Key Transparency Protocol

3.1. Log Tree

Log trees are used for storing information in the chronological order that it was added and are constructed as left-balanced binary trees.¶

A binary tree is balanced if its size is a power of two and for any parent node in the tree, its left and right subtrees have the same size. A binary tree is left-balanced if for every parent, either the parent is balanced, or the left subtree of that parent is the largest balanced subtree that could be constructed from the leaves present in the parent's own subtree. Given a list of n items, there is a unique left-balanced binary tree structure with these elements as leaves. Note also that every parent always has both a left and right child.¶

Log trees initially consist of a single leaf node. New leaves are added to the right-most edge of the tree along with a single parent node, to construct the left-balanced binary tree with n+1 leaves.¶

While leaves contain arbitrary data, the value of a parent node is always the hash of the combined values of its left and right children.¶

Log trees are powerful in that they can provide both inclusion proofs, which demonstrate that a leaf is included in a log, and consistency proofs, which demonstrate that a new version of a log is an extension of a past version of the log.¶

An inclusion proof is given by providing the copath values of a leaf. The proof is verified by hashing together the leaf with the copath values and checking that the result equals the root hash value of the log. Consistency proofs are a more general version of the same idea. With a consistency proof, the prover provides the minimum set of intermediate node values from the current tree that allows the verifier to compute both the old root value and the current root value. An algorithm for this is given in section 2.1.2 of [RFC6962].¶

3.2. Prefix Tree

Prefix trees are used for storing a set of values while preserving the ability to efficiently produce proofs of membership and non-membership in the set.¶

Each leaf node in a prefix tree represents a specific value, while each parent node represents some prefix which all values in the subtree headed by that node have in common. The subtree headed by a parent's left child contains all values that share its prefix followed by an additional 0 bit, while the subtree headed by a parent's right child contains all values that share its prefix followed by an additional 1 bit.¶

The root node, in particular, represents the empty string as a prefix. The root's left child contains all values that begin with a 0 bit, while the right child contains all values that begin with a 1 bit.¶

A prefix tree can be searched by starting at the root node, and moving to the left child if the first bit of a value is 0, or the right child if the first bit is 1. This is then repeated for the second bit, third bit, and so on until the search either terminates at a leaf node (which may or may not be for the desired value), or a parent node that lacks the desired child.¶

New values are added to the tree by searching it according to the same process. If the search terminates at a parent without a left or right child, a new leaf is simply added as the parent's missing child. If the search terminates at a leaf for the wrong value, one or more intermediate nodes are added until the new leaf and the existing leaf would no longer reside in the same place. That is, until we reach the first bit that differs between the new value and the existing value.¶

The value of a leaf node is the encoded set member, while the value of a parent node is the hash of the combined values of its left and right children (or a stand-in value when one of the children doesn't exist).¶

A proof of membership is given by providing the leaf hash value, along with the hash value of each copath entry along the search path. A proof of non-membership is given by providing an abridged proof of membership that follows the search path for the intended value, but ends either at a stand-in value or a leaf for a different value. In either case, the proof is verified by hashing together the leaf with the copath hash values and checking that the result equals the root hash value of the tree.¶

3.3. Combined Tree

Log trees are desirable because they can provide efficient consistency proofs to assure verifiers that nothing has been removed from a log that was present in a previous version. However, log trees can't be efficiently searched without downloading the entire log. Prefix trees are efficient to search and can provide inclusion proofs to convince verifiers that the returned search results are correct. However, it's not possible to efficiently prove that a new version of a prefix tree contains the same data as a previous version with only new values added.¶

In the combined tree structure, which is based on [Merkle2], a log tree maintains a record of each time any key's value is updated, while a prefix tree maintains the set of index-version pairs. Importantly, the root hash value of the prefix tree after adding a new index-version pair is stored in a leaf of the log tree alongside a privacy-preserving commitment to the update. With some caveats, this combined structure supports both efficient consistency proofs and can be efficiently searched.¶

Note that, although the Transparency Log maintains a single logical prefix tree, each modification of this tree results in a new root hash, which is then stored in the log tree. Therefore, when instructions refer to "looking up a key in the prefix tree at a given log entry," this actually means searching in the specific version of the prefix tree that corresponds to the root hash stored at that log entry.¶

4.1. Implicit Binary Search Tree

Intuitively, the leaves of the log tree can be considered a flat array representation of a binary tree. This structure is similar to the log tree, but distinguished by the fact that not all parent nodes have two children. In this representation, "leaf" nodes are stored in even-numbered indices, while "intermediate" nodes are stored in odd-numbered indices:¶

