Vitaly Shmatikov, and
Computer Science Department
Stanford, CA 94305
The Secure Sockets Layer (SSL) protocol is analyzed using a finite-state enumeration tool called Mur . The analysis is presented using a sequence of incremental approximations to the SSL 3.0 handshake protocol. Each simplified protocol is ``model-checked'' using Mur , with the next protocol in the sequence obtained by correcting errors that Mur finds automatically. This process identifies the main shortcomings in SSL 2.0 that led to the design of SSL 3.0, as well as a few anomalies in the protocol that is used to resume a session in SSL 3.0. In addition to some insight into SSL, this study demonstrates the feasibility of using formal methods to analyze commercial protocols.
In previous work , a general-purpose finite-state analysis tool has been successfully applied to the verification of small security protocols such as the Needham-Schroeder public key protocol, Kerberos, and the TMN cellular telephone protocol. The tool, Mur [3, 10], was designed for hardware verification and related analysis. In an effort to understand the difficulties involved in analyzing larger and more complex protocols, we use Mur to analyze the SSL 3.0 handshake protocol. This protocol is important, since it is the de facto standard for secure Internet communication, and a challenge, since it has more steps and greater complexity than the other security protocols analyzed using automated finite-state exploration. In addition to demonstrating that finite-state analysis is feasible for protocols of this complexity, our study also points to several anomalies in SSL 3.0. However, we have not demonstrated the possibility of compromising sensitive data in any implementation of the protocol.
In the process of analyzing SSL 3.0, we have developed a ``rational reconstruction'' of the protocol. More specifically, after initially attempting to familiarize ourselves with the handshake protocol, we found that we could not easily identify the purpose of each part of certain messages. Therefore, we set out to use our analysis tool to identify, for each message field, an attack that could arise if that field were omitted from the protocol. Arranging the simplified protocols in the order of increasing complexity, we obtain an incremental presentation of SSL. Beginning with a simple, intuitive, and insecure exchange of the required data, we progressively introduce signatures, hashed data, and additional messages, culminating in a close approximation of the actual SSL 3.0 handshake protocol.
In addition to allowing us to understand the protocol more fully in a relatively short period of time, this incremental reconstruction also provides some evidence for the ``completeness" of our analysis. Specifically, Mur exhaustively tests all possible interleavings of protocol and intruder actions, making sure that a set of correctness conditions is satisfied in all cases. It is easy for such analysis to be ``incomplete" by not checking all of the correctness conditions intended by the protocol designers or users. In developing our incremental reconstruction of SSL 3.0, we were forced to confirm the importance of each part of each message. In addition, since no formal or high-level description of SSL 3.0 was available, we believe that the description of SSL 3.0 that we extracted from the Internet Draft  may be of interest.
Our analysis covers both the standard handshake protocol used to initiate a secure session and the shorter protocol used to resume a session [6, Section 5.5,]. Mur analysis uncovered a weak form of version rollback attack (see Section 4.9.2) that can cause a version 3.0 client and a version 3.0 server to commit to SSL 2.0 when the protocol is resumed. Another attack on the resumption protocol (described in Sections 4.8 and 4.9.1) is possible in SSL implementations that strictly follow the Internet draft  and allow the participants to send application data without waiting for an acknowledgment of their Finished messages. Finally, an attack on cryptographic preferences (see Section 4.6) succeeds if the participants support weak encryption algorithms which can be broken in real time. Apart from these three anomalies, we were not able to uncover any errors in our final protocol. Since SSL 3.0 was designed to be backward-compatible, we also implemented and checked a full model for SSL 2.0 as part of the SSL 3.0 project. In the process, Mur uncovered the major problems with SSL 2.0 that motivated the design of SSL 3.0.
Our Mur analysis of SSL is based on the assumption that cryptographic functions cannot be broken. For this and other reasons (discussed below), we cannot claim that we found all attacks on SSL. But our analysis has been efficient in helping discover an important class of attacks.
