Privacy Preserving Measurement                                M. ThomsonInternet-Draft                                                   MozillaIntended status: Standards Track                                 D. CookExpires: 23 August 2026                                             ISRG                                                        19 February 2026     A Prio Instantiation for Vector Sums with an L1 Norm Bound on                             Contributions                     draft-ietf-ppm-l1-bound-sum-01Abstract   A Prio Verifiable Distributed Aggregation Function is defined that   supports vector or histogram addition, where the sum of the values in   the contribution is less than a chosen value.About This Document   This note is to be removed before publishing as an RFC.   The latest revision of this draft can be found at https://ietf-wg-   ppm.github.io/draft-ietf-ppm-l1-bound-sum/draft-ietf-ppm-l1-bound-   sum.html.  Status information for this document may be found at   https://datatracker.ietf.org/doc/draft-ietf-ppm-l1-bound-sum/.   Discussion of this document takes place on the Privacy Preserving   Measurement Working Group mailing list (mailto:ppm@ietf.org), which   is archived at https://mailarchive.ietf.org/arch/browse/ppm/.   Subscribe at https://www.ietf.org/mailman/listinfo/ppm/.   Source for this draft and an issue tracker can be found at   https://github.com/ietf-wg-ppm/draft-ietf-ppm-l1-bound-sum.Status of This Memo   This Internet-Draft is submitted in full conformance with the   provisions of BCP 78 and BCP 79.   Internet-Drafts are working documents of the Internet Engineering   Task Force (IETF).  Note that other groups may also distribute   working documents as Internet-Drafts.  The list of current Internet-   Drafts is at https://datatracker.ietf.org/drafts/current/.   Internet-Drafts are draft documents valid for a maximum of six months   and may be updated, replaced, or obsoleted by other documents at any   time.  It is inappropriate to use Internet-Drafts as reference   material or to cite them other than as "work in progress."Thomson & Cook           Expires 23 August 2026                 [Page 1]Internet-Draft              Prio L1 Bound Sum              February 2026   This Internet-Draft will expire on 23 August 2026.Copyright Notice   Copyright (c) 2026 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject to BCP 78 and the IETF Trust's Legal   Provisions Relating to IETF Documents (https://trustee.ietf.org/   license-info) in effect on the date of publication of this document.   Please review these documents carefully, as they describe your rights   and restrictions with respect to this document.  Code Components   extracted from this document must include Revised BSD License text as   described in Section 4.e of the Trust Legal Provisions and are   provided without warranty as described in the Revised BSD License.Table of Contents   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   3   3.  Prio3L1BoundSum Definition  . . . . . . . . . . . . . . . . .   3     3.1.  Chunk Length Selection  . . . . . . . . . . . . . . . . .   4     3.2.  Encoding and Decoding . . . . . . . . . . . . . . . . . .   4     3.3.  Validity Circuit  . . . . . . . . . . . . . . . . . . . .   5   4.  DAP Integration . . . . . . . . . . . . . . . . . . . . . . .   6   5.  Security Considerations . . . . . . . . . . . . . . . . . . .   7   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   7   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   7     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   7     7.2.  Informative References  . . . . . . . . . . . . . . . . .   8   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .   8   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   81.  Introduction   Existing Prio instantiations of a Verifiable Distributed Aggregation   Function (VDAF) [VDAF] all support a simple summation of   measurements.  From Prio3Count (Section 7.4.1 of [VDAF]), which adds   measurements containing a single one or a zero value, to Prio3SumVec   (Section 7.4.3 of [VDAF]), which adds measurements containing a   vector where each dimension is a limited number of bits, all   instantations take the same basic form.   One case that is presently not included in the suite of   instantiations is the addition of vectors or histogram contributions,   where each measurement has an L1 bound.  The L1 norm of a vector is   defined as the sum of its components.  An L1 bound limits that sum to   some maximum.Thomson & Cook           Expires 23 August 2026                 [Page 2]Internet-Draft              Prio L1 Bound Sum              February 2026   This document defines the Prio3L1BoundSum instantiation.  This   instantiation limits the L1 norm of a vector or histogram to a value   less than or equal to a predetermined maximum.   This instantiation has similarities with other instantiations.   Unlike Prio3Histogram (Section 7.4.4 of [VDAF]), in which   measurements need to have an L1 norm of exactly 1, a valid   measurement for Prio3L1BoundSum can have an L1 norm equal to any   value between 0 and the chosen limit.  