An Investigation into Randomized Response Mechanisms in RTT Measurements for QUIC

Internet Research Task Force                             A. Andersdotter
Internet-Draft                                                     CENTR
Intended status: Informational                                  S. Sahib
Expires: February 15, 2021                                    Salesforce
                                                         August 14, 2020

An Investigation into Randomized Response Mechanisms in RTT Measurements
                                for QUIC


   The latency spin bit is an optional feature included in the QUIC
   transport protocol, as standardized by the Internet Engineering Task
   Force (IETF).  It enables passive, on-path observations for
   estimation of latency.  This document presents the results of an
   inquiry into the potential of using randomized response mechanisms
   (RRM) to reduce privacy loss in latency measurements.  It concludes
   that RRM could be used to introduce choice for clients in preserving
   privacy in latency measurements.  But the trade-offs, especially
   since the latency spin bit is already optional, do not favour RRM.

Status of This Memo

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Randomized Response Mechanisms  . . . . . . . . . . . . . . .   2
   3.  Application to latency spin bit . . . . . . . . . . . . . . .   4
   4.  Spin bit assumptions  . . . . . . . . . . . . . . . . . . . .   6
   5.  Model specification . . . . . . . . . . . . . . . . . . . . .   8
   6.  Simulation  . . . . . . . . . . . . . . . . . . . . . . . . .   9
   7.  Edge transition RRM . . . . . . . . . . . . . . . . . . . . .   9
     7.1.  One and a half round-trip explained . . . . . . . . . . .   9
     7.2.  A closer look at the loop . . . . . . . . . . . . . . . .  10
     7.3.  Using model to restrict measurements  . . . . . . . . . .  11
   8.  Discussion  . . . . . . . . . . . . . . . . . . . . . . . . .  12
   9.  Informative References  . . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

1.  Introduction

   At the IETF104 convening of the Privacy Enhancements and Assessments
   Research Group (PEARG), a presentation on Differential Privacy
   ([AA-CL]) gave rise to the idea of trying to apply randomized
   response methods to the QUIC spin bit described in [TRAMMEL] and
   [KUEHLEWIND].  The spin bit, now incorporated in Section 17.3.1
   [I-D-QUIC], has generated controversy from a privacy perspective,
   both in the Working Group meetings and on the QUIC email list.
   Controversies were re-ignited through the publication of a Human
   Rights Consideration in [TENOEVER-MARTINI] in 2019.  Applying RRM is
   an attempt to address two problems: the privacy loss incurred through
   the spin bit, and considering the potential of using RRM to have more
   than one bit assisting in latency measurement as per previous

2.  Randomized Response Mechanisms

   Randomized response trials were originally suggested by social
   scientist Stanley Warner to increase response rates in surveys on
   sensitive topics, such as political affiliation or sexuality
   [WARNER].  At the flip of a coin (or other random device), a survey
   taker would answer the opposite question to the one that the survey
   giver wanted to ask.  For instance, if the survey giver wants to find
   out whether a person has been affiliated with a communist group, the

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   survey taker would instead answer, at some fixed probability, whether
   they had never been affiliated with a communist group.  The effect is
   the same as if the survey taker would give a false answer to the
   survey question with some known probability.

   This method provoked a flurry of statistical research throughout the
   1970s and 80s, with statisticians considering a range of problems in
   estimation and variance reduction for estimators in the presence of
   noise on survey responses [RAO].

   Recently, randomized response mechanisms has again gained traction,
   through the work of Cynthia Dwork et al on differential privacy
   [DWORK] or mechanisms for statistical data collection over
   (presumably large) user sets, such as [RAPPOR].  These developments
   had led to renewed interest in randomized response mechanisms in the
   statistical community, with text books [FOX] and handbooks [RAO]
   covering a large range of possible situations where randomizing
   responses over a set of outcomes on an individual respondent basis
   may still enable useful inferences about the population to which the
   individual belongs.

