S.A.kalaiselvan blocking misbehaving users in anonymizing

National Conference on Advances in Computer Science and Information Technology ISBN:978-81-924031-8-2
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Blocking Misbehaving Users in Anonymizing
Networks in TOR1
Kalaiselvan SA,2
Gowri M
1
Assistant professor/CSE,Arignar Anna Instituteof Science & Technology,Sriperumbudur-
2
II Year M.Tech(IT),Bharath University,Chennai -
1
kalaiselvan_be@ymail.com, 2
m.gowri.cse@gmail.com
Abstract—Anonymizing networks such as Tor allow users to
access Internet services privately by using a series of routers to
hide the client’s IP address from the server. The success of such
networks, however, has been limited by users employing this
anonymity for abusive purposes such as defacing popular Web
sites. Web site administrators routinely rely on IP-address
blocking for disabling access to misbehaving users, but blocking
IP addresses is not practical if the abuser routes through an
anonymizing network. As a result, administrators block all known
exit nodes of anonymizing networks, denying anonymous access
to misbehaving and behaving users alike. To address this
problem, we present Nymble, a system in which servers can
“blacklist” misbehaving users, thereby blocking users without
compromising their anonymity. Our system is thus agnostic to
different servers’ definitions of misbehavior—servers can
blacklist users for whatever reason, and the privacy of blacklisted
users is maintained.
Index Terms—Anonymous blacklisting, privacy, revocation.
I.INTRODUCTION
ANONYMIZING networks such as Tor [18] route traffic
through independent nodes in separate administrative domains
to hide a client’s IP address. Unfortunately, some users have
misused such networks—under the cover of anonymity, users
have repeatedly defaced popular Web sites such as Wikipedia.
Since Web site administrators cannot blacklist individual
malicious users’ IP addresses, they blacklist the entire
anonymizing network. Such measures eliminate malicious
activity through anonymizing networks at the cost of denying
anonymous access to behaving users. In other words, a few
“bad apples” can spoil the fun for all. (This has happened
repeatedly with Tor.1) There are several solutions to this
problem, each providing some degree of accountability. In
pseudonymous credential systems [14], [17], [23], [28], users
log into Web sites using pseudonyms, which can be added to a
blacklist if a user misbehaves. Unfortunately, this approach
results in pseudonymity for all users, and weakens the
anonymity provided by the anonymizing network. Anonymous
credential systems [10], [12] employ group signatures. Basic
group signatures [1], [6], [15] allow servers to revoke a
misbehaving user’s anonymity by complaining to a group
manager. Servers must query the group manager for every
authentication, and thus, lacks scalability. Traceable signatures
[26] allow the group manager to release a trapdoor that allows
all signatures generated by a particular user to be traced; such
an approach does not provide the backward unlinkability [30]
that we desire, where a user’s accesses before the complaint
remain anonymous. Backward unlinkability allows for what we
call subjective blacklisting, where servers can blacklist users for
whatever reason since the privacy of the blacklisted user is not
at risk. In contrast, approaches without backward unlinkability
need to pay careful attention to when and why a user must have
all their connections linked, and users must worry about
whether their behaviors will be judged fairly. Subjective
blacklisting is also better suited to servers
such as Wikipedia, where misbehaviors such as questionable
edits to a Webpage, are hard to define in mathematical terms. In
some systems, misbehavior can indeed be defined precisely. For
instance, double spending of an “e-coin” is considered a
misbehavior in anonymous e-cash systems [8], [13], following
which the offending user is deanonymized. Unfortunately, such
systems work for only narrow definitions of misbehavior—it is
difficult to map more complex notions of misbehavior onto
“double spending” or related approaches [32]. With dynamic
accumulators [11], [31], a revocation operation results in a new
accumulator and public parameters for the group, and all other
existing users’ credentials must be updated, making it
impractical. Verifier-local revocation (VLR) [2], [7], [9] fixes
this shortcoming by requiring the server (“verifier”) to perform
only local updates during revocation.
Unfortunately,VLRrequires heavy computation at the server
that is linear in the size of the blacklist. For example, for a
blacklist with 1,000 entries, each authentication would take tens
of seconds,2 a prohibitive cost in practice. In contrast, our
scheme takes the server about one millisecond per
authentication, which is several thousand times faster than
VLR. We believe these low overheads will incentivize servers
to adopt such a solution when weighed against the potential
benefits of anonymous publishing (e.g., whistle-blowing,
reporting, anonymous tip lines, activism, and so on.).3
1.1 Our Solution
We present a secure system called Nymble, which
provides all anonymous authentication, backward unlinkability,
subjective blacklisting, fast authentication speeds, rate-limited
anonymous connections, revocation auditability (where users

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can verify whether they have been blacklisted), and also
addresses the Sybil attack [19] to make its deployment practical.
In Nymble, users acquire an ordered collection of nymbles, a
special type of pseudonym, to connect toWebsites. Without
additional information, these nymbles are computationally hard
to link,4 and hence, using the stream of nymbles simulates
anonymous access to services. Web sites, however, can blacklist
users by obtaining a seed for a particular nymble, allowing them
to link future nymbles from the same user—those used before
the complaint remain unlinkable. Servers can therefore blacklist
anonymous users without knowledge of their IP addresses while
allowing behaving users to connect anonymously. Our system
ensures that users are aware of their blacklist status before they
present a nymble, and disconnect immediately if they are
blacklisted. Although our work applies to anonymizing
networks in general, we consider Tor for purposes of
exposition. In fact, any number of anonymizing networks can
rely on the same Nymble system, blacklisting anonymous users
regardless of their anonymizing network(s) of choice.