Unlike Prio3MultiHotCountVec   (Section 7.4.5 of [VDAF]), in which each component can only be zero   or one, components in Prio3L1BoundSum can take any value up to the L1   bound as long as their sum is within that bound.   Section 3 defines the Prio3L1BoundSum VDAF.2.  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 [RFC2119] [RFC8174] when, and only when, they appear in all   capitals, as shown here.   This document uses the terminology, notation conventions, and   functions defined in Section 2 of [VDAF].3.  Prio3L1BoundSum Definition   The Prio3L1BoundSum instantiation of Prio [CGB17] supports the   addition of a vector of integers.  It also uses bit_length(), which   returns the minimum number of bits needed to encode an integer value.   The instantiation is summarized in Table 1.       +===========+==============================================+       | Parameter | Value                                        |       +===========+==============================================+       | field     | Field128 (Section 6.1.2 of [VDAF])           |       +-----------+----------------------------------------------+       | Valid     | L1BoundSum(field, length, max, chunk_length) |       +-----------+----------------------------------------------+       | PROOFS    | 1                                            |       +-----------+----------------------------------------------+       | XOF       | XofTurboShake128 (Section 6.2.1 of [VDAF])   |       +-----------+----------------------------------------------+                   Table 1: Prio3L1BoundSum ParametersThomson & Cook           Expires 23 August 2026                 [Page 3]Internet-Draft              Prio L1 Bound Sum              February 2026   The function takes three parameters: length, max_value, and   chunk_length.  The vector contains "length" components, each of which   is a non-negative integer less than or equal to max_value.   The value of max_value can be any positive integer.  A value of 1   causes Prio3L1BoundSum to be nearly identical to Prio3Histogram,   except that Prio3Histogram cannot encode an all-zero report.3.1.  Chunk Length Selection   The chunk_length parameter can be chosen in approximately the same   way as for Prio3SumVec, as detailed in Section 7.4.3.1 of [VDAF].   The difference is that Prio3L1BoundSum involves validation of bits *   (length + 1) values, where bits = max_value.bit_length().  This might   increase the most efficient value for chunk_length relative to a   similar encoding of Prio3SumVec.3.2.  Encoding and Decoding   The encoded form of each measurement appends a bitwise decomposition   of the L1 norm (the sum of the vector components) to the encoding:   def encode(self, measurement: list[int]) -> list[F]:       encoded = []       erci = encode_range_checked_int       for v in measurement:           encoded += erci(self.field, v, self.max_value)       weight = erci(self.field, sum(measurement), self.max_value)       return encoded + weight   The encoded measurement has a total length of (length + 1) * bits.   The encoding function encode_range_checked_int is described in   Section 7.4.2 of [VDAF].   The encoded information is not included in the output share that is   submitted for aggregation.  That is, the truncate() function emits   only the core measurements.   def truncate(self, meas: list[F]) -> list[F]:       return [          decode_range_checked_int(self.field, m, self.max_value)          for m in chunks(meas, self.max_value.bit_length())       ]   This uses a chunks(v, c) function that takes a list of values, v, and   a chunk length, c, to split v into multiple lists from v, where each   chunk has a length c.Thomson & Cook           Expires 23 August 2026                 [Page 4]Internet-Draft              Prio L1 Bound Sum              February 2026   The decode() function is therefore identical to that in Prio3SumVec.   def decode(self, output: list[F], _count) -> list[int]:       return [x.int() for x in output]3.3.  Validity Circuit   The validity circuit for Prio3L1BoundSum uses an extended version of   the validity circuit used by Prio3SumVec, see Section 7.4.3 of   [VDAF].   The encoded measurement is checked to ensure that every component of   the vector – plus the added L1 norm – is encoded in the specified   number of bits.  That is, the circuit checks that each component has   a value between 0 (inclusive) and max_value (exclusive) by first   checking the value is correctly composed from bits, where each bit is   either zero or one.  This process is identical to the Prio3SumVec   check, except that one additional value is checked.   The validity circuit then checks whether the added L1 norm value is   consistent with the encoded vector elements.  The L1 norm is checked   by decoding the measurement values, including the L1 norm.  The   decoded values are used to recompute the L1 norm as the sum of the   individual components.  The difference between reported and computed   values is checked to confirm that the values are identical.   