Distributed Aggregation Protocol for Privacy Preserving Measurement

Introduction This document describes the Distributed Aggregation Protocol (DAP) for privacy preserving measurement. The protocol is executed by a large set of clients and a small set of servers. The servers' goal is to compute some aggregate statistic over the clients' inputs without learning the inputs themselves. This is made possible by distributing the computation among the servers in such a way that, as long as at least one of them executes the protocol honestly, no input is ever seen in the clear by any server.

Change Log (*) Indicates a change that breaks wire compatibility with the previous draft. 04:

Introduce resource oriented HTTP API. (#278, #398, #400) (*)
Clarify security requirements for choosing VDAF verify key. (#407, #411)
Require clients to provide nonce and random input when sharding inputs. (#394, #425) (*)
Add interval of time spanned by constituent reports to Collection message. (#397, #403) (*)
Update share validation requirements based on latest security analysis. (#408, #410)
Bump draft-irtf-cfrg-vdaf-03 to 05 . (#429) (*)
Bump version tag from "dap-03" to "dap-04". (#424) (*)

03:

Enrich the "fixed_size" query type to allow the Collector to request a recently aggregated batch without knowing the batch ID in advance. ID discovery was previously done out-of-band. (*)
Allow Aggregators to advertise multiple HPKE configurations. (*)
Clarify requirements for enforcing anti-replay. Namely, while it is sufficient to detect repeated report IDs, it is also enough to detect repeated IDs and timestamps.
Remove the extensions from the Report and add extensions to the plaintext payload of each ReportShare. (*)
Clarify that extensions are mandatory to implement: If an Aggregator does not recognize a ReportShare's extension, it must reject it.
Clarify that Aggregators must reject any ReportShare with repeated extension types.
Specify explicitly how to serialize the Additional Authenticated Data (AAD) string for HPKE encryption. This clarifies an ambiguity in the previous version. (*)
Change the length tag for the aggregation parameter to 32 bits. (*)
Use the same prefix ("application") for all media types. (*)
Make input share validation more explicit, including adding a new ReportShareError variant, "report_too_early", for handling reports too far in the future. (*)
Improve alignment of problem details usage with . Replace "reportTooLate" problem document type with "repjortRejected" and clarify handling of rejected reports in the upload sub-protocol. (*)
Bump version tag from "dap-02" to "dap-03". (*)

02:

Define a new task configuration parameter, called the "query type", that allows tasks to partition reports into batches in different ways. In the current draft, the Collector specifies a "query", which the Aggregators use to guide selection of the batch. Two query types are defined: the "time_interval" type captures the semantics of draft 01; and the "fixed_size" type allows the Leader to partition the reports arbitrarily, subject to the constraint that each batch is roughly the same size. (*)
Define a new task configuration parameter, called the task "expiration", that defines the lifetime of a given task.
Specify requirements for HTTP request authentication rather than a concrete scheme. (Draft 01 required the use of the DAP-Auth-Token header; this is now optional.)
Make "task_id" an optional parameter of the "/hpke_config" endpoint.
Add report count to CollectResp message. (*)
Increase message payload sizes to accommodate VDAFs with input and aggregate shares larger than 2^16-1 bytes. (*)
Bump draft-irtf-cfrg-vdaf-01 to 03 . (*)
Bump version tag from "dap-01" to "dap-02". (*)
Rename the report nonce to the "report ID" and move it to the top of the structure. (*)
Clarify when it is safe for an Aggregator to evict various data artifacts from long-term storage.

Conventions and Definitions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

Aggregate result:: The output of the aggregation function over a given set of measurements and aggregation parameter. As defined in .
Aggregate share:: A share of the aggregate result emitted by an Aggregator. Aggregate shares are reassembled by the Collector into the aggregate result, which is the final output of the aggregation function. As defined in .
Aggregation function:: The function computed over the Clients' measurements. As defined in .
Aggregation parameter:: Parameter used to prepare a set of measurements for aggregation (e.g., the candidate prefixes for Poplar1 from ). As defined in .
Aggregator:: An endpoint that receives input shares from Clients and validates and aggregates them with the help of the other Aggregators.
Batch:: A set of reports that are aggregated into an aggregate result.
Batch duration:: The time difference between the oldest and newest report in a batch.
Batch interval:: A parameter of a query issued by the Collector that specifies the time range of the reports in the batch.
Client:: A party that uploads a report.
Collector:: The endpoint that selects the aggregation parameter and receives the aggregate result.
Helper:: An Aggregator that executes the aggregation and collection sub-protocols as instructed by the leader.
Input share:: An Aggregator's share of a measurement. The input shares are output by the VDAF sharding algorithm. As defined in .
Output share:: An aggregator's share of the prepared measurement resulting from successful execution of the VDAF preparation phase. Many output shares are combined into an aggregate share during the VDAF aggregation phase. As defined in .
Leader:: A distinguished Aggregator that coordinates aggregation and collection amongst the Aggregators.
Measurement:: A plaintext input emitted by a Client (e.g., a count, summand, or string), before any encryption or secret sharing is applied. Depending on the VDAF in use, multiple values may be grouped into a single measurement. As defined in .
Minimum batch size:: The minimum number of reports in a batch.
Public share:: The output of the VDAF sharding algorithm broadcast to each of the Aggregators. As defined in .
Report:: A cryptographically protected measurement uploaded to the Leader by a Client. Comprised of a set of report shares.
Report Share:: An encrypted input share comprising a piece of a report.

This document uses the presentation language of to define messages in the DAP protocol. Encoding and decoding of these messages as byte strings also follows .

Overview The protocol is executed by a large set of Clients and a small set of servers. Servers are referred to as "Aggregators". Each Client's input to the protocol is its measurement (or set of measurements, e.g., counts of some user behavior). Given the input set of measurements x_1, ..., x_n held by n users, the goal of DAP is to compute y = F(p, x_1, ..., x_n) for some function F while revealing nothing else about the measurements. We call F the "aggregation function". This protocol is extensible and allows for the addition of new cryptographic schemes that implement the VDAF interface specified in . Candidates include:

Prio3 (), which allows for aggregate statistics such as sum, mean, histograms, etc.
Poplar1 (), which allows for finding the most popular strings uploaded by a set of Clients (e.g., the URL of their home page) as well as counting the number of Clients that hold a given string. This VDAF is the basis of the Poplar protocol of , which is designed to solve the heavy hitters problem in a privacy preserving manner.

VDAFs rely on secret sharing to protect the privacy of the measurements. Rather than sending its input in the clear, each client shards its measurements into a sequence of "input shares" and sends an input share to each of the Aggregators. This provides two important properties:

Given only a subset of the input shares, it is impossible to deduce the plaintext measurement from which they were generated.
It allows the Aggregators to compute the aggregation function by first aggregating up their input shares locally into "aggregate shares", then combining the aggregate shares into the aggregate result.

System Architecture The overall system architecture is shown in .

System Architecture | | | | Client +----------> Leader <---------> Collector | | | +-----> | | | +--------+ | +-----^------+ +-----------+ | | +--------+ | | | | | | | Client +----+ +-----V------+ | | | | +--------+ | Helper | | | +------------+ ]]> [[OPEN ISSUE: This shows two helpers, but the document only allows one for now. https://github.com/ietf-wg-ppm/draft-ietf-ppm-dap/issues/117]] The main participants in the protocol are as follows:

Collector:: The entity which wants to obtain the aggregate of the measurements generated by the Clients. Any given measurement task will have a single Collector.
Client(s):: The endpoints which directly take the measurement(s) and report them to the DAP protocol. In order to provide reasonable levels of privacy, there must be a large number of clients.
Aggregator:: An endpoint which receives report shares. Each Aggregator works with the other Aggregators to compute the aggregate result. This protocol defines two types of Aggregators: Leaders and Helpers. For each measurement task, there is a single Leader and Helper.
Leader:: The Aggregator responsible for coordinating the protocol. It receives the reports, splits them into report shares, and distributes the report shares to the Helpers, and orchestrates the process of computing the aggregate result as requested by the Collector.
Helper:: Helpers are responsible for executing the protocol as instructed by the Leader. The protocol is designed so that Helpers can be relatively lightweight, with most of the state held at the Leader.

The basic unit of DAP is the "task" which represents a single measurement process (though potentially taken over multiple time windows). The definition of a task includes the following parameters:

The type of each measurement.
The aggregation function to compute (e.g., sum, mean, etc.).
The set of Aggregators and necessary cryptographic keying material to use.
The VDAF to execute, which to some extent is dictated by the previous choices.
The minimum "batch size" of reports which can be aggregated.
The rate at which measurements can be taken, i.e., the "minimum batch duration".

These parameters are distributed out of band to the Clients and to the Aggregators. They are distributed by the Collector in some authenticated form. Each task is identified by a unique 32-byte ID which is used to refer to it in protocol messages. During the duration of the task, each Client records its own measurement value(s), packages them up into a report, and sends them to the leader. Each share is separately encrypted for each Aggregator so that even though they pass through the Leader, the Leader is unable to see or modify them. Depending on the task, the Client may only send one report or may send many reports over time. The Leader distributes the shares to the Helpers and orchestrates the process of verifying them (see ) and assembling them into a final aggregate result for the Collector. Depending on the VDAF, it may be possible to incrementally process each report as it comes in, or may be necessary to wait until the entire batch of reports is received.

Validating Inputs An essential task of any data collection pipeline is ensuring that the data being aggregated is "valid". In DAP, input validation is complicated by the fact that none of the entities other than the Client ever sees that client's plaintext measurement. In order to address this problem, the aggregators engage in a secure, multi-party computation specified by the chosen VDAF in order to prepare a report for aggregation. At the beginning of this computation, each Aggregator is in possession of an input share uploaded by the client. At the end of the computation, each Aggregator is in possession of either an "output share" that is ready to be aggregated or an indication that a valid output share could not be computed. To facilitate this computation, the input shares generated by the client include information used by the aggregators during aggregation in order to validate their corresponding output shares. For example, Prio3 includes a distributed zero-knowledge proof of the input's validity which the Aggregators can jointly verify and reject the report if it cannot be verified. However, they do not learn anything about the individual report other than that it is valid. The specific properties attested to in the proof vary depending on the measurement being taken. For instance, to measure the time the user took performing a given task the proof might demonstrate that the value reported was within a certain range (e.g., 0-60 seconds). By contrast, to report which of a set of N options the user select, the report might contain N integers and the proof would demonstrate that N-1 were 0 and the other was 1. It is important to recognize that "validity" is distinct from "correctness". For instance, the user might have spent 30s on a task but the client might report 60s. This is a problem with any measurement system and DAP does not attempt to address it; it merely ensures that the data is within acceptable limits, so the client could not report 10^6s or -20s.