1.2 Contributions of This Paper
Our research makes the following contributions:
Blacklisting anonymous users. We provide a means by which
servers can blacklist users of an anonymizing network while
maintaining their privacy. . Practical performance. Our protocol
makes use of inexpensive symmetric cryptographic operations
to significantly outperform the alternatives.Open-source
implementation. With the goal of contributing a workable
system, we have built an open-source implementation of
Nymble, which is publicly available.5 We provide performance
statistics to show that our system is indeed practical. Some of
the authors of this paper have published two anonymous
authentication schemes, BLAC [33] and PEREA [34], which
eliminate the need for a trusted third party for revoking users.
While BLAC and PEREA provide better privacy by eliminating
the TTP, Nymble provides authentication rates that are several
orders of magnitude faster than BLAC and PEREA (see Section
6). Nymble thus represents a practical solution for blocking
misbehaving users of anonymizing networks. We note that an
extended version of this paper is available as a technical report
[16].
Fig. 1. The Nymble system architecture showing the various modes of
interaction. Note that users interact with the NM and servers though the
anonymizing network.
2. AN OVERVIEW TO NYMBLE
We now present a high-level overview of the Nymble
system, and defer the entire protocol description and security
analysis to subsequent sections. 2.1 Resource-Based Blocking
To limit the number of identities a user can obtain (called the
Sybil attack [19]), the Nymble system binds nymbles to
resources that are sufficiently difficult to obtain in great
numbers. For example, we have used IP addresses as the
resource in our implementation, but our scheme generalizes to
other resources such as email addresses, identity certificates,
and trusted hardware. We address the practical issues related
with resource-based blocking in Section 8, and suggest other
alternatives for resources. We do not claim to solve the Sybil
attack. This problem is faced by any credential system [19],
[27], and we suggest some promising approaches based on
resource-based blocking since we aim to create a real-world
deployment. 2.2 The Pseudonym Manager The user must first
contact the Pseudonym Manager (PM) and demonstrate control
over a resource; for IP-address blocking, the user must connect
to the PM directly (i.e., not through a known anonymizing
network), as shown in Fig. 1. We assume the PM has
knowledge about Tor routers, for example, and can ensure that
users are communicating with it directly.6 Pseudonyms are
deterministically chosen based on the controlled resource,
ensuring that the same pseudonym is always issued for the same
resource. Note that the user does not disclose what server he or
she intends to connect to, and the PM’s duties are limited to
mapping IP addresses (or other resources) to pseudonyms. As
we will explain, the user contacts the PM only once per
linkability window (e.g., once a day). 2.3 The Nymble Manager
After obtaining a pseudonym from the PM, the user connects to
the Nymble Manager (NM) through the anonymizing network,
and requests nymbles for access to a particular server (such as
Wikipedia). A user’s requests to the NM are therefore
pseudonymous, and nymbles are generated using the user’s

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pseudonym and the server’s identity. These nymbles are thus
specific to a particular user-server pair. Nevertheless, as long as
the PM and the NM do not collude, the Nymble system cannot
identify which user is connecting to what server; the NM knows
only the pseudonym-server pair, and the PM knows only the
user identity-pseudonym pair.
Fig. 2. The life cycle of a misbehaving user. If the server complains in
time period tc about a user’s connection in t_, the user becomes linkable
starting in tc. The complaint in tc can include nymble tickets from only
tc_1 and earlier.
To provide the requisite cryptographic protection and security
properties, the NM encapsulates nymbles within nymble tickets.
Servers wrap seeds into linking tokens, and therefore, we will
speak of linking tokens being used to link future nymble tickets.
The importance of these constructs will become apparent as we
proceed.
2.4 Time
Nymble tickets are bound to specific time periods. As
illustrated in Fig. 2, time is divided into linkability windows of
duration W, each of which is split into L time periods of
duration T (i.e., W =L * T ).We will refer to time periods and
linkability windows chronologically as t1; t2; . . . ; tL and w1; w2;
. . . , respectively. While a user’s access within a time period is
tied to a single nymble ticket, the use of different nymble tickets
across time periods grants the user anonymity between time
periods. Smaller time periods provide users with higher rates of
anonymous authentication, while longer time periods allow
servers to rate-limit the number of misbehaviors from a
particular user before he or she is blocked. For example, T
could be set to five minutes, and W to one day (and thus, L =
288). The link ability window allows for dynamism since
resources such as IP addresses can get reassigned and it is
undesirable to blacklist such resources indefinitely, and it
ensures forgiveness of misbehavior after a certain period of
time. We assume all entities are time synchronized (for
example, with time.nist.gov via the Network Time Protocol
(NTP)), and can thus calculate the current linkability window
and time period.
2.5 Blacklisting a User
If a user misbehaves, the server may link any future
connection from this user within the current linkability window
(e.g., the same day). Consider Fig. 2 as an example: A user
connects and misbehaves at a server during time period t_ within
linkability window w*. The server later detects this misbehavior
and complains to the NM in time period tc (t* < tc ≤ tL) of the
same linkability window w*. As part of the complaint, the server
presents the nimble ticket of the misbehaving user and obtains
the corresponding seed from the NM. The server is then able to
link future connections by the user in time periods tc, tc + 1,... tL
of the same linkability window w* to the complaint. Therefore,
once the server has complained about a user, that user is
blacklisted for the rest of the day, for example (the linkability
window). Note that the user’s connections in t1; t2... . t*, t*+ 1 .
. . . tc remain unlinkable (i.e., including those since the
misbehavior and until the time of complaint). Even though
misbehaving users can be blocked from making connections in
the future, the users’ past connections remain unlinkable, thus
providing backward unlinkability and subjective blacklisting.