   Randomized response trials were originally created for binary
   environments: if a series of measurements have only two possible
   outcomes (0 or 1, yes or no, true or false, for example), allowing
   individual respondents to answer "falsely" at a predictable rate will
   still preserve the ability to make inferences on the entire set of
   respondents.  The latency spin bit, being a bit, is a binary outcome
   variable.  Each time it is measured, the idea is that it can either
   "truthfully" report its value as what it should be according to
   [TRAMMEL], or it could, at some known rate or probability, report the
   opposite value.

   RRMs are easily illustrated for binary response problems.  Let's take
   as an example "Did you go to the last IETF meeting?"  The answer to
   this question is either yes or no.  Let us suppose that 25% of all
   responses are known to be false, and that 80% of all respondents
   answered yes.  Then 60% of the respondents who answered yes can be
   assumed to have done so truthfully, while 5% of the respondents who
   answered no have done so falsely. 65% of the respondents can
   therefore be estimated to have actually attended the last IETF

   RRMs can also be applied to multiple choice questions.  Estimation of
   true proportions becomes more difficult as the number of possible
   answers per question goes up.  Further examples, including formulas
   and calculations, can be found in [RAO] and [FOX].

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3.  Application to latency spin bit

   As described in [TRAMMEL], the latency spin bit is a mechanism for
   measuring round-trip-times (RTT) in the QUIC protocol.  The
   investigation in this document relies on [TRAMMEL] for its
   understanding of the basic operation of the latency spin bit, and in
   particular the following paragraphs and figures from the document are
   quoted to facilitate the description of RRM below:

   [Begin quote] Initially, during connection establishment, no packets
   with a spin bit are in flight, as shown in Figure 1.

           +--------+   -  -  -  -  -   +--------+
           |        |     -------->     |        |
           | Client |                   | Server |
           |        |     <--------     |        |
           +--------+   -  -  -  -  -   +--------+

      Figure 1: Initial state, no spin bit between client and server

   Either the server, the client, or both can begin sending packets with
   short headers after connection establishment, as shown in Figure 2;
   here, no spin edges are yet in transit.

           +--------+   0  0  -  -  -   +--------+
           |        |     -------->     |        |
           | Client |                   | Server |
           |        |     <--------     |        |
           +--------+   -  -  0  0  0   +--------+

       Figure 2: Client and server begin sending packets with spin 0

   Once the server's first 0-marked packet arrives at the client, the
   client sets its spin value to 1, and begins sending packets with the
   spin bit set, as shown in Figure 3.  The spin edge is now in transit
   toward the server.

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           +--------+   1  0  0  0  0   +--------+
           |        |     -------->     |        |
           | Client |                   | Server |
           |        |     <--------     |        |
           +--------+   0  0  0  0  0   +--------+

                     Figure 3: The bit begins spinning

   Five ticks later, this packet arrives at the server, which takes its
   spin value from it and reflects that value back on the next packet it
   sends, as shown in Figure 4.  The spin edge is now in transit toward
   the client.

           +--------+   1  1  1  1  1   +--------+
           |        |     -------->     |        |
           | Client |                   | Server |
           |        |     <--------     |        |
           +--------+   0  0  0  0  1   +--------+

                  Figure 4: Server reflects the spin edge

   Five ticks later, the 1-marked packet arrives at the client, which
   inverts its spin value and sends the inverted value on the next
   packet it sends, as shown in Figure 5.

           obs. points  X  Y
           +--------+   0  1  1  1  1   +--------+
           |        |     -------->     |        |
           | Client |                   | Server |
           |        |     <--------     |        |
           +--------+   1  1  1  1  1   +--------+

                  Figure 5: Client inverts the spin edge

   [End quote]

   In each iteration going from Figure 4 to Figure 5 a sequence of 0s or
   1s the length of which is k0 for iteration 0, k1 for iteration 1, and
   so forth, can be observed (by on-path observers X or Y in Figure 5).

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   The length of each sequence equals the amount of ticks required to
   pass from the client back to the client.  After observation n lengths
   of such sequences, (k[0], ..., k[n]), an average can be taken over
   k[j].  This average can be multiplied by the amount of time per tick
   (a quantity which is assumed to be known) to get a value for the
   round-trip time (RTT).