Following the structure of this binary tree when executing searches makes auditing the Transparency Log much more efficient because users can easily reason about which nodes will be accessed when conducting a search. As such, only nodes along a specific search path need to be checked for correctness.¶

The following Python code demonstrates the computations used for following this tree structure:¶

# The exponent of the largest power of 2 less than x. Equivalent to:
#   int(math.floor(math.log(x, 2)))
def log2(x):
    if x == 0:
        return 0
    k = 0
    while (x >> k) > 0:
        k += 1
    return k-1

# The level of a node in the tree. Leaves are level 0, their parents
# are level 1, etc. If a node's children are at different levels,
# then its level is the max level of its children plus one.
def level(x):
    if x & 0x01 == 0:
        return 0
    k = 0
    while ((x >> k) & 0x01) == 1:
        k += 1
    return k

# The root index of a search if the log has `n` entries.
def root(n):
    return (1 << log2(n)) - 1

# The left child of an intermediate node.
def left(x):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')
    return x ^ (0x01 << (k - 1))

# The right child of an intermediate node.
def right(x, n):
    k = level(x)
    if k == 0:
        raise Exception('leaf node has no children')
    x = x ^ (0x03 << (k - 1))
    while x >= n:
        x = left(x)
    return x

The root function returns the index in the log at which a search should start. The left and right functions determine the subsequent index to be accessed, depending on whether the search moves left or right.¶

For example, in a search where the log has 50 entries, instead of starting the search at the typical "middle" entry of 50/2 = 25, users would start at entry root(50) = 31. If the next step in the search is to move right, the next index to access would be right(31, 50) = 47. As more entries are added to the log, users will consistently revisit entries 31 and 47, while they may never revisit entry 25 after even a single new entry is added to the log.¶

4.2. Binary Ladder

When executing searches on a Transparency Log, the implicit tree described in Section 4.1 is navigated according to a binary search. At each individual log entry, the binary search needs to determine whether it should move left or right. That is, it needs to determine, out of the set of key-version pairs stored in the prefix tree, whether the highest version present at a given log entry is greater than, equal to, or less than a target version.¶

A binary ladder is a series of lookups in a single log entry's prefix tree, which is used to establish whether the target version of a key is present or not. It consists of the following lookups, stopping after the first lookup that produces a proof of non-inclusion:¶

1. First, version x of the key is looked up, where x is consecutively higher powers of two minus one (0, 1, 3, 7, ...). This is repeated until x is the largest such value less than or equal to the target version.¶

2. Second, the largest x that was looked up is retained, and consecutively smaller powers of two are added to it until it equals the target version. Each time a power of two is added, this version of the key is looked up.¶

As an example, if the target version of a key to lookup is 20, a binary ladder would consist of the following versions: 0, 1, 3, 7, 15, 19, 20. If all of the lookups succeed (i.e., result in proofs of inclusion), this indicates that the target version of the key exists in the log. If the ladder stops early because a proof of non-inclusion was produced, this indicates that the target version of the key did not exist, as of the given log entry.¶

When executing a search in a Transparency Log for a specific version of a key, a binary ladder is provided for each node on the search path, verifiably guiding the search toward the log entry where the desired key-version pair was first inserted (and therefore, the log entry with the desired update).¶

Requiring proof that this series of versions are present in the prefix tree, instead of requesting proof of just version 20, ensures that all users are able to agree on which version of the key is most recent, which is discussed further in the next section.¶

4.3. Most Recent Version

Often, users wish to search for the "most recent" version of a key. That is, the key with the highest counter possible.¶

To determine this, users request a full binary ladder for each node on the frontier of the log. The frontier consists of the root node of a search, followed by the entries produced by repeatedly calling right until reaching the last entry of the log. Using the same example of a search where the log has 50 entries, the frontier would be entries: 31, 47, 49.¶

A full binary ladder is similar to the binary ladder discussed in the previous section, except that it identifies the exact highest version of a key that exists, as of a particular log entry, rather than stopping at a target version. It consists of the following lookups:¶

1. First, version x of the key is looked up, where x is a consecutively higher power of two minus one (0, 1, 3, 7, ...). This is repeated until the first proof of non-inclusion is produced.¶

2. Once the first proof of non-inclusion is produced, a binary search is conducted between the highest version that was proved to be included, and the version that was proved to not be included. Each step of the binary search produces either a proof of inclusion or non-inclusion, which guides the search left or right, until it terminates.¶