2.6 Notifying the User of Blacklist Status
Users who make use of anonymizing networks expect
their connections to be anonymous. If a server obtains a seed for
that user, however, it can link that user’s subsequent
connections. It is of utmost importance then that users be
notified of their blacklist status before they present a nymble
ticket to a server. In our system, the user can download the
server’s blacklist and verify her status. If blacklisted, the user
disconnects immediately. Since the blacklist is
cryptographically signed by the NM, the authenticity of the
blacklist is easily verified if the blacklist was updated in the
current time period (only one update to the blacklist per time
period is allowed). If the blacklist has not been updated in the
current time period, theNMprovides servers with “daisies”
every time period so that users can verify the freshness of the
blacklist (“blacklist from time period told is fresh as of time
period tnow”). As discussed in Section 4.3.4, these daisies are
elements of a hash chain, and provide a lightweight alternative
to digital signatures. Using digital signatures and daisies, we
thus ensure that race conditions are not possible in verifying the
freshness of a blacklist.Auser is guaranteed that he or she will
not be linked if the user verifies the integrity and freshness of
the blacklist before sending his or her nymble ticket.
2.7 Summary of Updates to the Nymble Protocol
We highlight the changes to Nymble since our
conference paper [24]. Previously, we had proved only the
privacy properties associated with nymbles as part of a two-
tiered hash chain. Here, we prove security at the protocol level.
This process gave us insights into possible (subtle) attacks
against privacy, leading us to redesign our protocols and refine
our definitions of privacy. For example, users are now either

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legitimate or illegitimate, and are anonymous within these sets
(see Section 3). This redefinition affects how a user establishes
a “Nymble connection” (see Section 5.5), and now prevents the
server from distinguishing between users who have already
connected in the same time period and those who are
blacklisted, resulting in larger anonymity sets.
A thorough protocol redesign has also resulted in several
optimizations. We have eliminated blacklist version numbers
and users do not need to repeatedly obtain the current version
number from the NM. Instead servers obtain proofs of freshness
every time period, and users directly verify the freshness of
blacklists upon download. Based on a hashchain approach, the
NM issues lightweight daisies to servers as proof of a
blacklist’s freshness, thus making blacklist updates highly
efficient. Also, instead of embedding seeds, on which users
must perform computation to verify their blacklist status, the
NM now embeds a unique identifier nymble*, which the user
can directly recognize. Finally, we have compacted several data
structures, especially the servers’ blacklists, which are
downloaded by users in each connection, and report on the
various sizes in detail in Section 6.Wealso report on our open-
source implementation of Nymble, completely rewritten as a C
library for efficiency.
3. SECURITY MODEL
Nymble aims for four security goals. We provide
informal definitions here; a detailed formalism can be found in
our technical report [16], which explains how these goals must
also resist coalition attacks.
3.1 Goals and Threats
An entity is honest when its operations abide by the
system’s specification. An honest entity can be curious: it
attempts to infer knowledge from its own information (e.g., its
secrets, state, and protocol communications). An honest entity
becomes corrupt when it is compromised by an attacker, and
hence, reveals its information at the time of compromise, and
operates under the attacker’s full control, possibly deviating
from the specification. Blacklistability assures that any honest
server can indeed block misbehaving users. Specifically, if an
honest server complains about a user that misbehaved in the
current linkability window, the complaint will be successful and
the user will not be able to “nymble-connect,” i.e., establish a
Nymble-authenticated connection, to the server successfully in
subsequent time periods (following the time of complaint) of
that linkability window. Rate-limiting assures any honest server
that no user can successfully nymble-connect to it more than
once within any single time period. Nonframeability guarantees
that any honest user who is legitimate according to an honest
server can nymble-connect to that server. This prevents an
attacker from framing a legitimate honest user, e.g., by getting
the user blacklisted for someone else’s misbehavior. This
property assumes each user has a single unique identity. When
IP addresses are used as the identity, it is possible for a user to
“frame” an honest user who later obtains the same IP address.
Nonframeablity holds true only against attackers with different
identities (IP addresses). A user is legitimate according to a
server if she has not been blacklisted by the server, and has not
exceeded the rate limit of establishing Nymble connections.
Honest servers must be able to differentiate between legitimate
and illegitimate users. Anonymity protects the anonymity of
honest users, regardless of their legitimacy according to the
(possibly corrupt) server; the server cannot learn any more
information beyond whether the user behind (an attempt to
make) a nymble connection is legitimate or illegitimate.
Fig. 3. Who trusts whom to be how for what guarantee.
3.2 Trust Assumptions
We allow the servers and the users to be corrupt and
controlled by an attacker. Not trusting these entities is important
because encountering a corrupt server and/or user is a realistic
threat. Nymble must still attain its goals under such
circumstances. With regard to the PM and NM, Nymble makes
several assumptions on who trusts whom to be how for what
guarantee. We summarize these trust assumptions as a matrix in
Fig. 3. Should a trust assumption become invalid, Nymble will
not be able to provide the corresponding guarantee. For
example, a corrupt PM or NM can violate Blacklistability by
issuing different pseudonyms or credentials to blacklisted users.
A dishonest PM (resp., NM) can frame a user by issuing her the
pseudonym (resp., credential) of another user who has already
been blacklisted. To undermine the Anonymity of a user, a
dishonest PM (resp., NM) can first impersonate the user by
cloning her pseudonym (resp., credential) and then attempt to
authenticate to a server—a successful attempt reveals that the
user has already made a connection to the server during the time
period. Moreover, by studying the complaint log, a curious NM
can deduce that a user has connected more than once if she has
been complained about two or more times. As already described
in Section 2.3, the user must trust that at least the NM or PM is
honest to keep the user and server identity pair private.