The two prior analyses of SSL 3.0 that we are aware of are an informal assessment carried out by Wagner and Schneier  and a formal analysis by Dietrich using a form of belief logic . (We read the Wagner and Schneier study before carrying out our analysis, but did not become aware of the Dietrich study until after we had completed the bulk of our work.) Wagner and Schneier comment on the possibility of anomalies associated with resumption, which led us to concentrate our later efforts on this area. It is not clear to us at the time of this writing whether we found any resumption anomalies that were not known to these investigators. However, in email comments resulting from circulation of an earlier document , we learned that while our second anomaly was not noticed by Wagner and Schneier, it was later reported to them by Michael Wiener. Neither anomaly seems to have turned up in the logic-based study of .
A preliminary report on this study was presented in a panel at the September 1997 DIMACS Workshop on Design and Formal Verification of Security Protocols and appears on the web site (http://dimacs.rutgers.edu/Workshops/Security/) and CD ROM associated with this workshop. Our study of resumption was carried out after our workshop submission and is not described in the workshop document.
Our general methodology for modeling security protocols in Mur is described in our previous paper , and will be only outlined in this section. The basic approach is similar to the CSP approach to model checking of cryptographic protocols described in [8, 11].
Mur  is a protocol or, more generally, finite-state machine verification tool. It has been successfully applied to several industrial protocols, especially in the domains of multiprocessor cache coherence protocols and multiprocessor memory models [4, 12, 15]. The purpose of finite-state analysis, commonly called ``model checking,'' is to exhaustively search all execution sequences. While this process often reveals errors, failure to find errors does not imply that the protocol is completely correct, because the Mur model may simplify certain details and is inherently limited to configurations involving a small number of, say, clients and servers.
To use Mur for verification, one has to model the protocol in the Mur language and augment this model with a specification of the desired properties. The Mur system automatically checks, by explicit state enumeration, if all reachable states of the model satisfy the given specification. For the state enumeration, either breadth-first or depth-first search can be selected. Reached states are stored in a hash table to avoid redundant work when a state is revisited. The memory available for this hash table typically determines the largest tractable problem.
The Mur language is a simple high-level language for describing nondeterministic finite-state machines. Many features of the language are familiar from conventional programming languages. The main features not found in a ``typical'' high-level language are described in the following paragraphs.
The state of the model consists of the values of all global variables. In a startstate statement, initial values are assigned to global variables. The transition from one state to another is performed by rules. Each rule has a Boolean condition and an action, which is a program segment that is executed atomically. The action may be executed if the condition is true (i.e., the rule is enabled) and typically changes global variables, yielding a new state. Most Mur models are nondeterministic since states typically allow execution of more than one rule. For example, in the model of the SSL protocol, the intruder (which is part of the model) usually has the nondeterministic choice of several messages to replay.
Mur has no explicit notion of processes. Nevertheless a process can be implicitly modeled by a set of related rules. The parallel composition of two processes in Mur is simply done by using the union of the rules of the two processes. Each process can take any number of steps (actions) between the steps of the other. The resulting computational model is that of asynchronous, interleaving concurrency. Parallel processes communicate via shared variables; there are no special language constructs for communication.
The Mur language supports scalable models. In a scalable model, one is able to change the size of the model by simply changing constant declarations. When developing protocols, one typically starts with a small protocol configuration. Once this configuration is correct, one gradually increases the protocol size to the largest value that still allows verification to complete. In many cases, an error in the general (possibly infinite state) protocol will also show up in a down-scaled (finite state) version of the protocol. Mur can only guarantee correctness of the down-scaled version of the protocol, but not correctness of the general protocol. For example, in the model of the SSL protocol, the numbers of clients and servers are scalable and defined by constants.
The desired properties of a protocol can be specified in Mur by invariants, which are Boolean conditions that have to be true in every reachable state. If a state is reached in which some invariant is violated, Mur prints an error trace - a sequence of states from the start state to the state exhibiting the problem.