For the purpose of finding the highest version possible, requesting a full binary ladder for each entry along the frontier is functionally the same as doing so for only the last log entry. However, inspecting the entire frontier allows the user to verify that the search path leading to the last log entry represents a monotonic series of version increases, which minimizes opportunities for log misbehavior.¶

Once the user has verified that the frontier lookups are monotonic and determined the highest version, the user then continues a binary search for this specific version.¶

4.4. Monitoring

As new entries are added to the log tree, the search path that's traversed to find a specific version of a key may change. New intermediate nodes may become established in between the search root and the leaf, or a new search root may be created. The goal of monitoring a key is to efficiently ensure that, when these new parent nodes are created, they're created correctly so that searches for the same versions continue converging to the same entries in the log.¶

To monitor a given search key, users maintain a small amount of state: a map from a position in the log to a version counter. The version counter is the highest version of the search key that's been proven to exist at that log position. Users initially populate this map by setting the position of an entry they've looked up, to map to the version of the key stored in that entry. A map may track several different versions of a search key simultaneously, if a user has been shown different versions of the same search key.¶

To update this map, users receive the most recent tree head from the server and follow these steps, for each entry in the map:¶

1. Compute the entry's direct path (in terms of the Implicit Binary Search Tree) based on the current tree size.¶

2. If there are no entries in the direct path that are to the right of the current entry, then skip updating this entry (there's no new information to update it with).¶

3. For each entry in the direct path that's to the right of the current entry, from low to high:¶

   1. Receive and verify a binary ladder from that log entry, for the version currently in the map. This proves that, at the indicated log entry, the highest version present is greater than or equal to the previously-observed version.¶

   2. If the above check was successful, remove the current position-version pair from the map and replace it with a position-version pair corresponding to the entry in the log that was just checked.¶

This algorithm progressively moves up the tree as new intermediate/root nodes are established and verifies that they're constructed correctly. Note that users can often execute this process with the output of Search or Update operations for a key, without waiting to make explicit Monitor queries.¶

It is also worth noting that the work required to monitor several versions of the same key scales sublinearly, due to the fact that the direct paths of the different versions will often intersect. Intersections reduce the total number of entries in the map and therefore the amount of work that will be needed to monitor the key from then on.¶

6.1. Verifiable Random Function

Each version of a search key that's inserted in a log will have a unique representation in the prefix tree. This is computed by providing the combined search key and version as inputs to the VRF:¶

struct {
  opaque search_key<0..2^8-1>;
  uint32 version;
} VrfInput;

6.2. Commitment

As discussed in Section 3.3, commitments are stored in the leaves of the log tree and correspond to updates of a key's value. Commitments are computed with HMAC [RFC2104], using the hash function specified by the ciphersuite. To produce a new commitment, the application generates a random 16 byte value called opening and computes:¶

commitment = HMAC(fixedKey, CommitmentValue)

where fixedKey is the 16 byte hex-decoded value:¶

d821f8790d97709796b4d7903357c3f5

and CommitmentValue is specified as:¶

struct {
  opaque opening<16>;
  opaque search_key<0..2^8-1>;
  UpdateValue update;
} CommitmentValue;

This fixed key allows the HMAC function, and thereby the commitment scheme, to be modeled as a random oracle. The search_key field of CommitmentValue contains the search key being updated (the search key provided by the user, not the VRF output) and the update field contains the value of the update.¶

The output value commitment may be published, while opening should be kept private until the commitment is meant to be revealed.¶

6.3. Prefix Tree

The leaf nodes of a prefix tree are serialized as:¶

struct {
    opaque key_version<VRF.Nh>;
} PrefixLeaf;

where key_version is the VRF output for the key-version pair, and VRF.Nh is the output size of the ciphersuite VRF in bytes.¶

The parent nodes of a prefix tree are serialized as:¶

struct {
  opaque value<Hash.Nh>;
} PrefixParent;

where Hash.Nh is the output length of the ciphersuite hash function. The value of a parent node is computed by hashing together the values of its left and right children:¶

parent.value = Hash(0x01 ||
                   nodeValue(parent.leftChild) ||
                   nodeValue(parent.rightChild))

nodeValue(node):
  if node.type == emptyNode:
    return make([]byte, Hash.Nh)
  else if node.type == leafNode:
    return Hash(0x00 || node.key_version)
  else if node.type == parentNode:
    return node.value

where Hash denotes the ciphersuite hash function.¶

6.4. Log Tree

The leaf and parent nodes of a log tree are serialized as:¶

struct {
  opaque commitment<Hash.Nh>;
  opaque prefix_tree<Hash.Nh>;
} LogLeaf;

struct {
  opaque value<Hash.Nh>;
} LogParent;