4.PRELIMINARIES
4.1 Notation
The notation a €R S represents an element drawn
uniformly at random from a nonempty set S.N0 is the set of
nonnegative integers, and N is the set N 0{0}. s [i] is the ith
element of list s. s║t the concatenation of (the unambiguous

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encoding of) lists s and t. The empty list is denoted by ø. We
sometimes treat lists of tuples as dictionaries. For example, if L
is the list ((Alice, 1234), (Bob, 5678)), then L[Bob] denotes the
tuple (Bob, 5678). If A is an (possibly probabilistic) algorithm,
then A(x) denotes the output when A is executed given the input
x. a := b means that b is assigned to a.
4.2 Cryptographic Primitives
Nymble uses the following building blocks (concrete
instantiations are suggested in Section 6):. Secure cryptographic
hash functions. These are oneway and collision-resistant
functions that resemble random oracles [5]. Denote the range of
the hash functions by H.
• Secure message authentication (MA) [3]. These
consist of the key generation (MA.KeyGen), and the
message authentication code (MAC) computation
(MA.Mac) algorithms. Denote the domain of MACs
by M.
• Secure symmetric-key encryption (Enc) [4]. These
consist of the key generation (Enc.KeyGen),
encryption (Enc.Encrypt), and decryption
(Enc.Decrypt) algorithms. Denote the domain of
ciphertexts by _.
• Secure digital signatures (Sig) [22]. These consist of
the key generation (Sig.KeyGen), signing (Sig.Sign),
and verification (Sig.Verify) algorithms. Denote the
domain of signatures by .
4.3 Data Structures
Nymble uses several important data structures:
4.3.1 Pseudonyms
The PM issues pseudonyms to users. A pseudonym
pnym has two components nym and mac: nym is a
pseudorandom mapping of the user’s identity (e.g., IP
address),7 the linkability window w for which the pseudonym is
valid, and the PM’s secret key ;mac is a MAC
that the NM uses to verify the integrity of the pseudonym.
Algorithms 1 and 2 describe the procedures of creating and
verifying pseudonyms.
4.3.2 Seeds and Nymbles
A nymble is a pseudorandom number, which serves as
an identifier for a particular time period. Nymbles (presented by
a user) across periods are unlinkable unless a server has
blacklisted that user. Nymbles are presented as part of a nymble
ticket, as described next. As shown in Fig. 4, seeds evolve
throughout a linkability window using a seed-evolution function
f; the seed for the next time period (seednext) is computed from
the seed for the current time period (seedcur) as
The nymble (nimblet) for a time period t is evaluated by
applying the nymble evaluation function g to its corresponding
seed (seedt), i.e.,
The NM sets seed0 to a pseudorandom mapping of the user’s
pseudonym pnym, the (encoded) identity sid of the server (e.g.,
domain name), the linkability window w for which the seed is
valid, and the NM’s secret key seedKeyN. Seeds are therefore
specific to user-server-window combinations As a consequence,
a seed is useful only for a particular server to link a particular
user during a particular linkability window. In our Nymble

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construction, f and g are two distinct cryptographic hash
functions. Hence, it is easy to compute future nymbles starting
from a particular seed by applying f and g appropriately, but
infeasible to compute nymbles otherwise. Without a seed, the
sequence of nymbles appears unlinkable, and honest users can
enjoy anonymity. Even when a seed for a particular time period
is obtained, all the nymbles prior to that time period remain
unlinkable.
4.3.3 Nymble Tickets and Credentials
A credential contains all the nymble tickets for a
particular linkability window that a user can present to a
particular server. Algorithm 3 describes the following procedure
of generating a credential upon request: A ticket contains a
nymble specific to a server, time period, and linkability
window. ctxt is encrypted data that the NM can use during a
complaint involving the nymble ticket. In particular, ctxt
contains the first nymble (nymble_) in the user’s sequence of
nymbles, and the seed used to generate that nymble. Upon a
complaint, the NM extracts the user’s seed and issues it to the
server by evolving the seed, and nymble_ helps the NM to
recognize whether the user has already been blacklisted
The MACs macN and macNS are used by the NM and the server,
respectively, to verify the integrity of the nimble ticket, as
described in Algorithms 4 and 5. As will be explained later, the
NM will need to verify the ticket’s integrity upon a complaint
from the server.
4.3.4 Blacklists
A server’s blacklist is a list of nymble*s corresponding
to all the nymbles that the server has complained about. Users
can quickly check their blacklisting status at a server by
checking to see whether their nymble*
appears in the server’s
blacklist (see Algorithm 6).
Blacklist integrity. It is important for users to be able to check
the integrity and freshness of blacklists, because, otherwise,
servers could omit entries or present older blacklists and link
users without their knowledge. The NM signs the blacklist (see
Algorithm 7), along with the server identity sid, the current time
period t, current linkability window w, and target (used for
freshness, explained soon), using its signing key signKeyN. As
will be explained later,during complaint procedure, the NM
needs to update the server’s blacklist, and thus needs to check
the integrity of the blacklist presented by the server. To make
this operation more efficient, the NM also generates an MAC
using its secret key macKeyN (line 7). At the end of the signing
procedure, the NM returns a blacklist certificate (line 7), which
contains the time period for which the certificate was issued, a
daisy (used for freshness, explained soon), mac, and sig.
Algorithms 8 and 9 describe how users and the NM can verify
the integrity and freshness of blacklists.