Message Transport Communications between DAP participants are carried over HTTPS . HTTPS provides server authentication and confidentiality. Use of HTTPS is REQUIRED.

HTTPS Request Authentication DAP is made up of several sub-protocols in which different subsets of the protocol's participants interact with each other. In those cases where a channel between two participants is tunneled through another protocol participant, DAP mandates the use of public-key encryption using to ensure that only the intended recipient can see a message in the clear. In other cases, DAP requires HTTPS client authentication. Any authentication scheme that is composable with HTTP is allowed. For example:

credentials are presented in an Authorization HTTP header, which can be added to any DAP protocol message.
TLS client certificates can be used to authenticate the underlying transport.

This flexibility allows organizations deploying DAP to use existing well-known HTTP authentication mechanisms that they already support. Discovering what authentication mechanisms are supported by a DAP participant is outside of this document's scope.

Errors Errors can be reported in DAP both at the HTTP layer and within challenge objects as defined in . DAP servers can return responses with an HTTP error response code (4XX or 5XX). For example, if the client submits a request using a method not allowed in this document, then the server MAY return HTTP status code 405 Method Not Allowed. When the server responds with an error status, it SHOULD provide additional information using a problem document . To facilitate automatic response to errors, this document defines the following standard tokens for use in the "type" field (within the DAP URN namespace "urn:ietf:params:ppm:dap:error:"):

Type	Description
unrecognizedMessage	The message type for a response was incorrect or the payload was malformed.
unrecognizedTask	An endpoint received a message with an unknown task ID.
unrecognizedAggregationJob	An endpoint received a message with an unknown aggregation job ID.
outdatedConfig	The message was generated using an outdated configuration.
reportRejected	Report could not be processed for an unspecified reason.
reportTooEarly	Report could not be processed because its timestamp is too far in the future.
batchInvalid	The batch boundary check for collector's query failed.
invalidBatchSize	There are an invalid number of reports in the batch.
batchQueriedTooManyTimes	The maximum number of batch queries has been exceeded for one or more reports included in the batch.
batchMismatch	Aggregators disagree on the report shares that were aggregated in a batch.
unauthorizedRequest	Authentication of an HTTP request failed (see ).
missingTaskID	HPKE configuration was requested without specifying a task ID.
queryMismatch	Query type indicated by a message does not match the task's query type.
roundMismatch	The aggregators disagree on the current round of the VDAF preparation protocol.

This list is not exhaustive. The server MAY return errors set to a URI other than those defined above. Servers MUST NOT use the DAP URN namespace for errors not listed in the appropriate IANA registry (see ). The "detail" member of the Problem Details document includes additional diagnostic information. When the task ID is known (see ), the problem document SHOULD include an additional "taskid" member containing the ID encoded in Base 64 using the URL and filename safe alphabet with no padding defined in Sections and of . In the remainder of this document, the tokens in the table above are used to refer to error types, rather than the full URNs. For example, an "error of type 'unrecognizedMessage'" refers to an error document with "type" value "urn:ietf:params:ppm:dap:error:unrecognizedMessage". This document uses the verbs "abort" and "alert with [some error message]" to describe how protocol participants react to various error conditions. This implies HTTP status code 400 Bad Request unless explicitly specified otherwise.

Protocol Definition DAP has three major interactions which need to be defined:

Uploading reports from the Client to the Aggregators, specified in
Computing the results for a given measurement task, specified in
Collecting aggregated results, specified in

Each of these interactions is defined in terms of "resources". In this section we define these resources and the messages used to act on them. A resource's path is resolved relative to a server's endpoint to construct a resource URI. Resource paths are specified as templates like: {role} is one of the API endpoints in the task's aggregator_endpoints (see ). The remainder of the path is resolved relative to the endpoint. DAP resource identifiers are opaque byte strings, so any occurrence of {resource-id} in a URL template (e.g., {task-id} or {report-id}) MUST be expanded to the URL-safe, unpadded Base 64 representation of the corresponding resource identifier, as specified in Sections and of . The following are some basic type definitions used in other messages: ; uint64 Duration; /* Number of seconds elapsed between two instants */ uint64 Time; /* seconds elapsed since start of UNIX epoch */ /* An interval of time of length duration, where start is included and (start + duration) is excluded. */ struct { Time start; Duration duration; } Interval; /* An ID used to uniquely identify a report in the context of a DAP task. */ opaque ReportID[16]; /* The various roles in the DAP protocol. */ enum { collector(0), client(1), leader(2), helper(3), (255) } Role; /* Identifier for a server's HPKE configuration */ uint8 HpkeConfigId; /* An HPKE ciphertext. */ struct { HpkeConfigId config_id; /* config ID */ opaque enc<1..2^16-1>; /* encapsulated HPKE key */ opaque payload<1..2^32-1>; /* ciphertext */ } HpkeCiphertext; /* Represent a zero-length byte string. */ struct {} Empty; ]]> DAP uses the 16-byte ReportID as the nonce parameter for the VDAF measurement_to_input_shares and prep_init methods (see ). Thus for a VDAF to be compatible with DAP, it MUST specify a NONCE_SIZE of 16 bytes.

Queries Aggregated results are computed based on sets of reports, called "batches". The Collector influences which reports are used in a batch via a "query." The Aggregators use this query to carry out the aggregation flow and produce aggregate shares encrypted to the Collector. This document defines the following query types: The time_interval query type is described in ; the fixed_size query type is described in . Future specifications may introduce new query types as needed (see ). A query includes parameters used by the Aggregators to select a batch of reports specific to the given query type. A query is defined as follows: The parameters pertaining to each query type are described in one of the subsections below. The query is issued in-band as part of the collect sub-protocol (). Its content is determined by the "query type", which in turn is encoded by the "query configuration" configured out-of-band. All query types have the following configuration parameters in common:

min_batch_size - The smallest number of reports the batch is allowed to include. In a sense, this parameter controls the degree of privacy that will be obtained: The larger the minimum batch size, the higher degree of privacy. However, this ultimately depends on the application and the nature of the measurements and aggregation function.
time_precision - Clients use this value to truncate their report timestamps; see . Additional semantics may apply, depending on the query type. (See for details.)

The parameters pertaining to specific query types are described in the relevant subsection below.

Time-interval Queries The first query type, time_interval, is designed to support applications in which reports are collected over a long period of time. The Collector specifies a "batch interval" that determines the time range for reports included in the batch. For each report in the batch, the time at which that report was generated (see ) MUST fall within the batch interval specified by the Collector. Typically the Collector issues queries for which the batch intervals are continuous, monotonically increasing, and have the same duration. For example, the sequence of batch intervals (1659544000, 1000), (1659545000, 1000), (1659545000, 1000), (1659546000, 1000) satisfies these conditions. (The first element of the pair denotes the start of the batch interval and the second denotes the duration.) Of course, there are cases in which Collector may need to issue queries out-of-order. For example, a previous batch might need to be queried again with a different aggregation parameter (e.g, for Poplar1). In addition, the Collector may need to vary the duration to adjust to changing report upload rates.

Fixed-size Queries The fixed_size query type is used to support applications in which the Collector needs the ability to strictly control the sample size. This is particularly important for controlling the amount of noise added to reports by Clients (or added to aggregate shares by Aggregators) in order to achieve differential privacy. For this query type, the Aggregators group reports into arbitrary batches such that each batch has roughly the same number of reports. These batches are identified by opaque "batch IDs", allocated in an arbitrary fashion by the Leader. To get the aggregate of a batch, the Collector issues a query specifying the batch ID of interest (see ). The Collector may not know which batch ID it is interested in; in this case, it can also issue a query of type current_batch, which allows the Leader to select a recent batch to aggregate. The leader SHOULD select a batch which has not yet began collection. In addition to the minimum batch size common to all query types, the configuration includes a parameter max_batch_size that determines maximum number of reports per batch. Implementation note: The goal for the Aggregators is to aggregate precisely min_batch_size reports per batch. Doing so, however, may be challenging for Leader deployments in which multiple, independent nodes running the aggregate sub-protocol (see ) need to be coordinated. The maximum batch size is intended to allow room for error. Typically the difference between the minimum and maximum batch size will be a small fraction of the target batch size for each batch. [OPEN ISSUE: It may be feasible to require a fixed batch size, i.e., min_batch_size == max_batch_size. We should know better once we've had some implementation/deployment experience.]

Task Configuration Prior to the start of execution of the protocol, each participant must agree on the configuration for each task. A task is uniquely identified by its task ID: A TaskID is a globally unique sequence of bytes. It is RECOMMENDED that this be set to a random string output by a cryptographically secure pseudorandom number generator. Each task has the following parameters associated with it:

aggregator_endpoints: A list of URLs relative to which each Aggregator's API endpoints can be found. Each endpoint's list MUST be in the same order. The Leader's endpoint MUST be the first in the list. The order of the encrypted_input_shares in a Report (see ) MUST be the same as the order in which aggregators appear in this list.
The query configuration for this task (see ). This determines the query type for batch selection and the properties that all batches for this task must have.
max_batch_query_count: The maximum number of times a batch of reports may be queried by the Collector.
task_expiration: The time up to which clients are expected to upload to this task. The task is considered completed after this time. Aggregators MAY reject reports that have timestamps later than task_expiration.
A unique identifier for the VDAF in use for the task, e.g., one of the VDAFs defined in .