The value of a parent node is computed by hashing together the values of its left and right children:¶

parent.value = Hash(hashContent(parent.leftChild) ||
                    hashContent(parent.rightChild))

hashContent(node):
  if node.type == leafNode:
    return 0x00 || nodeValue(node)
  else if node.type == parentNode:
    return 0x01 || nodeValue(node)

nodeValue(node):
  if node.type == leafNode:
    return Hash(node.commitment || node.prefix_tree)
  else if node.type == parentNode:
    return node.value

6.5. Tree Head Signature

The head of a Transparency Log, which represents the log's most recent state, is represented as:¶

struct {
  uint64 tree_size;
  opaque signature<0..2^16-1>;
} TreeHead;

where tree_size counts the number of entries in the log tree. If the Transparency Log is deployed with Third-party Management then the public key used to verify the signature belongs to the third-party manager; otherwise the public key used belongs to the service operator.¶

The signature itself is computed over a TreeHeadTBS structure, which incorporates the log's current state as well as long-term log configuration:¶

enum {
  reserved(0),
  contactMonitoring(1),
  thirdPartyManagement(2),
  thirdPartyAuditing(3),
  (255)
} DeploymentMode;

struct {
  CipherSuite ciphersuite;
  DeploymentMode mode;
  opaque signature_public_key<0..2^16-1>;
  opaque vrf_public_key<0..2^16-1>;

  select (Configuration.mode) {
    case contactMonitoring:
    case thirdPartyManagement:
      opaque leaf_public_key<0..2^16-1>;
    case thirdPartyAuditing:
      opaque auditor_public_key<0..2^16-1>;
  };
} Configuration;

struct {
  Configuration config;
  uint64 tree_size;
  opaque root_value<Hash.Nh>;
} TreeHeadTBS;

7.1. Log Tree

An inclusion proof for a single leaf in a log tree is given by providing the copath values of a leaf. Similarly, a bulk inclusion proof for any number of leaves is given by providing the fewest node values that can be hashed together with the specified leaves to produce the root value. Such a proof is encoded as:¶

opaque NodeValue<Hash.Nh>;

struct {
  NodeValue elements<0..2^16-1>;
} InclusionProof;

Each NodeValue is a uniform size, computed by passing the relevant LogLeaf or LogParent structures through the nodeValue function in Section 6.4. The contents of the elements array is kept in left-to-right order: if a node is present in the root's left subtree, its value must be listed before any values provided from nodes that are in the root's right subtree, and so on recursively.¶

Consistency proofs are encoded similarly:¶

struct {
  NodeValue elements<0..2^8-1>;
} ConsistencyProof;

Again, each NodeValue is computed by passing the relevant LogLeaf or LogParent structure through the nodeValue function. The nodes chosen correspond to those output by the algorithm in Section 2.1.2 of [RFC6962].¶

7.2. Prefix Tree

A proof from a prefix tree authenticates that a set of values are either members of, or are not members of, the total set of values represented by the prefix tree. Such a proof is encoded as:¶

enum {
  reserved(0),
  inclusion(1),
  nonInclusionLeaf(2),
  nonInclusionParent(3),
} PrefixSearchResultType;

struct {
  PrefixSearchResultType result_type;
  select (PrefixSearchResult.result_type) {
    case nonInclusionLeaf:
      PrefixLeaf leaf;
  };
  uint8 depth;
} PrefixSearchResult;

struct {
  PrefixSearchResult results<0..2^8-1>;
  NodeValue elements<0..2^16-1>;
} PrefixProof;

The results field contains the search result for each individual value. It is sorted lexicographically by corresponding value. The result_type field of each PrefixSearchResult struct indicates what the terminal node of the search for that value was:¶

• inclusion for a leaf node matching the requested value.¶

• nonInclusionLeaf for a leaf node not matching the requested value. In this case, the terminal node's value is provided given that it can not be inferred.¶

• nonInclusionParent for a parent node that lacks the desired child.¶

The depth field indicates the depth of the terminal node of the search, and is provided to assist proof verification.¶

The elements array consists of the fewest node values that can be hashed together with the provided leaves to produce the root. The contents of the elements array is kept in left-to-right order: if a node is present in the root's left subtree, its value must be listed before any values provided from nodes that are in the root's right subtree, and so on recursively. In the event that a node is not present, an all-zero byte string of length Hash.Nh is listed instead.¶