In outline, we have analyzed protocols using the following sequence of steps:
The intruder model described above is limited in its capabilities and does not have all the power that a real-life intruder may have. In the following, we discuss examples of these limitations.
Our intruder ignores both computational and number-theoretic properties of cryptographic functions. As a result, it cannot perform any cryptanalysis whatsoever. If it has the proper key, it can read an encrypted message (or forge a signature). Otherwise, the only action it can perform is to store the message for a later replay. We do not model any cryptographic attacks such as brute-force key search (with a related notion of computational time required to attack the encryption) or attacks relying on the mathematical properties of cryptographic functions.
Mur has no notion of probability. Therefore, we do not model ``propagation'' of attack probabilities through our finite-state system (e.g, how the probabilities of breaking the encryption, forging the signature, etc. accumulate as the protocol progresses). We also ignore, e.g., that the intruder may learn some probabilistic information about the participants' keys by observing multiple runs of the protocol.
Keys, nonces, etc. are treated as atomic entities in our model. Our intruder cannot break such data into separate bits. It also cannot perform an attack that results in the partial recovery of a secret (e.g., half of the secret bits).
In spite of the above limitations, we believe that Mur is a useful tool for analyzing security protocols. It considers the protocol at a high level and helps discover a certain class of bugs that do not involve attacks on cryptographic functions employed in the protocol. For example, Mur is useful for discovering ``authentication'' bugs, where the assumptions about key ownership, source of messages, etc. are implicit in the protocol but never verified as part of the message exchange. Also, Mur models can successfully discover attacks on plaintext information (such as version rollback attacks in SSL) and implicit assumptions about message sequence in the protocol (such as unacknowledged receipt of Finished messages in SSL). Other examples of errors discovered by finite-state analysis appear in [8, 9, 11] and in references cited in these papers.
The primary goal of the SSL 3.0 handshake protocol is to establish secret keys that ``provide privacy and reliability between two communicating applications'' . Henceforth, we call the communicating applications the client (C) and the server (S). The basic approach taken by SSL is to have C generate a fresh random number (the secret or shared secret) and deliver it to S in a secure manner. The secret is then used to compute a so-called master secret (or negotiated cipher), from which, in turn, the keys that protect and authenticate subsequent communication between C and S are computed. While the SSL handshake protocol governs the secret key computation, the SSL record layer protocol governs the subsequent secure communication between C and S.
As part of the handshake protocol, C and S exchange their respective cryptographic preferences, which are used to select a mutually acceptable set of algorithms for encrypting and signing handshake messages. In our analysis, we assume for simplicity that RSA is used for both encryption and signatures, and cryptographic preferences only indicate the desired lengths of keys. In addition, SSL 3.0 is designed to be backward-compatible so that a 3.0 server can communicate with a 2.0 client and vice versa. Therefore, the parties also exchange their respective version numbers.
The basic handshake protocol consists of three messages. With the ClientHello message, the client starts the protocol and transmits its version number and cryptographic preferences to the server. The server replies with the ServerHello message, also transmitting its version number and cryptographic preferences. Upon receipt of this message, the client generates the shared secret and sends it securely to the server in the secret exchange message.
Since we were not aware of any formal definition of SSL 3.0, we based our model of the handshake protocol on the Internet draft . The draft does not include a precise list of requirements that must be satisfied by the communication channel created after the handshake protocol completes. Based on our interpretation of the informal discussion in Sections 1 and 5.5 of the Internet draft, we believe that the resulting channel can be considered ``secure'' if and only if the following properties hold:
We propose that any violation of the foregoing invariants that goes undetected by the legitimate participants constitutes a successful attack on the protocol.