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Blacklist freshness. If the NM has signed the blacklist for the
current time period, users can simply verify the digital signature
in the certificate to infer that the blacklist is both valid (not
tampered with) and fresh (since the current time period matches
the time period in the blacklist certificate). To prove the
freshness of blacklists every time period, however, the servers
would need to get the blacklists digitally signed every time
period, thus imposing a high load on the NM. To speed up this
process, we use a hash chain [20], [29] to certify that “blacklist
from time period t is still fresh.” As illustrated in Fig. 5, for
each complaint, the NM generates a new random seed daisyL for
a hash chain corresponding to time period L. It then computes
daisyL_1; daisyL_2; . . . ; daisyt up to current time period t by
successively hashing the previous daisy to generate thenext with
a cryptographic hash function h. For example, daisy5 ¼
hðdaisy6Þ. As outlined later (in Algorithm 13), target is set to
daisyt. Now, until the next update to the blacklist, the NM need
only release daisies for the current time period instead of
digitally signing the blacklist. Given a certificate from an older
time period and daisyt for current time period t, users can verify
the integrity and freshness of the blacklist by computing the
target from daisyt.
Fig. 6. Different types of channels utilized in Nymble.
4.3.5 Complaints and Linking Tokens
A server complains to the NM about a misbehaving
user by submitting the user’s nymble ticket that was used in the
offending connection. The NM returns a seed, from which the
server creates a linking token, which contains the seed and the
corresponding nymble. Each server maintains a list of linking
tokens in a linking list, and updates each token on the list every
time period. When a user presents a nymble ticket, the server
checks the nymble within the ticket against the nymbles in the
linking-list entries. A match indicates that the user has been
blacklisted.
4.4 Communication Channels
Nymble utilizes three types of communication
channels, namely, type-Basic, -Auth, and -Anon (Fig. 6). We
assume that a public-key infrastructure (PKI) such as X.509 is
in place, and that the NM, the PM, and all the serversin Nymble
have obtained a PKI credential from a wellestablished and
trustworthy CA. (We stress that the users in Nymble, however,
need not possess a PKI credential.) These entities can thus
realize type-Basic and type-Auth channels to one another by
setting up a TLS8 connection using their PKI credentials. All
users can realize type-Basic channels to the NM, the PM, and
any server, again by setting up a TLS connection. Additionally,
by setting up a TLS connection over the Tor anonymizing
network,9 users can realize a type-Anon channel to the NM and
any server.
5.OUR NYMBLE CONSTRUCTION
5.1 System Setup
During setup, the NM and the PM interact as follows:
1. The NM executes NMInitState() (see Algorithm 10) and
initializes its state nmState to the algorithm’s output. 2. The NM
extracts macKeyNP from nmState and sends it to the PM over a
type-Auth channel. macKeyNP is a shared secret between the
NM and the PM, so that the NM can verify the authenticity of
pseudonyms issued by the PM. 3. The PM generates nymKeyP
by running Mac.Key- Gen() and initializes its state pmState to
the pair ðnymKeyP ; macKeyNP Þ. 4. The NM publishes
verKeyN in nmState in a way that the users in Nymble can
obtain it and verify its integrity at any time (e.g., during
registration).

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5.2 Server Registration
To participate in the Nymble system, a server with
identity sid initiates a type-Auth channel to the NM, and
registers with the NM according to the Server Registration
protocol below. Each server may register at most once in any
linkability window.
1. The NM makes sure that the server has not already
registered: If nmEntries in its nmState, it terminates with
failure; it proceeds otherwise.
2 . TheNM reads the current time period and linkability window
as tnow and wnow, respectively, and then obtains an svrState by
running (see Algorithm 11)
3. The NM appends svrState to its nmState, sends it to the
Server, and terminates with success.
4. The server, on receiving svrState, records it as its state, and
terminates with success.
In svrState, macKeyNS is a key shared between the NM and the
server for verifying the authenticity of nymble tickets;
timelastUpd indicates the time period when the blacklist was last
updated, which is initialized to tnow, the current time period at
registration.
5.3 User Registration
A user with identity uid must register with the PM
once in each linkability window. To do so, the user initiates a
type- Basic channel to the PM, followed by the User
Registration protocol described below.
1. The PM checks if the user is allowed to register. In our
current implementation, the PM infers the registering user’s IP
address from the communication channel, and makes sure that
the IP address does not belong to a known Tor exit node. If this
is not the case, the PM terminates with failure. 2. Otherwise, the
PM reads the current linkability window as wnow, and runs
The PM then gives pnym to the user, and terminates with
success.
3. The user, on receiving pnym, sets her state usrState and
terminates with success.
5.4 Credential Acquisition
To establish a Nymble connection to a server, a user
must provide a valid ticket, which is acquired as part of a
credential from the NM. To acquire a credential for server sid
during the current linkability window, a registered user initiates
a type-Anon channel to the NM, followed by the Credential
Acquisition protocol below.
1. The user extracts pnym from usrState and sends the pair
ðpnym; sidÞ to the NM.
2. The NM reads the current linkability window as wnow. It
takes sure the user’s pnym is valid: If returns false, the NM
terminates with failure; it proceeds otherwise.
3. The NM runs
4. The user, on receiving cred, creates usrEntry
ðsid; cred; falseÞ, appends it to its state usrState,
and terminates with success.
5.5 Nymble Connection Establishment
To establish a connection to a server sid, the user
initiates a type-Anon channel to the server, followed by the
Nymble connection establishment protocol described below.
5.5.1 Blacklist Validation
1. The server sends hblist; certi to the user, where blist is its
blacklist for the current time period and cert is the certificate on
blist. (We will describe how the server can update its blacklist
soon.)
2. The user reads the current time period and linkability window
as tðUÞ now and wðUÞ now and assumes these values to be current
for the rest of the protocol.
3. For freshness and integrity, the user checks if

9
9 7 8 8 1 9 2 4 0 3 1 8 2
If not, she terminates the protocol with failure.