In addition, in order to facilitate the aggregation and collect protocols, each of the Aggregators is configured with following parameters:

collector_config: The configuration of the Collector (described in ); see for information about the HPKE configuration algorithms.
vdaf_verify_key: The VDAF verification key shared by the Aggregators. This key is used in the aggregation sub-protocol (). The security requirements are described in .

Finally, the Collector is configured with the HPKE secret key corresponding to collector_hpke_config.

Uploading Reports Clients periodically upload reports to the Leader, which then distributes the individual report shares to each Helper.

HPKE Configuration Request Before the Client can upload its report to the Leader, it must know the HPKE configuration of each Aggregator. See for information on HPKE algorithm choices. Clients retrieve the HPKE configuration from each aggregator by sending an HTTP GET request to {aggregator}/hpke_config. Clients MAY specify a query parameter task_id whose value is the task ID whose HPKE configuration they want. If the Aggregator does not recognize the task ID, then it MUST abort with error unrecognizedTask. An Aggregator is free to use different HPKE configurations for each task with which it is configured. If the task ID is missing from the Client's request, the Aggregator MAY abort with an error of type missingTaskID, in which case the Client SHOULD retry the request with a well-formed task ID included. An Aggregator responds to well-formed requests with HTTP status code 200 OK and an HpkeConfigList value. The HpkeConfigList structure contains one or more HpkeConfig structures in decreasing order of preference. This allows an Aggregator to support multiple HPKE configurations simultaneously. [TODO: Allow aggregators to return HTTP status code 403 Forbidden in deployments that use authentication to avoid leaking information about which tasks exist.] ; struct { HpkeConfigId id; HpkeKemId kem_id; HpkeKdfId kdf_id; HpkeAeadId aead_id; HpkePublicKey public_key; } HpkeConfig; opaque HpkePublicKey<1..2^16-1>; uint16 HpkeAeadId; /* Defined in [HPKE] */ uint16 HpkeKemId; /* Defined in [HPKE] */ uint16 HpkeKdfId; /* Defined in [HPKE] */ ]]> [OPEN ISSUE: Decide whether to expand the width of the id.] Aggregators SHOULD allocate distinct id values for each HpkeConfig in a HpkeConfigList. The RECOMMENDED strategy for generating these values is via rejection sampling, i.e., to randomly select an id value repeatedly until it does not match any known HpkeConfig. The Client MUST abort if any of the following happen for any HPKE config request:

the GET request failed or did not return a valid HPKE config list;
the HPKE config list is empty; or
no HPKE config advertised by the aggregator specifies a supported a KEM, KDF, or AEAD algorithm triple.

Aggregators SHOULD use HTTP caching to permit client-side caching of this resource . Aggregators SHOULD favor long cache lifetimes to avoid frequent cache revalidation, e.g., on the order of days. Aggregators can control this cached lifetime with the Cache-Control header, as follows: Clients SHOULD follow the usual HTTP caching semantics for HPKE configurations. Note: Long cache lifetimes may result in clients using stale HPKE configurations; Aggregators SHOULD continue to accept reports with old keys for at least twice the cache lifetime in order to avoid rejecting reports.

Upload Request Clients upload reports by using an HTTP PUT to {leader}/tasks/{task-id}/reports, where {leader} is the first entry in the task's Aggregator endpoints. The payload is structured as follows: ; HpkeCiphertext encrypted_input_shares<1..2^32-1>; } Report; ]]>

report_metadata is public metadata describing the report.
- report_id is used by the Aggregators to ensure the report appears in at most one batch (see ). The Client MUST generate this by generating 16 random bytes using a cryptographically secure random number generator.
- time is the time at which the report was generated. The Client SHOULD round this value down to the nearest multiple of the task's time_precision in order to ensure that that the timestamp cannot be used to link a report back to the Client that generated it.
public_share is the public share output by the VDAF sharding algorithm. Note that the public share might be empty, depending on the VDAF.
encrypted_input_shares is the sequence of input shares encrypted to each of the Aggregators.

To generate a report, the Client begins by sharding its measurement into input shares and the public share using the VDAF's sharding algorithm (), using the report ID as the nonce: The last input comprises the randomness consumed by the sharding algorithm. The sharding randomness is a random byte string of length specified by the VDAF. The Client MUST generate this using a cryptographically secure random number generator. The Client then wraps each input share in the following structure: ; opaque payload<0..2^32-1>; } PlaintextInputShare; ]]> Field extensions is set to the list of extensions intended to be consumed by the given Aggregator. (See .) Field payload is set to the Aggregator's input share output by the VDAF sharding algorithm. Next, the Client encrypts each PlaintextInputShare plaintext_input_share as follows: where pk is the Aggregator's public key; server_role is the Role of the intended recipient (0x02 for the Leader and 0x03 for the Helper), plaintext_input_share is the Aggregator's PlaintextInputShare, and input_share_aad is an encoded message of type InputShareAad defined below, constructed from the same values as the corresponding fields in the report. The SealBase() function is as specified in for the ciphersuite indicated by the HPKE configuration. ; } InputShareAad; ]]> The order of the encrypted input shares appear MUST match the order of the task's aggregator_endpoints. That is, the first share should be the Leader's, the second share should be for the first Helper, and so on. The Leader responds to well-formed requests with HTTP status code 201 Created. Malformed requests are handled as described in . Clients SHOULD NOT upload the same measurement value in more than one report if the Leader responds with HTTP status code 201 Created. If the leader does not recognize the task ID, then it MUST abort with error unrecognizedTask. The Leader responds to requests whose leader encrypted input share uses an out-of-date or unknown HpkeConfig.id value, indicated by HpkeCiphertext.config_id, with error of type 'outdatedConfig'. If the leader supports multiple HPKE configurations, it can use trial decryption with each configuration to determine if requests match a known HPKE configuration. When the Client receives an 'outdatedConfig' error, it SHOULD invalidate any cached HpkeConfigList and retry with a freshly generated Report. If this retried upload does not succeed, the Client SHOULD abort and discontinue retrying. If a report's ID matches that of a previously uploaded report, the Leader MUST ignore it. In addition, it MAY alert the client with error reportRejected. See the implementation note in . The Leader MUST ignore any report pertaining to a batch that has already been collected (see for details). Otherwise, comparing the aggregate result to the previous aggregate result may result in a privacy violation. Note that this is enforced by all Aggregators, not just the Leader. The Leader MAY also abort the upload protocol and alert the client with error reportRejected. The Leader MAY ignore any report whose timestamp is past the task's task_expiration. When it does so, it SHOULD also abort the upload protocol and alert the Client with error reportRejected. Client MAY choose to opt out of the task if its own clock has passed task_expiration. The Leader may need to buffer reports while waiting to aggregate them (e.g., while waiting for an aggregation parameter from the Collector; see ). The Leader SHOULD NOT accept reports whose timestamps are too far in the future. Implementors MAY provide for some small leeway, usually no more than a few minutes, to account for clock skew. If the Leader rejects a report for this reason, it SHOULD abort the upload protocol and alert the Client with error reportTooEarly. In this situation, the Client MAY re-upload the report later on. If the Leader's ReportShare contains an unrecognized extension, or if two extensions have the same ExtensionType, then the Leader MAY abort the upload request with error "unrecognizedMessage". Note that this behavior is not mandatory because it requires the Leader to decrypt its ReportShare.

Upload Extensions Each PlaintextInputShare carries a list of extensions that Clients use to convey additional information to the Aggregator. Some extensions might be intended for all Aggregators; others may only be intended for a specific Aggregator. (For example, a DAP deployment might use some out-of-band mechanism for an Aggregator to verify that Reports come from authenticated Clients. It will likely be useful to bind the extension to the input share via HPKE encryption.) Each extension is a tag-length encoded value of the following form: ; } Extension; enum { TBD(0), (65535) } ExtensionType; ]]> Field "extension_type" indicates the type of extension, and "extension_data" contains information specific to the extension. Extensions are mandatory-to-implement: If an Aggregator receives a Report containing an extension it does not recognize, then it MUST reject the Report. (See for details.)

Upload Message Security The contents of each input share must be kept confidential from everyone but the Client and the Aggregator it is being sent to. In addition, Clients must be able to authenticate the Aggregator they upload to. HTTPS provides confidentiality between the DAP client and the leader, but this is not sufficient since the helper's report shares are relayed through the leader. Confidentiality of report shares is achieved by encrypting each report share to a public key held by the respective aggregator using . Clients fetch the public keys from each aggregator over HTTPS, allowing them to authenticate the server. Aggregators MAY require clients to authenticate when uploading reports. This is an effective mitigation against Sybil attacks in deployments where it is practical for each Client to have an identity provisioned (e.g., a user logged into an online service or a hardware device programmed with an identity). If it is used, Client authentication MUST use a scheme that meets the requirements in . In some deployments, it will not be practical to require Clients to authenticate (e.g., a widely distributed application that does not require its users to login to any service), so Client authentication is not mandatory in DAP. [[OPEN ISSUE: deployments that don't have client auth will need to do something about Sybil attacks. Is there any useful guidance or SHOULD we can provide? Sort of relevant: issue #89]]

Verifying and Aggregating Reports Once a set of Clients have uploaded their reports to the Leader, the Leader can begin the process of verifying and aggregating them with the Helpers. To enable the system to handle very large batches of reports, this process can be parallelized across smaller sets of reports. Verification of a set of reports is referred to as an "aggregation job". Each aggregation job is associated with exactly one DAP task, and a DAP task can have many aggregation jobs. Each job is associated with an ID that is unique within the context of a DAP task in order to distinguish different jobs from one another. Each aggregator uses this ID as an index into per-job storage, e.g., to keep track of report shares that belong to a given aggregation job. To run an aggregation job, the Leader sends a request to each Helper containing the report shares in the job. Each Helper then processes them (verifying the proofs and incorporating their values into the ongoing aggregate) and responds to the Leader. The exact structure of the aggregation job flow depends on the VDAF. Specifically:

Some VDAFs (e.g., Prio3) allow the leader to start aggregating reports proactively before all the reports in a batch are received. Others (e.g., Poplar1) require all the reports to be present and must be initiated by the collector.
Processing the reports -- especially validating them -- may require multiple round trips.