SSL 3.0 supports protocol resumption. In the initial run of the protocol, C and S establish a shared secret by going through the full protocol and computing secret keys that protect subsequent communication. SSL 3.0 allows the parties to resume their connection at a later time without repeating the full protocol. If the ClientHello message sent by C to S includes the identifier of an SSL session that is still active according to S's internal state, S assumes that C wants to resume a previous session. No new secret is exchanged in this case, but the master secret and the keys derived from it are recomputed using new nonces. (See Section 4.8 for an explanation of how nonces are used in the protocol to prevent replay attacks, and Appendix B to see how the master secret is computed from the nonces and shared secret.) Our Mur model supports protocol resumption.
Finally, it should be noted that whenever one of the parties detects an inconsistency in the messages it receives, or any of the protocol steps fails in transmission, the protocol is aborted and the parties revert to their initial state. This implies that SSL is susceptible by design to some forms of ``denial of service'' attacks: an intruder can simply send an arbitrary message to a client or server engaged in the handshake protocol, forcing protocol failure.
We start our incremental analysis with the simplest and most intuitive version of the protocol and give an attack found by Mur . We then add a little piece of SSL 3.0 that foils the attack, and let Mur discover an attack on the augmented protocol. We continue this iterative process until no more attacks can be found. The final protocol closely resembles SSL 3.0, with some simplifications that result from our assumption of perfect cryptography (see below).
The following notation will be used throughout the paper.
In general, our model assumes perfect cryptography. The following list explains what this assumption implies for all cryptographic functions used in SSL.
The first step of the basic protocol consists of C sending information about its identity, SSL version number, and cryptographic preferences (aka cryptosuite) to S. Upon receipt of C's Hello message, S sends back its version, cryptosuite (S selects one set of algorithms from the preference list submitted by C), and its public encryption key. C then generates a random secret and sends it to S, encrypted by S's public key.
Notice that the first Hello message (that from C to S) contains the identity of C. There is no way for S to know who initiated the protocol unless this information is contained in the message itself (perhaps implicitly in the network packet header).
Protocol A does not explicitly (and securely) associate the server's name with its public encryption key. This allows the intruder to insert its own key into the server's Hello message. The client then encrypts the generated secret with the intruder's key, enabling the intruder to read the message and learn the secret.
To fix the bug in Protocol A, we add verification of the public key. The server now sends its public key in a certificate signed by the certificate authority. As described before, the certificate has the following form: .
We assume that signatures are unforgeable. Therefore, the intruder will not be able to generate . The intruder may send the certificate for its own public key , but the client will reject it since it expects S's name in the certificate. Finally, the intruder may generate , but the client expects a message signed by CA, and will try to verify it using CA's verification key. Verification will fail since the message is not signed by CA, and the client will abort the protocol. Notice that SSL's usage of certificates to verify the server's public key depends on the trusted certificate authority assumption (see Section 4.2 above).
Protocol B includes no verification of the client's identity. This allows the intruder to impersonate the client by generating protocol messages and pretending they originate from C. In particular, the intruder is able to send its own secret to the server, which the latter will use to compute the master secret and the derived keys.
To fix the bug in Protocol B, the server has to verify that the secret it received was indeed generated by the party whose identity was specified in the first Hello message. For this purpose, SSL employs client signatures.
The client sends to the server its verification key in the CA-signed certificate . In addition, immediately after sending its secret encrypted with the server's public key, the client signs the hash of the secret and sends it to the server. Hashing the secret is necessary so that the intruder will not be able to learn the secret even if it intercepts the message. Since the server can learn the secret by decrypting the client key exchange message, it is able to compute the hash of the secret and compare it with the one sent by the client.
Notice that the server can be assured that is indeed C's verification key since the intruder cannot insert its own key in the CA-signed certificate assuming that signatures are unforgeable. Therefore, the server will always use to verify messages ostensibly signed by the client, and all messages of the form will be rejected. Even if the intruder were able to generate the message , the attack will be detected when the server computes and discovers that it is different from .