   Applying randomized response mechanisms (RRMs) perturbs the observed
   sequence lengths (k[0], ..., k[n]).  The perturbation will have the
   effect of lengthening, shortening, or making more arbitrary the
   lengths of the sequences, thereby increasing the variance, or disable
   the possibility, of an estimator of the true RTT value.

4.  Spin bit assumptions

   Deciding on a RRM scheme for RTT in QUIC requires a more explicitly
   defined mechanism for changing the spin value (the value of the spin
   bit being transmitted from the client or server) than presently is
   the case in [TRAMMEL].  For instance, the way in which the server is
   specified to change its spin value currently is:

   "The server initializes its spin value to 0.  When it receives a
   packet from the client, if that packet has a short header and if it
   increments the highest packet number seen by the server from the
   client, it sets the spin value to the spin bit in the received
   packet."  (Section 2)

   while the mechanism for changing the spin value in the client is

   "The client initializes its spin value to 0.  When it receives a
   packet from the server, if the packet has a short header and if it
   increments the highest packet number seen by the client from the
   server, it sets the spin value to the opposite of the spin bit in the
   received packet."  (Section 2)

   The goal of the designer in [TRAMMEL] is to cause the spin bit to
   change its value once per round-trip.  Our design goal is different.
   We want to have the spin bit only sometimes change its value once per
   round-trip, while it might other times change its value twice per
   round-trip, or not at all.  Additionally, we have the goal of
   ensuring that we can exercise control over what percentage of round-
   trips give useful measurements.  To simultaneously fill all of those
   requirements, we introduce the following additional constraints on
   updating the spin value:

   1.   Client and server have an internal spin value (NV) which decides
        the value of the next outgoing spin bit.

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   2.   Clients and server keep track of the second-to-last incoming
        spin bit (SLISB), and the last incoming spin bit (LISB).

   3.   The NV initializes to 0 at both the client and the server.

   4.   An inversion of the client's NV is triggered if SLISB and LISB
        have different values.  Notably, no comparison between the SLISB
        or LISB and the NV is made.  The value of the NV, which
        determines the value of the next spin bit transmitted, is set
        independently of the value of the SLISB and LISB.

   5.   An inversion does not happen with probability q, even when it

   6.   A reflection of the server's NV is also triggered if SLISB and
        LISB have different values.

   7.   A reflection does not happen with probability p, even when it

   8.   In the absence of a triggering event, the NV does not change its
        value and the client or server continue to transmit bits holding
        the current NV value.

   9.   Client and server act independently of one another, so that
        neither client or server have any way of determining whether the
        other has reflected or inverted ``truthfully''.

   10.  A special case is the first time a spin bit is recorded by a
        client or server (immediately after initialization).  In this
        case, the client and server both update the NV truthfully.

   We illustrate these assumptions with a truth table for the client in
   Figure 6 and for the server in Figure 7.

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             | NVclient | SLISB | LISB |     NV'client     |
             | (0)      | (-)   | (0)  | (1)*              |
             | 0        |  0    |  0   |  0                |
             | 0        |  0    |  1   |  0(q) or 1(1-q)   |
             | 0        |  1    |  0   |  0(q) or 1(1-q)   |
             | 0        |  1    |  1   |  0                |
             | 1        |  0    |  0   |  1                |
             | 1        |  0    |  1   |  1(q) or 0(1-q)   |
             | 1        |  1    |  0   |  1(q) or 0(1-q)   |
             | 1        |  1    |  1   |  1                |

    Figure 6: Client truth table for inversion of the client's internal
       spin bit value NVclient.  NV'client in the right-most column
    constitutes a truthful inversion with probability (1-q) and a lying
   inversion with probability q. * A special case is the firstround-trip
                           after initialization.

             | NVclient | SLISB | LISB |   NV'client    |
             | (0)      | (-)   | (0)  | (0)*           |
             | 0        | 0     | 0    | 0              |
             | 0        | 0     | 1    | 0(1-p) or 1(p) |
             | 0        | 1     | 0    | 0(1-p) or 1(p) |
             | 0        | 1     | 1    | 0              |
             | 1        | 0     | 0    | 1              |
             | 1        | 0     | 1    | 1(1-p) or 0(q) |
             | 1        | 1     | 0    | 1(1-p) or 0(q) |
             | 1        | 1     | 1    | 1              |

   Figure 7: Server truth table for reflection of the server's internal
     spin bit value NVserver. * A special case is the firstround-trip
                           after initialization.