Note that it is possible to aggregate reports from one batch while reports from the next batch are coming in. This is because each report is validated independently. This process is illustrated below in . In this example, the batch size is 20, but the Leader opts to process the reports in sub-batches of 10. Each sub-batch takes two round-trips to process.

Aggregation Flow (batch size=20). Multiple aggregation flows can be executed at the same time. \ <----------------------------- Aggregate response (Job = N) | Reports Aggregate request (continued, Job = N) ------------------> | 1-10 <----------------------------- Aggregate response (Job = N) / Aggregate request (Reports 11-20, Job = M) --------------> \ <----------------------------- Aggregate response (Job = M) | Reports Aggregate request (continued, Job = M) ------------------> | 11-20 <----------------------------- Aggregate response (Job = M) / ]]> The aggregation flow can be thought of as having three phases for transforming each valid input report share into an output share:

Initialization: Begin the aggregation flow by sharing report shares with each Helper. Each Aggregator, including the Leader, initializes the underlying VDAF instance using these report shares and the VDAF configured for the corresponding measurement task.
Continuation: Continue the aggregation flow by exchanging messages produced by the underlying VDAF instance until aggregation completes or an error occurs. These messages do not replay the shares.
Completion: Finish the aggregate flow, yielding an output share corresponding for each input report share in the batch.

Aggregate Initialization The Leader begins an aggregation job by choosing a set of candidate reports that pertain to the same DAP task and a unique job ID. The job ID is a 16-byte value, structured as follows: The leader can run this process for many sets of candidate reports in parallel as needed. After choosing a set of candidates, the leader begins aggregation by splitting each report into report shares, one for each Aggregator. The Leader and Helpers then run the aggregate initialization flow to accomplish two tasks:

Recover and determine which input report shares are invalid.
For each valid report share, initialize the VDAF preparation process (see ).

An invalid report share is marked with one of the following errors: The Leader and Helper initialization behavior is detailed below.

Leader Initialization The Leader begins the aggregate initialization phase with the set of candidate report shares as follows:

Generate a fresh AggregationJobID. This ID MUST be unique within the context of the corresponding DAP task. It is RECOMMENDED that this be set to a random string output by a cryptographically secure pseudorandom number generator.
Decrypt the input share for each report share as described in .
Check that the resulting input share is valid as described in .
Initialize VDAF preparation as described in .

If any step invalidates the report share, the Leader removes the report share from the set of candidate reports. Once the leader has initialized this state for all valid candidate report shares, it creates an AggregationJobInitReq message for each Helper to initialize the preparation of this candidate set. The AggregationJobInitReq message is structured as follows: ; HpkeCiphertext encrypted_input_share; } ReportShare; struct { QueryType query_type; select (PartialBatchSelector.query_type) { case time_interval: Empty; case fixed_size: BatchID batch_id; }; } PartialBatchSelector; struct { opaque agg_param<0..2^32-1>; PartialBatchSelector part_batch_selector; ReportShare report_shares<1..2^32-1>; } AggregationJobInitReq; ]]> [[OPEN ISSUE: Consider sending report shares separately (in parallel) to the aggregate instructions. Right now, aggregation parameters and the corresponding report shares are sent at the same time, but this may not be strictly necessary.]] This message consists of:

agg_param: The opaque, VDAF-specific aggregation parameter provided during the collection flow (),
part_batch_selector: The "partial batch selector" used by the Aggregators to determine how to aggregate each report:
- For fixed_size tasks, the Leader specifies a "batch ID" that determines the batch to which each report for this aggregation job belongs. [OPEN ISSUE: For fixed_size tasks, the Leader is in complete control over which batch a report is included in. For time_interval tasks, the Client has some control, since the timestamp determines which batch window it falls in. Is this desirable from a privacy perspective? If not, it might be simpler to drop the timestamp altogether and have the agg init request specify the batch window instead.]
The indicated query type MUST match the task's query type. Otherwise, the Helper MUST abort with error "queryMismatch". This field is called the "partial" batch selector because, depending on the query type, it may not determine a batch. In particular, if the query type is time_interval, the batch is not determined until the Collector's query is issued (see ).
report_shares: The sequence of report shares to aggregate. The encrypted_input_share field of the report share is the HpkeCiphertext whose index in Report.encrypted_input_shares is equal to the index of the aggregator in the task's aggregator_endpoints to which the AggregationJobInitReq is being sent.

Let {aggregator} denote the Helper's API endpoint. The Leader sends a PUT request to {aggregator}/tasks/{task-id}/aggregation_jobs/{aggregation-job-id} with its AggregationJobInitReq message as the payload. The media type is "application/dap-aggregation-job-init-req". The Leader's aggregation job is now in round 0. The Helper's response will be an AggregationJobResp message (see , which the Leader validates according to the criteria in . If the message is valid, the Leader moves to the aggregation job continuation phase with the enclosed prepare steps, as described in . Otherwise, the Leader should abandon the aggregation job entirely.

Helper Initialization Each Helper begins their portion of the aggregate initialization when they receive an AggregationJobInitReq message from the Leader. For each ReportShare conveyed by this message, the Helper attempts to initialize VDAF preparation (see ) just as the Leader does. If successful, it includes its prepare message in its response that the Leader will use to continue the process. To begin this process, the Helper first checks if it recognizes the task ID. If not, then it MUST abort with error unrecognizedTask. Then the Helper checks that the report IDs in AggregationJobInitReq.report_shares are all distinct. If two ReportShare values have the same report ID, then the helper MUST abort with error unrecognizedMessage. If this check succeeds, the helper then attempts to recover each input share in AggregationJobInitReq.report_shares as follows:

Decrypt the input share for each report share as described in .
Check that the resulting input share is valid as described in .
Initialize VDAF preparation and initial outputs as described in .

Once the Helper has processed each report share in AggregationJobInitReq.report_shares, the Helper creates an AggregationJobResp message to complete its initialization. This message is structured as follows: ; /* VDAF preparation message */ case finished: Empty; case failed: ReportShareError; }; } PrepareStep; struct { PrepareStep prepare_steps<1..2^32-1>; } AggregationJobResp; ]]> The message is a sequence of PrepareStep values, the order of which matches that of the ReportShare values in AggregationJobInitReq.report_shares. Each report that was marked as invalid is assigned the PrepareStepState failed. Otherwise, the PrepareStep is either marked as continued with the output prep_msg, or is marked as finished if the VDAF preparation process is finished for the report share. The Helper's aggregation job is now in round 0. On success, the Helper responds to the Leader with HTTP status code 201 Created and a body consisting of the AggregationJobResp, with media type "application/dap-aggregation-job-resp".

Input Share Decryption Each report share has a corresponding task ID, report metadata (report ID and, timestamp), the public share sent to each Aggregator, and the recipient's encrypted input share. Let task_id, report_metadata, public_share, and encrypted_input_share denote these values, respectively. Given these values, an aggregator decrypts the input share as follows. First, it constructs an InputShareAad message from task_id, report_metadata, and public_share. Let this be denoted by input_share_aad. Then, the aggregator looks up the HPKE config and corresponding secret key indicated by encrypted_input_share.config_id and attempts decryption of the payload with the following procedure: where sk is the HPKE secret key, and server_role is the role of the aggregator (0x02 for the leader and 0x03 for the helper). The OpenBase() function is as specified in for the ciphersuite indicated by the HPKE configuration. If the leader supports multiple HPKE configurations with non-distinct configuration identifiers, it can use trial decryption with each configuration. If decryption fails, the aggregator marks the report share as invalid with the error hpke_decrypt_error. Otherwise, the aggregator outputs the resulting PlaintextInputShare plaintext_input_share.

Input Share Validation Validating an input share will either succeed or fail. In the case of failure, the input share is marked as invalid with a corresponding ReportShareError error. Before beginning the preparation step, Aggregators are required to perform the following checks:

Check that the input share can be decoded as specified by the VDAF. If not, the input share MUST be marked as invalid with the error unrecognized_message.
Check if the report is too far into the future. Implementors can provide for some small leeway, usually no more than a few minutes, to account for clock skew. If a report is rejected for this reason, the Aggregator SHOULD mark the input share as invalid with the error report_too_early.
Check if the report's timestamp has passed the task's task_expiration time. If so, the Aggregator MAY mark the input share as invalid with the error "task_expired".
Check if the PlaintextInputShare contains unrecognized extensions. If so, the Aggregator MUST mark the input share as invalid with error "unrecognized_message".
Check if the ExtensionType of any two extensions in PlaintextInputShare are the same. If so, the Aggregator MUST mark the input share as invalid with error "unrecognized_message".
Check if the report may still be aggregated with the current aggregation parameter. This can be done by looking up all aggregation parameters previously used for this report and calling If this returns false, the input share MUST be marked as invalid with the error report_replayed.
- Implementation note: To detect replay attacks, each Aggregator is required to keep track of the set of reports it has processed for a given task. Because honest Clients choose the report ID at random, it is sufficient to store the set of IDs of processed reports. However, implementations may find it helpful to track additional information, like the timestamp, so that the storage used for anti-replay can be sharded efficiently.
If the report pertains to a batch that was previously collected, then make sure the report was already included in all previous collections for the batch. If not, the input share MUST be marked as invalid with error "batch_collected". This prevents Collectors from learning anything about small numbers of reports that are uploaded between two collections of a batch.
- Implementation note: The Leader considers a batch to be collected once it has completed a collection job for a CollectionReq message from the Collector; the Helper considers a batch to be collected once it has responded to an AggregateShareReq message from the Leader. A batches is determined by query () conveyed in these messages. Queries must satisfy the criteria covered in . These criteria are meant to restrict queries in a way make it easy to determine wither a report pertains to a batch that was collected. [TODO: If a section to clarify report and batch states is added this can be removed. See Issue #384]
Depending on the query type for the task, additional checks may be applicable:
- For fixed_size tasks, the Aggregators need to ensure that each batch is roughly the same size. If the number of reports aggregated for the current batch exceeds the maximum batch size (per the task configuration), the Aggregator MAY mark the input share as invalid with the error "batch_saturated". Note that this behavior is not strictly enforced here but during the collect sub-protocol. (See .) If both checks succeed, the input share is not marked as invalid.
Finally, if an Aggregator cannot determine if an input share is valid, it MUST mark the input share as invalid with error report_dropped. For example, if the Aggregator has evicted the state required to perform the check from long-term storage. (See for details.)