5.5.2 Privacy Check
Since multiple connection establishment attempts by a
user to the same server within the same time period can be
linkable, the user keeps track of whether she has already
disclosed a ticket to the server in the current time period by
maintaining a boolean variable ticketDisclosed for the server in
her state. Furthermore, since a user who has been blacklisted by
a server can have her connection establishment attempts linked
to her past establishment, the user must make sure that she has
not been blacklisted thus far. Consequently, if ticketDisclosed in
usrEntries½sid_ in the user’s usrState is true, or
UserCheckIfBlacklistedusrStateðsid; blistÞ true; then it is unsafe
for the user to proceed and the user sets safe to false and
terminates the protocol with failure.10
5.5.3 Ticket Examination
5.6 Service Provision and Access Logging
If both the user and the server terminate with success
in the Nymble connection Establishment described above, the
servermay start serving the user over the same channel. The
server records ticket and logs the access during the session or a
potential complaint in the future.
5.7 Auditing and Filing for Complaints
If at some later time, the server desires to blacklist the
user behind a Nymble connection, during the establishment of
which the server collected ticket from the user, the server files a
complaint by appending ticket to cmplnt-tickets in its svrState.
Filed complaints are batched up. They are processed
during the next blacklist update (to be described next).
5.8 Blacklist Update
Servers update their blacklists for the current time
period for two purposes. First, as mentioned earlier, the server
needs to provide the user with its blacklist (and blacklist
certificate) for the current time period during a Nymble
connection establishment. Second, the server needs to be able to
blacklist the misbehaving users by processing the newly filed
complaints (since last update). The procedure for updating
blacklists (and their certificates) differs depending on whether
complaints are involed. When there is no complaint (i.e., the
server’s cmplnt-tickets is empty), blacklists stay unchanged; the
certificates need only a “light refreshment.” When there are
complaints, on the other hand, new entries are added to the
blacklists and certificates need to be regenerated. Since these
updates are certified for integrity and freshness at the
granularity of time periods, multiple updates within a single
time period are disallowed (otherwise, servers could send users
stale blacklists).Our current implementation employs “lazy”
update: the server updates its blacklist upon its first Nymble
connection establishment request in a time period.
5.8.1 Without Complaints
1. The server with identity sid initiates a type-Auth channel to
the NM, and sends a request to the NM for a blacklist update.
2. The NM reads the current time period as tnow. It extracts
tlastUpd and daisyL from nmEntry for sid in nmState. If tlastUpd is
tnow, the server has already updated its blacklist for the current
time period, and the NM terminates the protocol as failure.
3. Otherwise, the NM updates tlastUpd to tnow. It computes daisy0
tnowþ1ÞðdaisyLÞ and sends tnow; daisy0Þ to the server.
4. The server replaces td and daisy in cert in blist in its svrState
with tnow and daisy0, respectively.
5.8.2 With Complaints
1. The server with identity sid initiates a type-Auth channel to
the NM and sends from its State as a blacklist update request.
2. The NM reads the current time period as tðNÞ now. It runs
NMHandleComplaintsnmState on input ðsid; tnow; wnow;
blist; cert; cmplnt-ticketsÞ. (See Algorithm 15.) If the
algorithm returns the NM considers the update request invalid,
in which case the NM terminates the protocol as failure.
3. Otherwise, the NM relays the algorithm’s output ðblist0;
cert0; seed,to the server.
4. The server updates its state svrState as follows: It replaces
blist and cert with blistkblist0 and cert0, respectively, and sets
cmplnt-tkts to ;. For each seed 2 seeds, the server creates a
token as ðseed; gðseedÞÞ and appends it to lnkng-tokens.
Finally, the server terminates with success. We now explain
what NMHandleComplaints does. The algorithm first checks
the integrity and freshness of the blacklist (lines 2-6) and that
the NM hasn’t already updated the server’s blacklist for the
current time period. It then checks if all complaints are valid for
some previous time period during the current
linkabilitywindow(lines 7-12). Finally, the algorithm prepares
an answer to the update request by invoking
NMComputeBLUpdate and NMComputeSeeds (see Algorithm
14) (lines 13-16). NMComputeBLUpdate (see Algorithm 13)
creates new entries to be appended to the server’s blacklist.
Each entry is either the actual nymble_ of the user being
complained about if the user has not been blacklisted already, or
a random nymble otherwise. This way, the server cannot learn if
two complaints are about the same user, and thus, cannot link
the Nymble connections to the same user. NMComputeSeeds

10
9 7 8 8 1 9 2 4 0 3 1 8 2
(see Algorithm 14) uses the same trick when computing a seed
that enables the server to link a blacklisted user.
5.9 Periodic Update
5.9.1 Per Time Period
At the end of each time period that is not the last of the
current linkability window, each registered server updates its
svrState by running (see Algorithm 7) which prepares the
linking tokn list for the new time period. Each entry is updated
by evolving the seed and computing the corresponding nymble.
Each registered user sets ticketDisclosed in every usrEntry in
usrState to false, signaling that the user has not disclosed any
ticket in the new time period.
5.9.2 Per Linkability Window
At the beginning of each linkability window, all the
entities, i.e., the PM, the NM, the servers, and the users erase
their state and start afresh. In other words, the NM and the PM
must resetup Nymble for the new current linkability window
and all servers and users must reregister if they still want to use
Nymble.
Fig. 7. The marshaled size of various Nymble data structures. The
X-axis refers to the number of entries—complaints in the blacklist update
request, tickets in the credential, tokens and seeds in the blacklist update
response, and nymbles in the blacklist
6.PERFORMANCE EVALUATION
We implemented Nymble and collected various
empirical performance numbers, which verify the linear (in the
number of “entries” as described below) time and space costs of
the various operations and data structures.

