Blocking Misbehaving Users in Anonymizing Networks: Nymbles

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Blocking Misbehaving Users in Anonymizing Networks: Nymbles

Blocking Misbehaving Users in Anonymizing Networks: Nymbles


IT Department, III-year, Anna University

Vivekanandha college of Engineering for Women, Tiruchengode,

Tamilnadu, India.


IT Department, III-year, Anna University

Vivekanandha college of Engineering for Women, Tiruchengode,

Tamilnadu, India.

Abstract Anonymizing networks such as allow users to access Internet services privately by using a series of routers to hide the clients 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 websites. Website 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 denitions of misbehavior servers can blacklist users for whatever reason, and the privacy of blacklisted users is maintained.

  1. INTRODUCTION (Heading 1)

    Anonymizing networks such as Tor [18] route traffic through independent nodes in separate administrative domains to hide a clients IP address. Unfortunately, some users have misused such networks

    under the cover of anonymity, users have repeatedly defaced popular websites 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 pro- viding some degree of accountability. In pseudonymous credential systems [14], [17], [23], [28], users log into websites 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 users 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 man-ager to release a trapdoor that allows all signatures generated by a particular user to be traced; such an approach does not provide the backward unlink ability

    [30] that we desire, where a users accesses before the complaint remain anonymous. Backward unlink ability 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 unlink ability 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.

    Fig 1 The Nymble system architecture 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 dened precisely. For instance, double- spending of an e-coin is considered misbehavior in anonymous e-cash systems [8], [13], following which the offending user is deanonymized. Unfortunately, such systems work for only narrow denitions 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. Verier local revocation (VLR) [2], [7], [9] xes this shortcoming by requiring the server (verier) to perform only local updates during revocation. Unfortunately, VLR requires 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 benet of anonymous publishing (e.g., whistle-blowing, reporting, anonymous tip lines, activism, and so on.).


    We now present a high-level overview of the Nymble system, and defer the entire protocol description and security analysis to subsequent sections.

    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. The Pseudonym Manager

      The user must rst 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 Figure 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 de- terministically 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 PMs duties are limited to mapping IP addresses (or other resources) to pseudonyms. As we will explain, the user contacts the PM only once per link ability window (e.g., once a day).

    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 users requests to the NM are therefore pseudonymous, and nymbles are generated using the users pseudonym and the servers 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.

      To provide the requisite cryptographic protetion 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.

    4. Time

      Nymble tickets are bound to specic time periods. As illustrated in Figure 2, time is divided into link ability windows of duration W, each of which is split into L time periods of duration T (i.e., W = LT ). We will refer to time periods and linkability windows chronologically as t1, t2, . . . , tL and w1, w2, .. . respectively. While a users 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 5 minutes, and W to 1 day (and thus L = 288).

      Fig 2 Misbehaving users life cycle.

      The linkability window allows for dynamism since resources such as IP addresses can get re-assigned and it is undesirable to blacklist such resources indenitely, and it ensures forgiveness of misbehavior after a certain period of time. We assume all entities are time synchronized and can thus calculate the current linkability window and time period. An excellent style manual for science writers is [7] if the server complains in time period tc about a users connection in t, the user becomes linkable starting in tc. The complaint in tc can include nymble tickets from only tc1 and earlier.

    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 Figure 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 nymble 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 users 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.

    6. Notifying the user of Blacklist Status

    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 Figure 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. Since the blacklist is cryptographically signed by the NM, the authenticity of the blacklist is easily veried 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 cur- rent time period, the NM provides 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. A user is guaranteed that he or she will not be linked if the user veries the integrity and freshness of the blacklist before sending his or her nymble ticket.


    Nymble aims for four security goals. We provide informal denitions here; a detailed formalism can be found in our technical report [16], which explains how these goals must also resist coalition attacks.

    A. Goals and Threats

    An entity is honest when its operations abide by the systems specication. 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 attackers full control, possibly deviating from the specication.

    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

    1. Notation


    the same IP address. Non-frameability 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.

    1. 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 Figure 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 Black-list ability by issuing different pseudonyms or dentials 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 rst impersonate the user by cloning her pseudonym (resp. credential) and then attempt to authenticate to a servera 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.

    The notation a R S represents an element

    drawn uniformly at random from non-empty set S. N0 is the set of non-negative integers, and N is the set N0\{0}. s[i] is the ith element of list s. s||t is the concatenation of (the unambiguous encoding of) lists s and t. The empty list is denoted by . 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 a (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.

    1. Cryptographic Primitives

      Nymble uses the following building blocks (concrete instantiations are suggested in Section 6):

      • Secure cryptographic hash functions. These are one- way and collision-resistant functions that resemble random oracles [5]. Denote the range of the hash functions by H.

      • p>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 verication (Sig.Verify) algorithms. Denote the domain of signatures by .

    2. Data Structures

      Nymble uses several important data structures:

      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 (seed cur) as

      Seednext = f (seed cur).

      The nymble (nymblet) for a time period t is evaluated by applying the nymble-evaluation function g to its corresponding

      Seed (seedt), i.e., nymblet = g (seedt).

      The NM sets seed 0 to a pseudo-random mapping

      of the users 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 NMs Secret key seedKeyN . Seeds are therefore specic 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.

    3. Communication Channels

    Nymble utilizes three types of communication channels, namely type-Basic, -Auth and -Anon (Figure 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 servers in Nymble have obtained a PKI credential from a well-established 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.