If all of the above checks succeed, the input share is not marked as invalid.

Input Share Preparation Input share preparation consists of running the preparation-state initialization algorithm for the VDAF associated with the task and computing the first state transition. This produces three possible values:

An error, in which case the input report share is marked as invalid.
An output share, in which case the aggregator stores the output share for future collection as described in .
An initial VDAF state and preparation message-share, denoted (prep_state, prep_share).

Each aggregator runs this procedure for a given input share with corresponding report ID as follows: vdaf_verify_key is the VDAF verification key shared by the Aggregators; agg_id is the aggregator ID (0x00 for the Leader and 0x01 for the helper); agg_param is the opaque aggregation parameter distributed to the Aggregators by the Collector; public_share is the public share generated by the client and distributed to each aggregator; and plaintext_input_share is the Aggregator's PlaintextInputShare. If either step fails, the Aggregator marks the report as invalid with error vdaf_prep_error. Otherwise, the value out is interpreted as follows. If this is the last round of the VDAF, then out is the aggregator's output share. Otherwise, out is the pair (prep_state, prep_share).

Aggregation Job Validation During the aggregation job initialization () or continuation () phases, the Leader will receive an AggregationJobResp message from the Helper, which needs to be validated before the Leader can move to the next phase of the aggregation protocol. An AggregationJobResp is valid only if it satisfies the following requirement:

The Helper's prepare_steps MUST include exactly the same report IDs in the same order as either the report_shares in the Leader's AggregationJobInitReq (if this is the first round of continuation) or the prepare_steps in the Leader's AggregationJobContinueReq (if this is a subsequent round).

[[OPEN ISSUE: consider relaxing this ordering constraint. See issue#217.]]

Aggregate Continuation In the continuation phase, the leader drives the VDAF preparation of each share in the candidate report set until the underlying VDAF moves into a terminal state, yielding an output share for all Aggregators or an error. This phase may involve multiple rounds of interaction depending on the underlying VDAF. Each round trip is initiated by the leader.

Leader Continuation The Leader begins each round of continuation for a report share based on its locally computed prepare message and the previous PrepareStep from the Helper. If PrepareStep is of type failed, then the leader acts based on the value of the ReportShareError:

If the error is ReportShareError.report_too_early, then the leader MAY try to re-send the report in a later AggregationJobInitReq.
For any other error, the leader marks the report as failed, removes it from the candidate report set and does not process it further.

If the type is finished and the Leader's preparation of this report share is also finished, then the report share is aggregated and can now be collected (see ). If the Leader is not finished, then the report cannot be processed further and MUST be removed from the candidate set. If the Helper's PrepareStep is of type continued, then the Leader proceeds as follows. Let leader_prep_share denote the Leader's prepare message-share and helper_prep_share denote the Helper's. The Leader computes the next state transition as follows: where [leader_prep_share, helper_prep_share] is a vector of two elements. If either of these operations fails, then the leader marks the report as invalid with error "prep_share_failed". Otherwise it interprets out as follows: If this is the last round of the VDAF, then out is the Leader's output share, in which case it stores the output share for further processing as described in . Otherwise, out is the pair (next_prep_state, next_prep_share), where next_prep_state is its updated state and next_prep_share is its next preparation message-share (which will be leader_prep_share in the next round of continuation). For the latter case, the helper sets prep_state to next_prep_state. The Leader now advances its aggregation job to the next round (round 1 if this is the first continuation after initialization) and then instructs the Helper to advance the aggregation job to the round the Leader has just reached by sending the new prep_msg message to the Helper in a POST request to the aggregation job URI used during initialization (see ). The body of the request is an AggregationJobContinueReq: ; } AggregationJobContinueReq; ]]> The round field is the round of VDAF preparation that the Leader just reached and wants the Helper to advance to. The prepare_steps field MUST be a sequence of PrepareSteps in the continued state containing the corresponding inbound prepare message. The media type is set to "application/dap-aggregation-job-continue-req". The Helper's response will be an AggregationJobResp message (see ), which the Leader validates according to the criteria in . If the message is valid, the Leader moves to the next round of continuation with the enclosed prepare steps. Otherwise, the Leader should abandon the aggregation job entirely.

Helper Continuation If the Helper does not recognize the task ID, then it MUST abort with error unrecognizedTask. Otherwise, the Helper continues with preparation for a report share by combining the previous message round's prepare message (carried by the AggregationJobReq) and its current preparation state (prep_state). This step yields one of three outputs:

An error, in which case the report share is marked as invalid.
An output share, in which case the helper stores the output share for future collection as described in .
Its next VDAF preparation state and message-share, denoted (next_prep_state, next_prep_share).

To carry out this step, for each PrepareStep in AggregationJob.prepare_steps received from the leader, the helper performs the following check to determine if it should continue preparing the report share:

If the status is failed, then mark the report as failed and reply with a failed PrepareStep to the Leader.
If the status is finished, then mark the report as finished and reply with a finished PrepareStep to the leader. The Helper then stores the output share and awaits collection; see .

Otherwise, preparation continues. The Helper MUST check its current round against the Leader's AggregationJobContinueReq.round value. If the Leader is one round ahead of the Helper, then the Helper combines the Leader's prepare message and the Helper's current preparation state as follows: where prep_msg is the previous VDAF prepare message sent by the leader and prep_state is the helper's current preparation state. This step yields one of three outputs:

An error, in which case the report share is marked as failed and the Helper replies to the Leader with a PrepareStep in the failed state.
An output share, in which case the Helper stores the output share for future collection as described in and replies to the Leader with a PrepareStep in the finished state.
An updated VDAF state and preparation message-share, denoted (next_prep_state, next_prep_msg), in which case the Helper replies to the Leader with a PrepareStep in the continued state containing prep_share.

After stepping each state, the Helper advances its aggregation job to the Leader's AggregationJobContinueReq.round. If the round in the Leader's request is 0, then the Helper MUST abort with an error of type unrecognizedMessage. If the round in the Leader's request is equal to the Helper's current round (i.e., this is not the first time the Leader has sent this request), then the Helper responds with the current round's prepare message-shares. The Helper SHOULD verify that the contents of the AggregationJobContinueReq are identical to the previous message (see ). If the Leader's round is behind or more than one round ahead of the Helper's current round, then the Helper MUST abort with an error of type roundMismatch. If successful, the Helper responds to the Leader with HTTP status 200 OK, media type application/dap-aggregation-job-resp and a body consisting of an AggregationJobResp (see ) compiled from the stepped PrepareSteps.

Recovering From Round Skew AggregationJobContinueReq messages contain a round field, allowing Aggregators to ensure that their peer is on an expected round of the VDAF preparation algorithm. In particular, the intent is to allow recovery from a scenario where the Helper successfully advances from round n to n+1, but its AggregationJobResp response to the Leader gets dropped due to something like a transient network failure. The Leader could then resend the request to have the Helper advance to round n+1 and the Helper should be able to retransmit the AggregationJobContinueReq that was previously dropped. To make that kind of recovery possible, Aggregator implementations SHOULD checkpoint the most recent round's preparation state and messages to durable storage such that Leaders can re-construct continuation requests and Helpers can re-construct continuation responses as needed. When implementing a round skew recovery strategy, Helpers SHOULD ensure that the Leader's AggregationJobContinueReq message did not change when it was re-sent (i.e., the two messages must contain the same set of report IDs and prepare messages). This prevents the Leader from re-winding an aggregation job and re-running a round with different parameters. [[OPEN ISSUE: Allowing the Leader to "rewind" aggregation job state of the Helper may allow an attack on privacy. For instance, if the VDAF verification key changes, the preparation shares in the Helper's response would change even if the consistency check is made. Security analysis is required. See #401.]] One way a Helper could address this would be to store a digest of the Leader's request, indexed by aggregation job ID and round, and refuse to service a request for a given aggregation job round unless it matches the previously seen request (if any).

Aggregate Message Security Aggregate sub-protocol messages must be confidential and mutually authenticated. The aggregate sub-protocol is driven by the leader acting as an HTTPS client, making requests to the helper's HTTPS server. HTTPS provides confidentiality and authenticates the helper to the leader. Leaders MUST authenticate their requests to helpers using a scheme that meets the requirements in .

Collecting Results In this phase, the Collector requests aggregate shares from each Aggregator and then locally combines them to yield a single aggregate result. In particular, the Collector issues a query to the Leader (), which the Aggregators use to select a batch of reports to aggregate. Each emits an aggregate share encrypted to the Collector so that it can decrypt and combine them to yield the aggregate result. This entire process is composed of two interactions:

Collect request and response between the collector and leader, specified in
Aggregate share request and response between the leader and each aggregator, specified in

Once complete, the collector computes the final aggregate result as specified in . This overall process is referred to as a "collection job".

Collection Job Initialization First, the Collector chooses a collection job ID: This ID MUST be unique within the context of the corresponding DAP task. It is RECOMMENDED that this be set to a random string output by a cryptographically secure pseudorandom number generator. To initiate the collection job, the collector issues a PUT request to {leader}/tasks/{task-id}/collection_jobs/{collection-job-id}. The body of the request is structured as follows: [OPEN ISSUE: Decide if and how the Collector's request is authenticated. If not, then we need to ensure that collection job URIs are resistant to enumeration attacks.] ; /* VDAF aggregation parameter */ } CollectionReq; ]]> The named parameters are:

query, the Collector's query. The indicated query type MUST match the task's query type. Otherwise, the Leader MUST abort with error "queryMismatch".
agg_param, an aggregation parameter for the VDAF being executed. This is the same value as in AggregationJobInitReq (see ).