5.  Model specification

   There are two conceivable ways to achieve RRM for RTT measurements:

   1.  The reflection and/or inversion is not activated by the arrival
       of an edge bit with some probability (``Edge transition RRM''),

   2.  the server or the client randomizes which bit it transmits at
       each bit (``Each bit RRM'').

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   In particular, in QUIC25 draft [I-D-QUIC], section 17.1.3, a
   randomization mechanism is called for that renders 7/8 of all spin
   bit measurements non-useful for the purpose of inferring latency.
   This encourages us to seek some mathematical solution that can at
   least guarantee that 7/8 of all traffic streams to which a spin bit
   is attached are not useful for RTT measurements.

6.  Simulation

   Simulation code for both cases discussed in this document ("RRM at
   each bit" and "RRM at edge transition") and instructions are hosted
   on GitHub [SIMULATION].

7.  Edge transition RRM

7.1.  One and a half round-trip explained

   Recall the assumptions in Section 4.  Suppose that a round trip takes
   2n time units.  If we initialize spin bits at the client and server
   to 0 (assumption 3), they will both see (SLISB, LISB)=(-,0) after n
   time units, and an NV change is triggered (assumption 10).  Now the
   client maintains an NV value of 1 while the server sets its NV value
   to 0.

   The client now transmits spin bits valued 1 to the server, while the
   server continues to transmit spin bits valued 0 to the client.  After
   another n time units (2n time units in total) the client sees a
   (SLISB, LISB)-tuple valued (0,0), while the server will see a (SLISB,
   LISB)-tuple (1,0) (assumption 2).  This triggers an attempted
   reflection by the server, meaning that its NV should be changed from
   0 to 1 (assumption 6), while a change in the client NV (1) is not
   triggered (assumption 4).  Suppose that the server truthfully
   reflects its NV to 1.  Now the client continues to transmit 1s to the
   server, while the server transmits 1s to the client.

   After yet another n time units (3n time units in total) the server
   will see the (SLISB, LISB)-tuple (1,1) and therefore do nothing
   (assumption 8), while the client sees the tuple (0,1) and tries to
   update its NV (assumption 4).  If the client does not do this, so
   that the client NV remains at 1, then the client will be transmitting
   1s to the server and the server will be transmitting 1s to the

   After 4n time units, the (SLISB, LISB)-tuples seen by both the client
   and the server will be (1,1), and both NVs will also be set to 1.
   Consequently, the (lack of) NV updates after 3n time units have
   landed us in the situation that there is no longer any possibility

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   for a (SLISB, LISB)-tuple to have different values, and we have ended
   up in a loop.

   This is encouraging, since a loop can be escaped by randomly re-
   initializing the spin bit after some time that we can choose.

7.2.  A closer look at the loop

   As in the previous section, let the RTT be 2n time units.  If
   NV[client] = NV[server] at time n, and the NVs remain equal to each
   other at time 2n, the process will be in a loop.  If we describe the
   four different combinations of NVs in the following way:

   (NV[client], NV[server]) = (0,0), (1,0), (0,1) or (1,1)

   then, in the example above (Section 7.1), we would have the following
   sequence of transitions:

   (0,0)[init] -> (1,0) -> (1,1) -> (1,1) \]

   Referring back to the truth tables in Figure 6 and Figure 7, we can
   work out how these transitions exactly happen.  For example, the
   transition (1,0) -> (1,1) can happen in the following two ways:

   The client attempts to update NV[client] after receiving a triggering
   (SLISB, LISB)-tuple but fails to invert or it does not receive a
   triggering (SLISB, LISB)-tuple at all, while the server updates
   NV[server] truthfully after receiving a triggering (SLISB, LISB)-
   tuple.  The server has one way of transitioning its NV from 0 to 1,
   while the client has two ways of transitioning its NV from 1 to 1.