11
9 7 8 8 1 9 2 4 0 3 1 8 2
6.1 Implementation and Experimental Setup
We implemented Nymble as a C++ library along with
Ruby and JavaScript bindings. One could, however, easily
compile bindings for any of the languages (such as Python,
PHP, and Perl) supported by the Simplified Wrapper and
Interface Generator (SWIG), for example. We utilize OpenSSL
for all the cryptographic primitives. We use SHA-256 for the
cryptographic hash functions; HMAC-SHA-256 for the
message authentication MA; AES-256 in CBC-mode for the
symmetric encryption Enc; and 2,048-bit RSASSA-PSA for the
digital signatures Sig. We chose RSA over DSA for digital
signatures because of its faster verification speed—in our
system, verification occurs more often than signing. We
evaluated our system on a 2.2 GHz Intel Core 2 Duo Macbook
Pro with 4 GB of RAM. The PM, the NM, and the server were
implemented as Mongrel (Ruby’s version of Apache) servers.
The user portion was implemented as a Firefox 3 extension in
JavaScript withXPCOMbindings to the NymbleC++ library. For
each experiment relating to protocol performance, we report the
average of 10 runs. The evaluation of data structure sizes is the
byte count of the marshaled data structures that would be sent
over the network.
6.2 Experimental Results
Fig. 7 shows the size of the various data structures. The X-axis
represents the number of entries in each data structure—
complaints in the blacklist update request, tickets in the
credential (equal to L, the number of time periods in a
linkability window), nymbles in the blacklist, tokens and seeds
in the blacklist update response, and nymbles in the blacklist.
For example, a linkability window of one day with five minute
time periods equates to L ¼ 288.11 The size of a credential in
this case is about 59 KB. The size of a blacklist update request
with 50 complaints is roughly 11 KB, whereas the size of a
blacklist update response for 50 complaints is only about 4 KB.
The size of a blacklist (downloaded by users before each
connection) with 500 nymbles is 17 KB. In general, each
structure grows linearly as the number of entries increases.
Credentials and blacklist update requests grow at the same rate
because a credential is acollection of tickets which is more or
less what is sent as a complaint list when the server wishes to
update its blacklist. In our implementation, we use Google’s
Protocol Buffers to (un)marshal these structures because it is
cross-platform friendly and language-agnostic. Fig. 8a shows
the amount of time it takes the NM to perform various
protocols. It takes about 9 ms to create a credential when L ¼
288. Note that this protocol occurs only once in every
linkability window for each user wanting toconnect to a
particular server. For blacklist updates, the initial jump in the
graph corresponds to the fixed overhead associated with signing
a blacklist. To execute the update blacklist protocol with 500
complaints, it takes theNMabout 54 ms. However, when there
are no complaints, it takes the NM on average less than a
millisecond to update the daisy .
Fig.
8. Nymble’s performance at (a) the NM and (b) the user and the
server when performing various protocols. (a) Blacklist updates
take several milliseconds and credentials can be generated in 9 ms
for the suggested parameter of L ¼ 288. (b) The bottleneck
operation of server ticket examination is less than 1 ms and
validating the blacklist takes the user only a few ms.
7. SECURITY ANALYSIS
Theorem 1. Our Nymble construction has Blacklistability,
Rate-limiting, Nonframeability, and Anonymity provided
that the trust assumptions in Section 3.2 hold true, and the
cryptographic primitives used are secure. We summarize the
proof of Theorem 1. Please refer to our technical report [16] for
a detailed version.
7.1 Blacklistability
An honest PM and NM will issue a coalition of c unique users
at most c valid credentials for a given server. Because of the
security of HMAC, only the NM can issue valid tickets, and for
any time period, the coalition has at most c valid tickets, and
can thus make at most c connections tothe server in any time
period regardless of the server’s blacklisting. It suffices to
show that if each of the c users has been blacklisted in some
previous time period of the current linkability window, the
coalition cannot authenticate in the current time period k_.
Assume the contrary that connection establishment k_ using one
of the coalition members’ ticket_ was successful even though
the user was blacklisted in a previous time period k0. Since
connection establishments k0 and k_ were successful, the
corresponding tickets ticket0 and ticket_ must be valid.
Assuming the security of digital signatures and HMAC, an

12
9 7 8 8 1 9 2 4 0 3 1 8 2
honest server can always contact an honest NM with a valid
ticket and the NM will successfully terminate during the
blacklist update. Since the server blacklisted the valid ticket0
and updates its linking list honestly, the ServerLinkTicket will
return fail on input ticket_, and thus, the connection k_ must fail,
which is a contradiction.
7.2 Nonframeability
Assume the contrary that the adversary successfully framed
honest user i_ with respect to an honest server in time period t_,
and thus, user i_ was unable to connect in time period t_ using
ticket_ even though none of his tickets were previously
blacklisted. Because of the security of HMAC, and since the
PM and NM are honest, the adversary cannot forge tickets for
user i_, and the server cannot already have seen ticket_; it must
be that ticket_ was linked to an entry in the linking list. Thus,
there exists an entry ðseed_; nymble_Þ in the server’s linking
list, such that the nymble in ticket_ equals nymble_. The server
must have obtained this entry in a successful blacklist update
for some valid ticketb, implying the NM had created this ticket
for some user ~i. If ~i 6¼ i_, then user ~i’s seed0 is different
from user i_’s seed0 so long as the PM is honest, and yet the two
seed0’s evolve to the same seed_, which contradicts the
collisionresistance property of the evolution function. Thus, we
have ~i ¼ i_. But, as already argued, the adversary cannot forge
i_’s ticketb, and it must be the case that i_’s ticketb was
blacklisted before t_, which contradicts our assumption that i_
was a legitimate user in time t_.