Depending on the VDAF scheme and how the Leader is configured, the Leader and Helper may already have prepared a sufficient number of reports satisfying the query and be ready to return the aggregate shares right away. However, this is not always the case. In fact, for some VDAFs, it is not be possible to begin running aggregation jobs () until the Collector initiates a collection job. This is because, in general, the aggregation parameter is not known until this point. In certain situations it is possible to predict the aggregation parameter in advance. For example, for Prio3 the only valid aggregation parameter is the empty string. For these reasons, the collection job is handled asynchronously. Upon receipt of a CollectionReq, the Leader begins by checking that it recognizes the task ID in the request path. If not, it MUST abort with error unrecognizedTask. Then, the Leader verifies that the request meets the requirements of the batch parameters using the procedure in . If so, it immediately responds with HTTP status 201. The Leader then begins working with the Helper to aggregate the reports satisfying the query (or continues this process, depending on the VDAF) as described in . After receiving the response to its CollectionReq, the Collector makes an HTTP POST request to the collection job URI to check on the status of the collect job and eventually obtain the result. If the collection job is not finished yet, the Leader responds with HTTP status 202 Accepted. The response MAY include a Retry-After header field to suggest a polling interval to the Collector. The Leader obtains each Helper's aggregate share following the aggregate-share request flow described in . When all aggregate shares are successfully obtained, the Leader responds to subsequent HTTP POST requests to the collection job with HTTP status code 200 OK and a body consisting of a Collection: ; } Collection; ]]> This structure includes the following:

part_batch_selector: Information used to bind the aggregate result to the query. For fixed_size tasks, this includes the batch ID assigned to the batch by the Leader. The indicated query type MUST match the task's query type. [OPEN ISSUE: What should the Collector do if the query type doesn't match?]
The number of reports included in the batch.
The smallest interval of time that contains the timestamps of all reports included in the batch, such that the interval's start and duration are both multiples of the task's time_precision parameter. Note that in the case of a time_interval type query (see ), this interval can be smaller than the one in the corresponding CollectionReq.query.
The vector of encrypted aggregate shares. They MUST appear in the same order as the aggregator endpoints list of the task parameters.

If obtaining aggregate shares fails, then the leader responds to subsequent HTTP POST requests to the collection job with an HTTP error status and a problem document as described in . The Leader MAY respond with HTTP status 204 No Content to requests to a collection job if the results have been deleted. The collector can send an HTTP DELETE request to the collection job, which indicates to the leader that it can abandon the collection job and discard all state related to it.

A Note on Idempotence The reason we use a POST instead of a GET to poll the state of a collection job is because of the fixed-size query mode (see ). Collectors may make a query against the current batch, and it is the Leader's responsibility to keep track of what batch is current for some task. Polling a collection job is the only point at which it is safe for the Leader to change its current batch, since it constitutes acknowledgement on the Collector's part that it received the response to some previous PUT request to the collection jobs resource. This means that polling a collection job can have the side effect of changing the current batch in the Leader, and thus using a GET is inappropriate.

Obtaining Aggregate Shares The Leader obtains each Helper's encrypted aggregate share before it completes a collection job. To do this, the Leader first computes a checksum over the set of output shares included in the batch. The checksum is computed by taking the SHA256 hash of each report ID from the client reports included in the aggregation, then combining the hash values with a bitwise-XOR operation. Then, for each Aggregator endpoint {aggregator} in the parameters associated with CollectionReq.task_id (see ) except its own, the Leader sends a POST request to {aggregator}/tasks/{task-id}/aggregate_shares with the following message: ; uint64 report_count; opaque checksum[32]; } AggregateShareReq; ]]> The message contains the following parameters:

batch_selector: The "batch selector", which encodes parameters used to determine the batch being aggregated. The value depends on the query type for the task:
- For time_interval tasks, the request specifies the batch interval.
- For fixed_size tasks, the request specifies the batch ID.
The indicated query type MUST match the task's query type. Otherwise, the Helper MUST abort with "queryMismatch".
agg_param: The opaque aggregation parameter for the VDAF being executed. This value MUST match the AggregationJobInitReq message for each aggregation job used to compute the aggregate shares (see ) and the aggregation parameter indicated by the Collector in the CollectionReq message (see ).
report_count: The number number of reports included in the batch.
checksum: The batch checksum.

To handle the Leader's request, the Helper first ensures that it recognizes the task ID in the request path. If not, it MUST abort with error unrecognizedTask. The Helper then verifies that the request meets the requirements for batch parameters following the procedure in . Next, it computes a checksum based on the reports that satisfy the query, and checks that the report_count and checksum included in the request match its computed values. If not, then it MUST abort with an error of type "batchMismatch". Next, it computes the aggregate share agg_share corresponding to the set of output shares, denoted out_shares, for the batch interval, as follows: Implementation note: For most VDAFs, it is possible to aggregate output shares as they arrive rather than wait until the batch is collected. To do so however, it is necessary to enforce the batch parameters as described in so that the aggregator knows which aggregate share to update. The Helper then encrypts agg_share under the collector's HPKE public key as described in , yielding encrypted_agg_share. Encryption prevents the Leader from learning the actual result, as it only has its own aggregate share and cannot compute the Helper's. The Helper responds to the Leader with HTTP status code 200 OK and a body consisting of an AggregateShare: encrypted_aggregate_share.config_id is set to the Collector's HPKE config ID. encrypted_aggregate_share.enc is set to the encapsulated HPKE context enc computed above and encrypted_aggregate_share.ciphertext is the ciphertext encrypted_agg_share computed above. After receiving the Helper's response, the Leader uses the HpkeCiphertext to finalize a collection job (see ). Once an AggregateShareReq has been issued for the batch determined by a given query, it is an error for the Leader to issue any more aggregation jobs for additional reports that satisfy the query. These reports will be rejected by helpers as described . Before completing the collection job, the leader also computes its own aggregate share agg_share by aggregating all of the prepared output shares that fall within the batch interval. Finally, it encrypts it under the collector's HPKE public key as described in .

Collection Job Finalization Once the Collector has received a collection job from the leader, it can decrypt the aggregate shares and produce an aggregate result. The Collector decrypts each aggregate share as described in . Once the Collector successfully decrypts all aggregate shares, it unshards the aggregate shares into an aggregate result using the VDAF's agg_shares_to_result algorithm. In particular, let agg_shares denote the ordered sequence of aggregator shares, ordered by aggregator index, let report_count denote the report count sent by the Leader, and let agg_param be the opaque aggregation parameter. The final aggregate result is computed as follows:

Aggregate Share Encryption Encrypting an aggregate share agg_share for a given AggregateShareReq is done as follows: where pk is the HPKE public key encoded by the collector's HPKE key, server_role is 0x02 for the Leader and 0x03 for a Helper, and agg_share_aad is a value of type AggregateShareAad with its values set from the corresponding fields of the AggregateShareReq. The SealBase() function is as specified in for the ciphersuite indicated by the HPKE configuration. The Collector decrypts these aggregate shares using the opposite process. Specifically, given an encrypted input share, denoted enc_share, for a given batch selector, decryption works as follows: where sk is the HPKE secret key, server_role is the role of the server that sent the aggregate share (0x02 for the leader and 0x03 for the helper), and agg_share_aad is an AggregateShareAad message constructed from the task ID in the collect request and a batch selector. The value of the batch selector used in agg_share_aad is computed by the Collector from its query and the response to its query as follows:

For time_interval tasks, the batch selector is the batch interval specified in the query.
For fixed_size tasks, the batch selector is the batch ID assigned sent in the response.

The OpenBase() function is as specified in for the ciphersuite indicated by the HPKE configuration.

Collect Message Security Collect sub-protocol messages must be confidential and mutually authenticated. HTTPS provides confidentiality and authenticates the Leader to the Collector. Additionally, the Leader encrypts its aggregate share to a public key held by the Collector using . Collectors MUST authenticate their requests to Leaders using a scheme that meets the requirements in . [[OPEN ISSUE: collector public key is currently in the task parameters, but this will have to change #102]] The collector and helper never directly communicate with each other, but the helper does transmit an aggregate share to the collector through the leader, as detailed in . The aggregate share must be confidential from everyone but the helper and the collector. Confidentiality is achieved by having the helper encrypt its aggregate share to a public key held by the collector using . There is no authentication between the collector and the helper. This allows the leader to:

Send collect parameters to the helper that do not reflect the parameters chosen by the collector
Discard the aggregate share computed by the helper and then fabricate aggregate shares that combine into an arbitrary aggregate result

These are attacks on robustness, which we already assume to hold only if both aggregators are honest, which puts these malicious-leader attacks out of scope (see ). [[OPEN ISSUE: Should we have authentication in either direction between the helper and the collector? #155]]

Batch Validation Before an Aggregator responds to a CollectionReq or AggregateShareReq, it must first check that the request does not violate the parameters associated with the DAP task. It does so as described here. First the Aggregator checks that the batch respects any "boundaries" determined by the query type. These are described in the subsections below. If the boundary check fails, then the Aggregator MUST abort with an error of type "batchInvalid". Next, the Aggregator checks that batch contains a valid number of reports, as determined by the query type. If the size check fails, then the Aggregator MUST abort with error of type "invalidBatchSize". Next, the Aggregator checks that the batch has not been aggregated too many times. This is determined by the maximum number of times a batch can be queried, max_batch_query_count. Unless the query has been issued less than max_batch_query_count times, the Aggregator MUST abort with error of type "batchQueriedTooManyTimes". Finally, the Aggregator checks that the batch does not contain a report that was included in any previous batch. If this batch overlap check fails, then the Aggregator MUST abort with error of type "batchOverlap". For time_interval tasks, it is sufficient (but not necessary) to check that the batch interval does not overlap with the batch interval of any previous query. If this batch interval check fails, then the Aggregator MAY abort with error of type "batchOverlap". [[OPEN ISSUE: #195 tracks how we might relax this constraint to allow for more collect query flexibility. As of now, this is quite rigid and doesn't give the collector much room for mistakes.]]