The proof is verified by hashing together the provided elements, in the left/right arrangement dictated by the tree structure, and checking that the result equals the root value of the prefix tree.¶

7.3. Combined Tree

A proof from a combined log and prefix tree follows the execution of a binary search through the leaves of the log tree, as described in Section 3.3. It is serialized as follows:¶

struct {
  opaque proof<VRF.Np>;
} VRFProof;

struct {
  PrefixProof prefix_proof;
  opaque commitment<Hash.Nh>;
} ProofStep;

struct {
  optional<uint32> version;
  VRFProof vrf_proofs<0..2^8-1>;
  ProofStep steps<0..2^8-1>;
  InclusionProof inclusion;
} SearchProof;

If searching for the most recent version of a key, the most recent version is provided in version. If searching for a specific version, this field is omitted.¶

Each element of vrf_proofs contains the output of evaluating the VRF on a different version of the search key. The versions chosen correspond either to the binary ladder described in Section 4.2 (when searching for a specific version of a key), or to the full binary ladder described in Section 4.3 (when searching for the most recent version of a key). The proofs are sorted from lowest version to highest version.¶

Each ProofStep structure in steps is one log entry that was inspected as part of the binary search. The first step corresponds to the "middle" leaf of the log tree (calculated with the root function in Section 4.1). From there, each subsequent step moves left or right in the tree, according to the procedure discussed in Section 4.2 and Section 4.3.¶

The prefix_proof field of a ProofStep is the output of executing a binary ladder, excluding any ladder steps for which a proof of inclusion is expected, and a proof of inclusion was already provided in a previous ProofStep for a log entry to the left of the current one.¶

The commitment field of a ProofStep contains the commitment to the update at that leaf. The inclusion field of SearchProof contains a batch inclusion proof for all of the leaves accessed by the binary search.¶

The proof can be verified by checking that:¶

1. The elements of steps represent a monotonic series over the leaves of the log, and¶

2. The steps array has the expected number of entries (no more or less than are necessary to execute the binary search).¶

Once the validity of the search steps has been established, the verifier can compute the root of each prefix tree represented by a prefix_proof and combine it with the corresponding commitment to obtain the value of each leaf. These leaf values can then be combined with the proof in inclusion to check that the output matches the root of the log tree.¶

9.1. Search

Users initiate a Search operation by submitting a SearchRequest to the Transparency Log containing the key that they're interested in. Users can optionally specify a version of the key that they'd like to receive, if not the most recent one.¶

struct {
  optional<uint32> last;

  opaque search_key<0..2^8-1>;
  optional<uint32> version;
} SearchRequest;

In turn, the Transparency Log responds with a SearchResponse structure:¶

struct {
  FullTreeHead full_tree_head;

  SearchProof search;
  opaque opening<16>;
  UpdateValue value;
} SearchResponse;

Users verify a search response by following these steps:¶

1. Evaluate the search proof in search according to the steps in Section 7.3. This will produce a verdict as to whether the search was executed correctly and also a candidate root value for the tree. If it's determined that the search was executed incorrectly, abort with an error.¶

2. With the candidate root value for the tree, verify the given FullTreeHead.¶

3. Verify that the commitment in the terminal search step opens to SearchResponse.value with opening SearchResponse.opening.¶

Depending on the deployment mode of the Transparency Log, the value field may or may not require additional verification, specified in Section 8, before its contents may be consumed.¶

9.2. Update

Users initiate an Update operation by submitting an UpdateRequest to the Transparency Log containing the new key and value to store.¶

struct {
  optional<uint32> last;

  opaque search_key<0..2^8-1>;
  opaque value<0..2^32-1>;
} UpdateRequest;

If the request passes application-layer policy checks, the Transparency Log adds the new key-value pair to the log and returns an UpdateResponse structure:¶

struct {
  FullTreeHead full_tree_head;

  SearchProof search;
  opaque opening<16>;
  UpdatePrefix prefix;
} UpdateResponse;

Users verify the UpdateResponse as if it were a SearchResponse for the most recent version of search_key. To aid verification, the update response provides the UpdatePrefix structure necessary to reconstruct the UpdateValue.¶

9.3. Monitor

Users initiate a Monitor operation by submitting a MonitorRequest to the Transparency Log containing information about the keys they wish to monitor.¶

struct {
  opaque search_key<0..2^8-1>;
  uint32 highest_version;
  uint64 entries<0..2^8-1>;
} MonitorKey;

struct {
  optional<uint32> last;