7.3 Anonymity
We show that an adversary learns only that some legitimate user
connected or that some illegitimate user’s connection failed,
i.e., there are two anonymity sets of legitimate and illegitimate
users. Distinguishing between two illegitimate users. We argue
that any two chosen illegitimate users out of the control of the
adversary will react indistinguishably. Since All honest users
execute the Nymble connection Establishment protocol in
exactly the same manner up until the end of the Blacklist
validation stage (Section 5.5.1), it suffices to show that every
illegitimate user will evaluate safe to false, and hence, terminate
the protocol with failure at the end of the Privacy check stage
(Section 5.5.2). For an illegtimate user (attempting a new
connection) who has already disclosed a ticket during a
connection establishment earlier in the same time period,
ticketDisclosed for the server will have been set to true and safe
is evaluated to false during establishment k_. An illegitimate
user who has not disclosed a ticket during the same time period
must already be blacklisted. Thus, he server complained about
some previous ticket_ of the use. Since the NM is honest, the
user’s nymble_ appears in some previous blacklist of the server.
Since an honest NM never deletes entries from a blacklist, it
will appear in all subsequent blacklists, and safe is evaluated to
false for the current blacklist. Servers cannot forge blacklists or
present blacklists for earlier time periods (as, otherwise, the
digital signature would be forgeable, or the hash in the daisy
chain could be inverted). Distinguishing between two legitimate
users. The authenticit of the channel implies that a legitimate
user knows the correct identity of the server, and thus, Boolean
ticketDisclosed for the server remains false. Furthermore,
serCheckIfBlacklisted returns false (assuming the security of
digital signatures) and safe is evaluated to true for the legitimate
user. Now, in the ticket presented by the user, only nymble and
ctxt are functions of the user’s identity. Since the Adversary
does not know the decryption key, the CCA2 security of he
encryption implies that ctxt reveals no information about the
user’s identity to the adversary. Finally, since the server has not
obtained any seeds for the user, under the Random Oracle
model, the nymble presented by the user is indistinguishable
from random an cannot be linked with other nymbles presented
by the user. Furthermore, if and when the server complains
about a user’s tickets in the future, the NM ensures that only
one real seed is issued (subsequent seeds corresponding to the
same user are random values), and thus, the server cannot
distinguish between legitimate users for a particular time period
by issuing complaints in a future time period.
7.4 Across Multiple Linkability Windows
With multiple linkability windows, our Nymble construction still
has Accountability and Nonframeability because each icket is valid
for and only for a specific linkability window; it still has
Anonymity because pseudonyms are an output of a collision-
resistant function that takes the linkability window as input.
8. DISCUSSION
IP-address blocking. By picking IP addresses as the resource for
limiting the Sybil attack, our current implementation closely
mimics IP-address blocking employed by Internet services.
There are, however, some inherent limitations to using IP
addresses as the scarce resource. If a user can obtain multiple
addresses, she can circumvent both nymble-based and regular
IP-address blocking. Subnetbased blocking alleviates this
problem, and while it is possible to modify our system to
support subnet-based blocking, new privacy challenges emerge;
a more thorough description is left for future work. Other
resources. Users of anonymizing networks would be reluctant to
use resources that directly reveal their identity (e.g., passports
or a national PKI). Email addresses could provide more privacy,
but provide weak blacklistability guarantees because users can
easily create new email addresses. Other possible resources
include client puzzles [25] and e-cash, where users are required
to perform a certain amount of computation or pay money to
acquire a credential. These approaches would limit the number
of credentials obtained by a single individual by raising the cost
of acquiring credentials. Server-specific linkability windows.
An enhancement would be to provide support to vary T and L
for different servers. As described, our system does not support
varying linkability windows, but does support varying time
periods. This is because the PM is not aware of the server the

13
9 7 8 8 1 9 2 4 0 3 1 8 2
user wishes to connect to, yet it must issue pseudonyms specific
to a linkability window. We do note that the use of resources
such as client puzzles or e-cash would eliminate the need for a
PM, and users could obtain Nymbles directly TSANG ET AL.:
NYMBLE: BLOCKING MISBEHAVING USERS IN
ANONYMIZING NETWORKS 267 from the NM. In that case,
server-specific linkability windows could be used. Side-channel
attacks. While our current implementation does not fully protect
against side-channel attacks, we mitigate the risks. We have
implemented various algorithms in a way that their execution
time leaks little information that cannot already be inferred from
the algorithm’s output. Also, since a confidential channel does
not hide the size of the communication, we have constructed the
protocols so that each kind of protocol message is of the same
size regardless of the identity or current legitimacy of the user.
9. CONCLUSIONS
We have proposed and built a comprehensive credential system
called Nymble, which can be used to add a layer of
accountability to any publicly known anonymizing network.
Servers can blacklist misbehaving users while maintaining their
privacy, and we show how these properties can be attained in a
way that is practical, efficient, and sensitive to the needs of both
users and services.We hope that ur work will increase the
mainstream acceptance of anonymizing networks such as Tor,
which has, thus far, been completely blocked by several
services because of users who abuse their anonymity.
ACKNOWLEDGMENTS The authors wishto thank Peter C.
Johnson and Daniel Peebles for their help in the early stages of
prototyping. They are also grateful for the suggestions and help
from Roger Dingledine and Nick Mathewson. This research was
supported in part by the US National Science Foundation, under
grant CNS-0524695, and the Bureau of Justice Assistance, u der
grant 2005-DD-BX-1091. The views and conclusions do-not
necessarily reflect the views of the sponsors. Nymble first
appeared in a PET ’07 paper [24].
This paper presents a significantly improved construction and a
complete rewrite and evaluation of our (open-source)
implementation (see Section 2.7 for a summary of changes). We
dedicate this paper to the memory of Patrick Tsang.
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