]G+cm[Hashnk(ρ)]G+cm[Hashnk(ρ,ψ)]G+Commitrnfnf(v,ρ)[Hashnk(ρ)]G+Commitrnfnf(v,ρ)[Hashnk(ρ,ψ)]G+[rnf]I+cm[Hashnk(ρ)]G+[rnf]I+cmNote(addr,v,H,θ,rcm)(addr,v,H,rnf,rcm)(addr,v,H,θ,rcm)(addr,v,H,rnf,rcm)(addr,v,H,θ,ψ,rcm)(addr,v,H,rnf,ψ,rcm)(addr,v,H,θ,ψ,rcm)(addr,v,H,ψ,rcm)(addr,v,ρ,ψ,rcm)(addr,v,ρ,rcm)(addr,v,ρ,rnf,ψ,rcm)(addr,v,ρ,rnf,rcm)(addr,v,ρ,rnf,ψ,rcm)(addr,v,ρ,rnf,rcm)BalanceDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLEDLENote PrivacyHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFHashDHEKDFNote Privacy (OOB)PerfectPerfectPerfectPerfectPerfectPerfectPerfectPRFHashPRFHashPRFHashPerfectPerfectPerfectPerfectSpend UnlinkabilityDDHEDDHEDDHE∨PreHashDDHE∨PreHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashDDHE†∨PRFHashFaerie ResistanceROGH∧DLEROGH∧DLECollHash∧ROGH∧DLECollHash∧ROGH∧DLEROGH∧DLEROGH∧DLEROGH∧DLEDLEDLEDLEDLEDLEDLEDLE In the above alternatives: H is calculated by the sender as H=GH(ρ), and would be provided in the action. I is an fixed independent base, independent of G and any others returned by GH. For the options that use H, when spending a note, if it's a real note, then H is as computed for that note, so it is a unique RO output; if it's a dummy note, we enforce that it is some fixed base independent of other bases. The Commitnf variants enabled nullifier domain separation based on note value, without directly depending on cm (which in its native type is a base field element, not a group element). We decided instead to follow Sapling by defining an intermediate representation of cm as a group element, that is only used in nullifier computation.","breadcrumbs":"Design » Considered alternatives","id":"24","title":"Considered alternatives"},"25":{"body":"Orchard signatures are an instantiation of RedDSA with a cofactor of 1. TODO: Should it be possible to sign partial transactions? If we're going to merge down all the signatures into a single one, and also want this, we need to ensure there's a feasible MPC.","breadcrumbs":"Design » Signatures","id":"25","title":"Signatures"},"26":{"body":"","breadcrumbs":"Design » Circuit","id":"26","title":"Circuit"},"3":{"body":"","breadcrumbs":"Concepts","id":"3","title":"Concepts"},"4":{"body":"","breadcrumbs":"Concepts » Preliminaries","id":"4","title":"Preliminaries"},"5":{"body":"","breadcrumbs":"User Documentation","id":"5","title":"User Documentation"},"6":{"body":"","breadcrumbs":"User Documentation » Creating keys and addresses","id":"6","title":"Creating keys and addresses"},"7":{"body":"","breadcrumbs":"User Documentation » Creating notes","id":"7","title":"Creating notes"},"8":{"body":"","breadcrumbs":"User Documentation » Spending notes","id":"8","title":"Spending notes"},"9":{"body":"","breadcrumbs":"User Documentation » Integration into an existing chain","id":"9","title":"Integration into an existing 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