   We know the probabilities that reflections or inversions will not
   happen (assumptions 5 and 7 in Section 4), but also need to know when
   a triggering (SLISB, LISB)-tuple will be received.  A client receives
   such a tuple at time kn if the server truthfully updated its NV at
   time (k-1)n.  In fact, a loop occurs as soon as the server does not
   update its NV truthfully.  A (SLISB, LISB)-tuple received by the
   client will necessarily have the form

   (NV[server,t=n(k-1)], NV[server,t=n(k-2)]

   and an NV update is triggered only if this tuple contains two
   different values.  From assumption 10 in Section 4 we have that

   NV[server,t=0] = NV[server,t=n] at t=0, n

   and is updated only because NV[client] is updated at t=n by the same
   assumption.  The fact that they are equal means that necessarily

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   NV[client,t=2n] = NV[client,t=2n]

   with NV[client,t] assuming a new value only if $NV[server,s] changes.
   But if the server would lie once (and not update its NV), we get

   NV[server,t=n(k-1)] = NV[server,t=nk] = NV[server,t=n(k+1)]

   rendering the server unable to transmit values that can trigger an
   update of the client NV value.

7.3.  Using model to restrict measurements

   With the insights from Section 7.2 we can choose p and q from
   Section 4, and define some re-initialization criteria for the spin
   bit, for an alternative mechanism to achieve the targets set out in
   the QUIC spin bit specification in [I-D-QUIC]:

   "Each endpoint unilaterally decides if the spin bit is enabled or
   disabled for a connection.  Implementations MUST allow administrators
   of clients and servers to disable the spin bit either globally or on
   a per-connection basis.  Even when the spin bit is not disabled by
   the administrator, endpoints MUST disable their use of the spin bit
   for a random selection of at least one in every 16 network paths, or
   for one in every 16 connection IDs.  As each endpoint disables the
   spin bit independently, this ensures that the spin bit signal is
   disabled on approximately one in eight network paths." (sec. 17.3.1)

   In order to estimate the round-trip time, an on-path observer needs
   to have access to at least one full round-trip worth of passing spin
   bits.  The first such accessible round-trip after initialization is
   the sequence of 1s transmitted by the client, if truthfully reflected
   by the server with probability (1-p).  The second such accessible
   round-trip is the sequence of 0s that follow upon additionally
   truthful inversions and reflections by the client and server
   respectively.  The cumulative probability of two accessible round-
   trips is therefore (1-p)(1-q)(1-p), and in general

   P[X round-trips are complete and measurable] = (1-p)^x (1-q)^(x-1)

   From this we can derive the expected value

   E[X] (1-p) S[x [(1-p)(1-q)]^(x-1) = (1-p)/((1-(1-p)(1-q))^2)

   where S[.] is the sum over x.

   By the specification quoted above, we want this to be approximately
   equal to 7/8.  A range of values for (p,q) can satisfy this

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   criterion, and, for instance, if the client always tells the truth
   (i.e. q=0) then p=1/8, meaning that the server lies 1/8 of the time.

   Once the client or server have lied for the first time, all future
   spin bit values cannot be used for measuring round-trip time unless
   the NV update process is re-initiated.  This could be achieved
   through the client arbitrarily updating its NV in contradiction with
   assumption 8 of Section 4 after some period of time, which could be
   chosen according to a geometric distribution of some expectation r.
   However, in the time leading up to re-initialization the utility for
   an on-path observer of recording the spin bit value is nil.

   It follows that the actual proportion of useless measurements will be
   far higher than the 1/8 that is specified in the draft.

   A solution is to choose p, q so that the expected value of the number
   of useful round-trip measurements is higher than 7/8.  If we solve
   for p, q when E[X] = 56/59, we would want the client to re-initiate
   the NV update procedure after an average of 5 round-trip periods to
   get an expected 56/64 = 7/8 useful measurements.  This supposes, of
   course, that the client has a way of establishing the approximate
   round-trip time that is independent of the spin bit.