Instead of signing the hashed secret, the client can sign the secret directly and send it to the server encrypted by the server's public key. The SSL definition, however, does not include encryption in this step [6, Section 5.6.8,]. We used hashing instead of encryption as well since we intend our incremental reconstruction of SSL to follow the definition as closely as possible. One of the anonymous reviewers suggested that hashing is used instead of encryption so that the encrypted part of the message (i.e., a secret as opposed to a signed secret) fits within the modulus size of the server's encryption function.
Even though the intruder can modify neither keys nor shared secret in Protocol C, it is able to attack the plaintext information transmitted in the Hello messages. This includes the parties' version numbers and cryptographic preferences.
By modifying version numbers, the intruder can convince an SSL 3.0 client that it is communicating with a 2.0 server, and a 3.0 server that it is communicating with a 2.0 client. This will cause the parties to communicate using SSL 2.0, giving the intruder an opportunity to exploit any of the known weaknesses of SSL 2.0.
By modifying the parties' cryptographic preferences, the intruder can force them into selecting a weaker encryption and/or signing algorithm than they normally would. This may make it easier for the intruder to decrypt the client's secret exchange message, or to forge the client's signature.
The parties can prevent attacks on plaintext by repeating the exchange of versions and cryptographic preferences once the handshake protocol is complete; the additional messages will be called verification messages. Since the intruder cannot learn the shared secret, it cannot compute the master secret and the derived keys and thus cannot interfere with the parties' communication after they switch to the negotiated cipher.
Suppose the intruder altered the cryptographic preferences in the client's Hello message. When the client sends its version and cryptosuite to the server under the just negotiated encryption, the intruder cannot change them. The server will detect the discrepancy and abort the protocol. This is also true for the server's version and cryptosuite.
The above protocol is secure against attacks on version numbers and cryptographic preferences except in the following circumstances:
If an attack on version number in the first Hello message causes the parties to switch to a different protocol such as SSL 2.0, they will not exchange verification messages and the attack will not be detected. See Section 4.9.2 for further discussion of anomalies related to the version rollback attack.
By changing cryptosuites in the Hello messages, the intruder may force the parties to use a very weak public-key encryption algorithm that can be broken in real time (i.e., while the current run of the handshake protocol is in progress). If the intruder can break the encrypted message containing the client's secret, it can compute the master secret and the derived keys and will thus be able to forge post-handshake verification messages. The only defense against this kind of attack is to prohibit SSL implementations from using weak cryptographic algorithms in the handshake protocol even if hello messages from the protocol counterparty indicate preference for such algorithms.
In Protocol D, the parties verify only plaintext information after the handshake negotiation is complete. Since the intruder cannot forge signatures, invert hash functions, or break encryption without the correct private key, it can neither learn the client's secret, nor substitute its own. It may appear that D provides complete security for the communication channel between C and S. However, Mur discovered an attack on client's identity that succeeds even if all cryptographic algorithms are perfect.
Intruder I intercepts C's hello message to server S, and initiates the handshake protocol with S under its own name. All messages sent by S are re-transmitted to C, while most of C's messages, including the post-handshake verification messages, are re-transmitted to S. (See the protocol run below for details. Re-transmission of C's verification message is required to change the sender identifier, which is not shown explicitly below.) As a result, both C and S will complete the handshake protocol successfully, but C will be convinced that it is talking to S, while S will be convinced that it is talking to I.
Notice that I does not have access to the secret shared between C and S. Therefore, it will not be able to generate or decrypt encrypted messages after the protocol is complete, and will only be able to re-transmit C's messages. However, the server will believe that the messages are coming from I, whereas in fact they were sent by C.
This kind of attack, while somewhat unusual in that it explicitly reveals the intruder's identity, may prove harmful for a number of reasons. For example, it deprives C of the possibility to claim later that it communicated with S, since S will not be able to support C's claims (S may not even know about C's existence). If S is a pay server providing some kind of online service in exchange for anonymous ``electronic coins'' such as eCash , I may be able to receive service from S using C's cash. Recall, however, that I can only receive the service if it is not encrypted, which might be the case for large volumes of data.