Time-interval Queries

Boundary Check The batch boundaries are determined by the time_precision field of the query configuration. For the batch_interval included with the query, the Aggregator checks that:

batch_interval.duration >= time_precision (this field determines, effectively, the minimum batch duration)
both batch_interval.start and batch_interval.duration are divisible by time_precision

These measures ensure that Aggregators can efficiently "pre-aggregate" output shares recovered during the aggregation sub-protocol.

Size Check The query configuration specifies the minimum batch size, min_batch_size. The Aggregator checks that len(X) >= min_batch_size, where X is the set of reports in the batch.

Fixed-size Queries

Boundary Check For fixed_size tasks, the batch boundaries are defined by opaque batch IDs. Thus the Aggregator needs to check that the query is associated with a known batch ID:

For a CollectionReq containing a query of type by_batch_id, the Leader checks that the provided batch ID corresponds to a batch ID it returned in a previous Collection for the task.
For an AggregateShareReq, the Helper checks that the batch ID provided by the Leader corresponds to a batch ID used in a previous AggregationJobInitReq for the task.

Size Check The query configuration specifies the minimum batch size, min_batch_size, and maximum batch size, max_batch_size. The Aggregator checks that len(X) >= min_batch_size and len(X) <= max_batch_size, where X is the set of reports in the batch.

Operational Considerations The DAP protocol has inherent constraints derived from the tradeoff between privacy guarantees and computational complexity. These tradeoffs influence how applications may choose to utilize services implementing the specification.

Protocol participant capabilities The design in this document has different assumptions and requirements for different protocol participants, including clients, aggregators, and collectors. This section describes these capabilities in more detail.

Client capabilities Clients have limited capabilities and requirements. Their only inputs to the protocol are (1) the parameters configured out of band and (2) a measurement. Clients are not expected to store any state across any upload flows, nor are they required to implement any sort of report upload retry mechanism. By design, the protocol in this document is robust against individual client upload failures since the protocol output is an aggregate over all inputs.

Aggregator capabilities Helpers and leaders have different operational requirements. The design in this document assumes an operationally competent leader, i.e., one that has no storage or computation limitations or constraints, but only a modestly provisioned helper, i.e., one that has computation, bandwidth, and storage constraints. By design, leaders must be at least as capable as helpers, where helpers are generally required to:

Support the aggregate sub-protocol, which includes validating and aggregating reports; and
Publish and manage an HPKE configuration that can be used for the upload protocol.

In addition, for each DAP task, helpers are required to:

Implement some form of batch-to-report index, as well as inter- and intra-batch replay mitigation storage, which includes some way of tracking batch report size. Some of this state may be used for replay attack mitigation. The replay mitigation strategy is described in .

Beyond the minimal capabilities required of helpers, leaders are generally required to:

Support the upload protocol and store reports; and
Track batch report size during each collect flow and request encrypted output shares from helpers.

In addition, for each DAP task, leaders are required to:

Implement and store state for the form of inter- and intra-batch replay mitigation in .

Collector capabilities Collectors statefully interact with aggregators to produce an aggregate output. Their input to the protocol is the task parameters, configured out of band, which include the corresponding batch window and size. For each collect invocation, collectors are required to keep state from the start of the protocol to the end as needed to produce the final aggregate output. Collectors must also maintain state for the lifetime of each task, which includes key material associated with the HPKE key configuration.

Data resolution limitations Privacy comes at the cost of computational complexity. While affine-aggregatable encodings (AFEs) can compute many useful statistics, they require more bandwidth and CPU cycles to account for finite-field arithmetic during input-validation. The increased work from verifying inputs decreases the throughput of the system or the inputs processed per unit time. Throughput is related to the verification circuit's complexity and the available compute-time to each aggregator. Applications that utilize proofs with a large number of multiplication gates or a high frequency of inputs may need to limit inputs into the system to meet bandwidth or compute constraints. Some methods of overcoming these limitations include choosing a better representation for the data or introducing sampling into the data collection methodology. [[TODO: Discuss explicit key performance indicators, here or elsewhere.]]

Aggregation utility and soft batch deadlines A soft real-time system should produce a response within a deadline to be useful. This constraint may be relevant when the value of an aggregate decreases over time. A missed deadline can reduce an aggregate's utility but not necessarily cause failure in the system. An example of a soft real-time constraint is the expectation that input data can be verified and aggregated in a period equal to data collection, given some computational budget. Meeting these deadlines will require efficient implementations of the input-validation protocol. Applications might batch requests or utilize more efficient serialization to improve throughput. Some applications may be constrained by the time that it takes to reach a privacy threshold defined by a minimum number of reports. One possible solution is to increase the reporting period so more samples can be collected, balanced against the urgency of responding to a soft deadline.

Protocol-specific optimizations Not all DAP tasks have the same operational requirements, so the protocol is designed to allow implementations to reduce operational costs in certain cases.

Reducing storage requirements In general, the aggregators are required to keep state for tasks and all valid reports for as long as collect requests can be made for them. In particular, aggregators must store a batch as long as the batch has not been queried more than max_batch_query_count times. However, it is not always necessary to store the reports themselves. For schemes like Prio3 in which reports are verified only once, each aggregator only needs to store its aggregate share for each possible batch interval, along with the number of times the aggregate share was used in a batch. This is due to the requirement that the batch interval respect the boundaries defined by the DAP parameters. (See .) However, Aggregators are also required to implement several per-report checks that require retaining a number of data artifacts. For example, to detect replay attacks, it is necessary for each Aggregator to retain the set of report IDs of reports that have been aggregated for the task so far. Depending on the task lifetime and report upload rate, this can result in high storage costs. To alleviate this burden, DAP allows Aggregators to drop this state as needed, so long as reports are dropped properly as described in . Aggregators SHOULD take steps to mitigate the risk of dropping reports (e.g., by evicting the oldest data first). Furthermore, the aggregators must store data related to a task as long as the current time has not passed this task's task_expiration. Aggregator MAY delete the task and all data pertaining to this task after task_expiration. Implementors SHOULD provide for some leeway so the collector can collect the batch after some delay.

Compliance Requirements In the absence of an application or deployment-specific profile specifying otherwise, a compliant DAP application MUST implement the following HPKE cipher suite:

KEM: DHKEM(X25519, HKDF-SHA256) (see )
KDF: HKDF-SHA256 (see )
AEAD: AES-128-GCM (see )

Security Considerations DAP assumes an active attacker that controls the network and has the ability to statically corrupt any number of clients, aggregators, and collectors. That is, the attacker can learn the secret state of any party prior to the start of its attack. For example, it may coerce a client into providing malicious input shares for aggregation or coerce an aggregator into diverting from the protocol specified (e.g., by divulging its input shares to the attacker). In the presence of this adversary, DAP aims to achieve the privacy and robustness security goals described in 's Security Considerations section. Currently, the specification does not achieve these goals. In particular, there are several open issues that need to be addressed before these goals are met. Details for each issue are below.

When crafted maliciously, collect requests may leak more information about the measurements than the system intends. For example, the spec currently allows sequences of collect requests to reveal an aggregate result for a batch smaller than the minimum batch size. [OPEN ISSUE: See issue#195. This also has implications for how we solve issue#183.]
Even benign collect requests may leak information beyond what one might expect intuitively. For example, the Poplar1 VDAF can be used to compute the set of heavy hitters among a set of arbitrary bit strings uploaded by clients. This requires multiple evaluations of the VDAF, the results of which reveal information to the aggregators and collector beyond what follows from the heavy hitters themselves. Note that this leakage can be mitigated using differential privacy. [OPEN ISSUE: We have yet not specified how to add DP.]
The core DAP spec does not defend against Sybil attacks. In this type of attack, the adversary adds to a batch a number of reports that skew the aggregate result in its favor. For example: The result may reveal additional information about the honest measurements, leading to a privacy violation; or the result may have some property that is desirable to the adversary ("stats poisoning"). The upload sub-protocol includes an extensions mechanism that can be used to prevent --- or at least mitigate --- these types of attacks. See . [OPEN ISSUE: No such extension has been implemented, so we're not yet sure if the current mechanism is sufficient.]

Threat model [OPEN ISSUE: This subsection is a bit out-of-date.] In this section, we enumerate the actors participating in the Prio system and enumerate their assets (secrets that are either inherently valuable or which confer some capability that enables further attack on the system), the capabilities that a malicious or compromised actor has, and potential mitigations for attacks enabled by those capabilities. This model assumes that all participants have previously agreed upon and exchanged all shared parameters over some unspecified secure channel.

Client/user

Assets

Unshared inputs. Clients are the only actor that can ever see the original inputs.
Unencrypted input shares.

Capabilities

Individual users can reveal their own input and compromise their own privacy.
Clients (that is, software which might be used by many users of the system) can defeat privacy by leaking input outside of the Prio system.
Clients may affect the quality of aggregations by reporting false input.
- Prio can only prove that submitted input is valid, not that it is true. False input can be mitigated orthogonally to the Prio protocol (e.g., by requiring that aggregations include a minimum number of contributions) and so these attacks are considered to be outside of the threat model.
Clients can send invalid encodings of input.

Mitigations

The input validation protocol executed by the aggregators prevents either individual clients or a coalition of clients from compromising the robustness property.
If aggregator output satisfies differential privacy , then all records not leaked by malicious clients are still protected.

Aggregator

Assets

Unencrypted input shares.
Input share decryption keys.
Client identifying information.
Aggregate shares.
Aggregator identity.

Capabilities

Aggregators may defeat the robustness of the system by emitting bogus output shares.
If clients reveal identifying information to aggregators (such as a trusted identity during client authentication), aggregators can learn which clients are contributing input.
1. Aggregators may reveal that a particular client contributed input.
2. Aggregators may attack robustness by selectively omitting inputs from certain clients.
  - For example, omitting submissions from a particular geographic region to falsely suggest that a particular localization is not being used.
Individual aggregators may compromise availability of the system by refusing to emit aggregate shares.
Input validity proof forging. Any aggregator can collude with a malicious client to craft a proof that will fool honest aggregators into accepting invalid input.
Aggregators can count the total number of input shares, which could compromise user privacy (and differential privacy ) if the presence or absence of a share for a given user is sensitive.