  MonitorKey owned_keys<0..2^8-1>;
  MonitorKey contact_keys<0..2^8-1>;
} MonitorRequest;

Users include each of the keys that they own in owned_keys. If the Transparency Log is deployed with Contact Monitoring (or simply if the user wants a higher degree of confidence in the log), they also include any keys they've looked up in contact_keys.¶

Each MonitorKey structure contains the key being monitored in search_key, the highest version of the key that the user has observed in highest_version, and a list of entries in the log tree corresponding to the keys of the map described in Section 4.4.¶

The Transparency Log verifies the MonitorRequest by following these steps, for each MonitorKey structure:¶

1. Verify that the requested keys in owned_keys and contact_keys are all distinct.¶

2. Verify that the user owns every key in owned_keys, and is allowed (or was previously allowed) to lookup every key in contact_keys, based on the application's policy.¶

3. Verify that the highest_version for each key is less than or equal to the most recent version of each key.¶

4. Verify that each entries array is sorted in ascending order, and that all entries are within the bounds of the log.¶

5. Verify each entry lies on the direct path of different versions of the key.¶

If the request is valid, the Transparency Log responds with a MonitorResponse structure:¶

struct {
  uint32 version;
  VRFProof vrf_proofs<0..2^8-1>;
  ProofStep steps<0..2^8-1>;
} MonitorProof;

struct {
  FullTreeHead full_tree_head;
  MonitorProof owned_proofs<0..2^8-1>;
  MonitorProof contact_proofs<0..2^8-1>;
  InclusionProof inclusion;
} MonitorResponse;

The elements of owned_proofs and contact_proofs correspond one-to-one with the elements of owned_keys and contact_keys. Each MonitorProof in contact_proofs is meant to convince the user that the key they looked up is still properly included in the log and has not been surreptitiously concealed. Each MonitorProof in owned_proofs conveys the same guarantee that no past lookups have been concealed, and also proves that MonitorProof.version is the most recent version of the key.¶

The version field of a MonitorProof contains the version that was used for computing the binary ladder, and therefore the highest version of the key that will be proven to exist. The vrf_proofs field contains VRF proofs for different versions of the search key, starting at the first version that's different between the binary ladders for MonitorKey.highest_version and MonitorProof.version.¶

The steps field of a MonitorProof contains the proofs required to update the user's monitoring data following the algorithm in Section 4.4. That is, each ProofStep of a MonitorProof contains a binary ladder for the version MonitorProof.version. The steps are provided in the order that they're consumed by the monitoring algorithm. If same proof is consumed by the monitoring algorithm multiple times, it is provided in the MonitorProof structure only the first time.¶

For MonitorProof structures in owned_keys, it is also important to prove that MonitorProof.version is the highest version of the key available. This means that such a MonitorProof must contains full binary ladders for MonitorProof.version along the frontier of the log. As such, any ProofStep under the owned_keys field that's along the frontier of the log includes a full binary ladder for MonitorProof.version instead of a regular binary ladder. For additional entries on the frontier of the log that are to the right of the leftmost frontier entry already provided, an additional ProofStep is added to MonitorProof. This additional ProofStep contains only the proofs of non-inclusion from a full binary ladder.¶

Users verify a MonitorResponse by following these steps:¶

1. Verify that the lengths of owned_proofs and contact_proofs are the same as the lengths of owned_keys and contact_keys.¶

2. For each MonitorProof structure, verify that MonitorProof.version is greater than or equal to the highest version of the key that's been previously observed.¶

3. For each MonitorProof structure, evalute the monitoring algorithm in Section 4.4. Abort with an error if the monitoring algorithm detects that the tree is constructed incorrectly, or if there are fewer or more steps provided than would be expected (keeping in mind that extra steps may be provided along the frontier of the log, if a MonitorProof is a member of owned_keys).¶

4. Construct a candidate root value for the tree by combining the PrefixProof and commitment of ProofStep, with the provided inclusion proof.¶

5. With the candidate root value, verify the provided FullTreeHead.¶

Some information is omitted from MonitorResponse in the interest of efficiency, due to the fact that the user would have already seen and verified it as part of conducting other queries. In particular, VRF proofs for different versions of each search key are not provided, given that these can be cached from the original Search or Update query.¶

11.1. KT Ciphersuites

uint16 CipherSuite;

11.2. KT Designated Expert Pool