The complete circuit is specified in Figure 1.Thomson & Cook           Expires 23 August 2026                 [Page 5]Internet-Draft              Prio L1 Bound Sum              February 2026   def eval(self, meas: list[F],            joint_rand: list[F], num_shares: int) -> list[F]:       bits = self.max_value.bit_length()       assert len(meas) == (self.length + 1) * bits       shares_inv = self.field(num_shares).inv()       parallel_sum = ParallelSum(Mul(), chunk_length)       num_chunks = ceil(len(meas) / self.chunk_length)       pad_len = self.chunk_length * num_chunks - len(meas)       meas += [self.field(0)] * pad_len       range_check = self.field(0)       for (r, m) in zip(joint_rand, chunks(meas, self.chunk_length)):           inputs = []           for i in range(self.chunk_length):               inputs += [                   r**(i + 1) * m[i],                   m[i] - shares_inv,               ]           range_check += parallel_sum.eval(self.field, inputs)       c = chunks(meas, bits)       components = [           decode_range_checked_int(self,field, m, self.max_value)           for m in c[:self.length]       ]       observed_weight = sum(components)       claimed_weight = decode_range_checked_int(           self.field, c[self.length], self.max_value       )       weight_check = observed_weight - claimed_weight       return [range_check, weight_check]             Figure 1: Evaluation function for Prio3L1BoundSum   This evaluation uses the decode_range_checked_int() function defined   in Section 7.4.2 of [VDAF].4.  DAP Integration   The integration of Prio3L1BoundSum in DAP [DAP] requires the   definition of an encoding for the configuration of the VDAF.   Figure 2 defines the encoding of Prio3L1BoundSumConfig, using the   syntax definitions from Section 3 of [RFC8446].Thomson & Cook           Expires 23 August 2026                 [Page 6]Internet-Draft              Prio L1 Bound Sum              February 2026   struct {     uint32 length;     uint32 max_value;     uint32 chunk_length;   } Prio3L1BoundSumConfig;         Figure 2: VDAF Configuration Encoding for Prio3L1BoundSum   This configuration is three 32-bit integers, each in network byte   order, with semantics described in Section 3, as follows:   length:  The total number of values in each measurement.   max_value:  The maximum value, inclusive, for the sum of all      measurement values.   chunk_length:  The size of each chunk used in the evaluation circuit;      see Figure 1.5.  Security Considerations   The Prio3L1BoundSum VDAF is subject to the same considerations as   other Prio-based VDAFs.  These considerations are detailed in   Section 9 of [VDAF].   In particular, this instantiation uses Field128 to ensure robustness   despite the use of joint randomness in proofs.  Joint randomness   increases the risk of an attacker finding a combination of invalid   inputs that passes validation.  A larger field increases the   computational cost of finding such a combination.6.  IANA Considerations   This document registers a codepoint for Prio3L1BoundSum in the   "Verifiable Distributed Aggregation Functions (VDAF)" registry as   defined by Section 10 of [VDAF].  This entry contains the following   fields:   Value:  0x00000007   Scheme:  Prio3L1BoundSum   Type:  VDAF   Reference:  RFCXXXX (this document)7.  References7.1.  Normative ReferencesThomson & Cook           Expires 23 August 2026                 [Page 7]Internet-Draft              Prio L1 Bound Sum              February 2026   [DAP]      Geoghegan, T., Patton, C., Pitman, B., Rescorla, E., and              C. A. Wood, "Distributed Aggregation Protocol for Privacy              Preserving Measurement", Work in Progress, Internet-Draft,              draft-ietf-ppm-dap-17, 30 January 2026,              <https://datatracker.ietf.org/doc/html/draft-ietf-ppm-dap-              17>.   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate              Requirement Levels", BCP 14, RFC 2119,              DOI 10.17487/RFC2119, March 1997,              <https://www.rfc-editor.org/rfc/rfc2119>.   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,              May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,              <https://www.rfc-editor.org/rfc/rfc8446>.   [VDAF]     Barnes, R., Cook, D., Patton, C., and P. Schoppmann,              "Verifiable Distributed Aggregation Functions", Work in              Progress, Internet-Draft, draft-irtf-cfrg-vdaf-18, 30              January 2026, <https://datatracker.ietf.org/doc/html/              draft-irtf-cfrg-vdaf-18>.7.2.  Informative References   [CGB17]    Boneh, D. and H. Corrigan-Gibbs, "Prio: Private, Robust,              and Scalable Computation of Aggregate Statistics", USENIX              Symposium on Networked Systems Design and Implementation              (NSDI), 2017,              <https://dl.acm.org/doi/10.5555/3154630.3154652>.Acknowledgments   Chris Patton provided extensive input into the construction of this   VDAF.Authors' Addresses   Martin Thomson   Mozilla   Email: mt@lowentropy.net   David Cook   ISRGThomson & Cook           Expires 23 August 2026                 [Page 8]Internet-Draft              Prio L1 Bound Sum              February 2026   Email: divergentdave@gmail.comThomson & Cook           Expires 23 August 2026                 [Page 9]