  1. System steup

    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 algorithms 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.KeyGen() and initializes its state pmState to the pair (nymKeyP , macKeyNP ).

    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(eg during registration).

  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 (Sid , ·, ·) nmEntries in its nmState, it terminates with failure; it proceeds otherwise.

    2. The NM reads the current time period and linkability window as tnow and wnow respectively, and then obtains a svrState by running (see Algorithm 11)

      NMRegisterServernmState(sid , tnow, wnow).

    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.

  3. User Registration

    A user with identity uid must register with the PM once 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 users 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

    2. Otherwise, the PM reads the current link ability window as wnow, and runs with success.

      pnym := PMCreatePseudonympmState (uid , wnow).

      The PM then gives pnym to the user, and terminates

    3. The user, on receiving pnym, sets her state usrState to (pnym, ), and terminates with success.

  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 (pnym, sid) to the NM.

  2. The NM reads the current linkability window as wnow. It makes sure the users pnym is valid: If

    NMVerifyPseudonymnmState (pnym, wnow) returns false, the NM terminates with failure; it proceeds otherwise.

  3. The NM runs which returns a credential cred . NMCreateCredentialnmState (pnym, sid , wnow),The NM sends cred to the user and terminates with success.

  4. The user, on receiving cred , creates usrEntry: = (sid, cred , false), appends it to its state usrState, and terminates with success.


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.

  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 Simplied Wrapper and Interface Generator (SWIG) for example. We utilize Open SSL 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 2048-bit RSASSA

    -PSA for the digital signatures

    We chose RSA over DSA for digital signatures because of its faster verication speedin our system, verication 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 (Rubys version of Apache) servers. The user portion was implemented as a Firefox 3 extension in JavaScript with XPCOM bindings to the Nymble C++ 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 marshalled data structures that would be sent over the network.

  2. Experimental Result

The X-axis represents the number of entries in each data structurecomplaints in the blacklist update request, tickets in the credential (equal to L, the number of time periods in a linkability window), nymbles in the black-list, tokens and seeds in the blacklist update response, and nymbles in the blacklist. For example, a linkability window of 1 day wth 5 minute time periods equates to L =

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 4KB. The size of a blacklist 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 a collection 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 Googles Protocol Buffers to (un)marshal these structures because it is cross-platform friendly and language-agnostic.

Figure 8(a) shows the amount of time it takes the NM to perform various protocols. It takes about 9 ms to create a credential when L = 288. Note that this protocol occurs only once every linkability window for each user wanting to connect to a particular server. For blacklist updates, the initial jump in the graph corresponds to the xed overhead associated with signing a blacklist. To execute the update blacklist protocol with 500 complaints it takes the NM about 54 ms. However, when there are no complaints, it takes the NM on average less than a millisecond to update the daisy.

Figure 8(b) shows the amount of time it takes the server and user to perform various protocols. These protocols are relatively inexpensive by design, i.e., the amount of computation performed by the users and servers should be minimal. For example, it takes less than 3 ms for a user to execute a security check on a blacklist with 500 nymbles. Note that this gure includes signature verication as well, and hence the xed-cost overhead exhibited in the graph. It takes less than a millisecond for a server to perform authentication of a ticket against a blacklist with 500 nymbles. Every time period (e.g., every 5 minutes), a server must update its state and blacklist. Given a linking list with 500 entries, the server will spend less than 2 ms updating the linking

list. If the server were to issue a blacklist update request with 500 complaints, it would take less than 3 ms for the server to update its blacklist.


Theorem 1: Our Nymble construction has Blacklistability, Rate-limiting, Non-frameability and anonymity provided that the trust assumption in session 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.

  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 to the server in any time period regardless of the servers 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 k_. Since connection establishments k_ and k were successful, the corresponding tickets ticket_ and ticket must be valid. Assuming the security of digital signatures and HMAC, an 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 ticket_ 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.

  2. Non-Frameability

    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 (seed, nymble) in the servers link- ing 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 =i, then user is seed 0 is different from user is seed 0 so long as the PM is honest, and yet the two seed 0s evolve to the same seed, which contradicts the collision-

    resistance property of the evolution function. Thus we have i = i. But as already argued, the adversary cannot forge is ticketb, and it must be the case that is ticketb was blacklisted before t, which

    contradicts our assumption that i was a legitimate user in time t.

  3. Anonymity

We show that an adversary learns only that some legitimate user connected or that some illegitimate users connection failed, i.e., there are two anonymity sets of

legitimate and illegitimate users.

For an illegitimate user (attempting a new connection) who has already disclosed a ticket during a connection establishment earlier in the same time period, ticket.

Disclosed 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 the server complained about some previous ticket of the user. Since the NM is honest, the users 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).

Furthermore, UserCheckIfBlacklisted 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 users identity. Since the adversary does not know the decryption key, the CCA2 security of the encryption implies that ctxt reveals no information about the users 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 and cannot be linked with other nymbles presented by the user. Furthermore, if and when the server complains about a users 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.

D.Across multiple linkability windows

With multiple linkability windows, our Nymble construction still has Accountability and Nonframeability because each ticket is valid for and only for a specic linkability window; it still has Anonymity because pseudonyms are an output of a collision-resistant function that takes the linkability window as input.


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 prop- erties can be attained in a way that is practical, efient, and sensitive to needs of both users and services.

We hope that our 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.

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