Mitigations

The linear secret sharing scheme employed by the client ensures that privacy is preserved as long as at least one aggregator does not reveal its input shares.
If computed over a sufficient number of reports, aggregate shares reveal nothing about either the inputs or the participating clients.
Clients can ensure that aggregate counts are non-sensitive by generating input independently of user behavior. For example, a client should periodically upload a report even if the event that the task is tracking has not occurred, so that the absence of reports cannot be distinguished from their presence.
Bogus inputs can be generated that encode "null" shares that do not affect the aggregate output, but mask the total number of true inputs.
- Either leaders or clients can generate these inputs to mask the total number from non-leader aggregators or all the aggregators, respectively.
- In either case, care must be taken to ensure that bogus inputs are indistinguishable from true inputs (metadata, etc), especially when constructing timestamps on reports.

[OPEN ISSUE: Define what "null" shares are. They should be defined such that inserting null shares into an aggregation is effectively a no-op. See issue#98.]

Leader The leader is also an aggregator, and so all the assets, capabilities and mitigations available to aggregators also apply to the leader.

Capabilities

Input validity proof verification. The leader can forge proofs and collude with a malicious client to trick aggregators into aggregating invalid inputs.
- This capability is no stronger than any aggregator's ability to forge validity proof in collusion with a malicious client.
Relaying messages between aggregators. The leader can compromise availability by dropping messages.
- This capability is no stronger than any aggregator's ability to refuse to emit aggregate shares.
Shrinking the anonymity set. The leader instructs aggregators to construct output parts and so could request aggregations over few inputs.

Mitigations

Aggregators enforce agreed upon minimum aggregation thresholds to prevent deanonymizing.
If aggregator output satisfies differential privacy , then genuine records are protected regardless of the size of the anonymity set.

Collector

Capabilities

Advertising shared configuration parameters (e.g., minimum thresholds for aggregations, joint randomness, arithmetic circuits).
Collectors may trivially defeat availability by discarding aggregate shares submitted by aggregators.
Known input injection. Collectors may collude with clients to send known input to the aggregators, allowing collectors to shrink the effective anonymity set by subtracting the known inputs from the final output. Sybil attacks could be used to amplify this capability.

Mitigations

Aggregators should refuse shared parameters that are trivially insecure (i.e., aggregation threshold of 1 contribution).
If aggregator output satisfies differential privacy , then genuine records are protected regardless of the size of the anonymity set.

Aggregator collusion If all aggregators collude (e.g. by promiscuously sharing unencrypted input shares), then none of the properties of the system hold. Accordingly, such scenarios are outside of the threat model.

Attacker on the network We assume the existence of attackers on the network links between participants.

Capabilities

Observation of network traffic. Attackers may observe messages exchanged between participants at the IP layer.
1. The time of transmission of input shares by clients could reveal information about user activity.
  - For example, if a user opts into a new feature, and the client immediately reports this to aggregators, then just by observing network traffic, the attacker can infer what the user did.
2. Observation of message size could allow the attacker to learn how much input is being submitted by a client.
  - For example, if the attacker observes an encrypted message of some size, they can infer the size of the plaintext, plus or minus the cipher block size. From this they may be able to infer which aggregations the user has opted into or out of.
Tampering with network traffic. Attackers may drop messages or inject new messages into communications between participants.

Mitigations

All messages exchanged between participants in the system should be encrypted.
All messages exchanged between aggregators, the collector and the leader should be mutually authenticated so that network attackers cannot impersonate participants.
Clients should be required to submit inputs at regular intervals so that the timing of individual messages does not reveal anything.
Clients should submit dummy inputs even for aggregations the user has not opted into.

[[OPEN ISSUE: The threat model for Prio --- as it's described in the original paper and --- considers either a malicious client (attacking robustness) or a malicious subset of aggregators (attacking privacy). In particular, robustness isn't guaranteed if any one of the aggregators is malicious; in theory it may be possible for a malicious client and aggregator to collude and break robustness. Is this a contingency we need to address? There are techniques in that account for this; we need to figure out if they're practical.]]

Client authentication or attestation [TODO: Solve issue#89]

Anonymizing proxies Client reports can contain auxiliary information such as source IP, HTTP user agent or in deployments which use it, client authentication information, which could be used by aggregators to identify participating clients or permit some attacks on robustness. This auxiliary information could be removed by having clients submit reports to an anonymizing proxy server which would then use Oblivious HTTP to forward inputs to the DAP leader, without requiring any server participating in DAP to be aware of whatever client authentication or attestation scheme is in use.

Batch parameters An important parameter of a DAP deployment is the minimum batch size. If an aggregation includes too few inputs, then the outputs can reveal information about individual participants. Aggregators use the batch size field of the shared task parameters to enforce minimum batch size during the collect protocol, but server implementations may also opt out of participating in a DAP task if the minimum batch size is too small. This document does not specify how to choose minimum batch sizes. The DAP parameters also specify the maximum number of times a report can be used. Some protocols, such as Poplar , require reports to be used in multiple batches spanning multiple collect requests.

Differential privacy Optionally, DAP deployments can choose to ensure their output F achieves differential privacy . A simple approach would require the aggregators to add two-sided noise (e.g. sampled from a two-sided geometric distribution) to outputs. Since each aggregator is adding noise independently, privacy can be guaranteed even if all but one of the aggregators is malicious. Differential privacy is a strong privacy definition, and protects users in extreme circumstances: Even if an adversary has prior knowledge of every input in a batch except for one, that one record is still formally protected. [OPEN ISSUE: While parameters configuring the differential privacy noise (like specific distributions / variance) can be agreed upon out of band by the aggregators and collector, there may be benefits to adding explicit protocol support by encoding them into task parameters.]

Robustness in the presence of malicious servers Most DAP protocols, including Prio and Poplar, are robust against malicious clients, but are not robust against malicious servers. Any aggregator can simply emit bogus aggregate shares and undetectably spoil aggregates. If enough aggregators were available, this could be mitigated by running the protocol multiple times with distinct subsets of aggregators chosen so that no aggregator appears in all subsets and checking all the outputs against each other. If all the protocol runs do not agree, then participants know that at least one aggregator is defective, and it may be possible to identify the defector (i.e., if a majority of runs agree, and a single aggregator appears in every run that disagrees). See #22 for discussion.

Verification key requirements The verification key for a task SHOULD be chosen before any reports are generated. It SHOULD be fixed for the lifetime of the task and not be rotated. One way to ensure this is to include the verification key in a derivation of the task ID. This consideration comes from current security analysis for existing VDAFs. For example, to ensure that the security proofs for Prio3 hold, the verification key MUST be chosen independently of the generated reports. This can be achieved as recommended above.

Infrastructure diversity Prio deployments should ensure that aggregators do not have common dependencies that would enable a single vendor to reassemble inputs. For example, if all participating aggregators stored unencrypted input shares on the same cloud object storage service, then that cloud vendor would be able to reassemble all the input shares and defeat privacy.

System requirements

Data types

IANA Considerations

Protocol Message Media Types This specification defines the following protocol messages, along with their corresponding media types types:

HpkeConfigList : "application/dap-hpke-config-list"
Report : "application/dap-report"
AggregationJobInitReq : "application/dap-aggregation-job-init-req"
AggregationJobResp : "application/dap-aggregation-job-resp"
AggregationJobContinueReq : "application/dap-aggregation-job-continue-req"
AggregateShareReq : "application/dap-aggregate-share-req"
AggregateShare : "application/dap-aggregate-share"
CollectionReq : "application/dap-collect-req"
Collection : "application/dap-collection"

The definition for each media type is in the following subsections. Protocol message format evolution is supported through the definition of new formats that are identified by new media types. IANA [shall update / has updated] the "Media Types" registry at https://www.iana.org/assignments/media-types with the registration information in this section for all media types listed above. [OPEN ISSUE: Solicit review of these allocations from domain experts.]

"application/dap-hpke-config-list" media type

Type name:

application

Subtype name:

dap-hpke-config-list

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-report" media type

Type name:

application

Subtype name:

dap-report

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-aggregation-job-init-req" media type

Type name:

application

Subtype name:

dap-aggregation-job-init-req

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-aggregation-job-resp" media type

Type name:

application

Subtype name:

dap-aggregation-job-resp

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-aggregation-job-continue-req" media type

Type name:

application

Subtype name:

dap-aggregation-job-continue-req

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-aggregate-share-req" media type

Type name:

application

Subtype name:

dap-aggregate-share-req

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-aggregate-share" media type

Type name:

application

Subtype name:

dap-aggregate-share

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-collect-req" media type

Type name:

application

Subtype name:

dap-collect-req

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

"application/dap-collection" media type

Type name:

application

Subtype name:

dap-collection

Required parameters:

N/A

Optional parameters:

None

Encoding considerations:

only "8bit" or "binary" is permitted

Security considerations:

see

Interoperability considerations:

N/A

Published specification:

this specification

Applications that use this media type:

N/A

Fragment identifier considerations:

N/A

Additional information:

Magic number(s):: N/A
Deprecated alias names for this type:: N/A
File extension(s):: N/A
Macintosh file type code(s):: N/A

Person and email address to contact for further information:

see Authors' Addresses section

Intended usage:

COMMON

Restrictions on usage:

N/A

Author:

see Authors' Addresses section

Change controller:

IESG

Query Types Registry This document requests creation of a new registry for Query Types. This registry should contain the following columns: [TODO: define how we want to structure this registry when the time comes]

Upload Extension Registry This document requests creation of a new registry for extensions to the Upload protocol. This registry should contain the following columns: [TODO: define how we want to structure this registry when the time comes]

URN Sub-namespace for DAP (urn:ietf:params:ppm:dap) The following value [will be/has been] registered in the "IETF URN Sub-namespace for Registered Protocol Parameter Identifiers" registry, following the template in : Initial contents: The types and descriptions in the table in above, with the Reference field set to point to this specification.

Acknowledgments The text in is based extensively on