   Additional privacy gains, or at least diminished availability of
   useful RTT measurements, would be achieved by solving for an expected
   value lower than 7/8.  Since not all measurements are rendered
   useless by applying RRM, there will eventually always be a time when
   an on-path observer can make inferences about round-trip time.

8.  Discussion

   It is possible to apply to RRM to QUIC RTT measurements in a way
   which delays estimation of RTT.  However, it is unclear whether RRM
   has advantages larger than already existing privacy mechanisms
   included in the QUIC draft (such as making the spin bit optional, or
   requiring that 1/8 of all streams are not measurable).  The privacy
   concern associated with a spin bit is that latency measurements will
   enable inference of the location or distance of the device associated
   with that particular IP address.  But the whole point of differential
   privacy mechanisms, including RRM, is using statistical methods to
   ensure that data can be made more privacy-preserving while also
   preserving the data utility.  In the case of the spin bit, it is the
   utility of the data that allegedly violates privacy, which means
   differential privacy is an intuitively bad tool to address privacy

   The spin bit is associated with an IP address, which creates
   linkability.  Any differential privacy mechanism will not remove

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   linkability from the spin bit, and so preserves that angle of privacy

   RRM could potentially be used to fulfill requirements from
   [I-D-QUIC], sec. 17.3.1, in a slightly more flexible way than is
   currently discussed at the IETF.  In particular, the parameters p, q
   and r could be adjusted to accommodate for any proportion of useful
   measurements.  If r is left for the client to decide, the client may
   even have influence over the extent to which RTT measurements through
   the QUIC spin bit is made more difficult (see e.g.  [RFC6973], sec.

   In order to realize such advantages the functioning of the QUIC spin
   bit does, however, need to be more stringently specified, in
   particular in line with our suggestions in Section 4.

9.  Informative References

   [AA-CL]    Andersdotter, A. and C. Laengstroem, "Differential Privacy
              (PEARG, IETF104)", March 2019,

   [DWORK]    Roth, A. and C. Dwork, "The Algorithmic Foundations of
              Differential Privacy", 2014,

   [FOX]      Fox, J., "Randomized Response and Related Methods:
              Surveying Sensitive Data", February 2017.

              Iyengar, J. and M. Thomson, "QUIC: A UDP-Based Multiplexed
              and Secure Transport", September 2019,

              Kuehlewind, M. and B. Trammel, "The QUIC Latency Spin Bit
              (draft-ietf-quic-spin-exp-01)", October 2018,

   [RAO]      Rao, T. and C. Rao, ""Review of Certain Recent Advances in
              Randomized Response Techniques" in C.R. Rao (Ed.),
              Handbook of Statistics, Elsevier B.V, Oxford (UK).", 2016.

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   [RAPPOR]   Erlingsson, U., Korolova, A., and V. Pihur, "RAPPOR:
              Randomized Aggregatable Privacy-Preserving Ordinal
              Response", arXiv:1407.6981v2 [cs.CR]", 2014.

   [RFC6973]  Cooper, A., Tschofenig, H., Aboba, B., Petersen, J.,
              Morris, J., Hansen, M., and R. Smith, "Privacy
              Considerations for Internet Protocols", RFC 6973,
              DOI 10.17487/RFC6973, July 2013,

              Sahib, S. and A. Andersdotter,
              rrt/tree/master/spinbit_simulation", November 2019,

              Martini, B. and N. Ten Oever, "QUIC Human Rights Review
              (draft-martini-hrpc-quichr-00)", October 2018,

   [TRAMMEL]  Trammel, B., Boucadair, M., Even, R., Fioccola, G.,
              Fossati, T., Ihlar, M., Morton, A., and E. Stephan,
              "Adding Explicit Passive Measurability of Two-Way Latency
              to the QUIC Transport Protocol (draft-trammell-quic-spin-
              03)", May 2018, <

   [WARNER]   Warner, S., ""Randomized response: a survey technique for
              eliminating evasive answer bias." J. Am. Stat. Assoc. 60
              (309), 63-69.", 1965.

Authors' Addresses

   Amelia Andersdotter
   Rue Belliard 30
   1040 Brussels


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   Shivan Sahib


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