To fix the bug in Protocol D, the parties verify all of their communication after the handshake is complete. Now the intruder may not re-transmit C's messages to S, because C's Hello message contained C, while the Hello message received by the server contained I. The discrepancy will be detected in post-handshake verification.
I observes a run of the protocol and records all of C's messages. Some time later, I initiates a new run of the protocol, ostensibly from C to S, and replays recorded C's messages in response to messages from S. Even though I is unable to read the recorded messages, it manages to convince S that the latter is talking to C, even though C did not initiate the protocol.
Next run of the protocol ...
By adding random nonces to each run of the protocol, SSL 3.0 ensures that there are always some differences between independent runs of the protocol. The intruder is thus unable to replay verification messages from one run in another run.
The exact semantics of the verification messages exchanged after switching to the negotiated cipher (i.e., Finished messages in the SSL terminology) is somewhat unclear. Section 5.6.9 of  states: ``No acknowledgment of the finished message is required; parties may begin sending encrypted data immediately after sending the finished message. Recipients of finished messages must verify that the contents are correct.'' The straightforward implementation of this definition led Mur to discover the following attack on Protocol F:
Since we did not model weak encryption that can be broken by the intruder, we also did not model the last step of the attack explicitly. Instead, if the model reached the state after the third step, the attack was considered successful.
Note that in the actual SSL 3.0 protocol is not used directly as the symmetric key between C and S. It serves as one of the inputs to a hash function that computes the actual symmetric key. Therefore, even if the intruder is able to figure out the symmetric key, this will not necessarily compromise the shared secret .
To obtain , the intruder has to force the parties into choosing weak public-key encryption for the secret exchange message, and then break the chosen encryption algorithm in real-time. This attack can only succeed if both parties support cryptosuites with very weak public-key encryption (e.g., with a very short RSA key). We are not aware of any existing SSL implementations for which this is the case.
To prevent the attack on Protocol F, it is sufficient to require that the parties consider the protocol incomplete until they each receive the correct verification message. Mur did not discover any bugs in the model implemented according to this semantics.
Alternatively, yet another piece of SSL can be added to Protocol F. If the client sends the server a hash of all messages before switching to the negotiated cipher, the server will be able to detect an attack on its cryptosuite earlier.
Mur was used to model Protocol Z with 2 clients, 1 intruder, 1 server, no more than 2 simultaneous open sessions per server, and no more than 1 resumption per session. No new bugs were discovered. However, Mur found two anomalies in the protocol employed to resume a session.
Adding the extra verification message suffices for the full handshake protocol but not for the resumption protocol. When a session is resumed, the parties switch to the negotiated cipher immediately after exchanging Hello messages. Therefore, the intruder can alter cryptographic preferences in the Hello messages and then delay the parties' Finished messages indefinitely, preventing them from detecting the attack. It appears that this attack does not jeopardize the security of SSL 3.0 in practice, since no secret is exchanged in the resumption protocol. In fact, it is not clear to us if the cryptosuites in the Hello messages are used at all in the resumption protocol.
In our model of Protocol Z, the participants switch to SSL 2.0 if a version number in the Hello messages is different from 3.0. (Since the Internet draft for SSL 2.0 has expired and is not publicly available at the moment, we included a specification of SSL 2.0 in Appendix A.)
The Finished messages in SSL 2.0 do not include version numbers or cryptosuites, therefore Protocol Z is susceptible to the attack on cryptographic preferences described in Section 4.5. In the following example, it is assumed for simplicity that client authentication is not used. Also, SSL 2.0 Hello messages have a slightly different format than SSL 3.0 Hello messages and do not contain explicit version information. To simplify presentation, we assume that the intruder converts a 3.0 Hello message into a 2.0 Hello message simply by changing the version number.
To prevent the version rollback attack, SSL 3.0 clients add their version number to the secret they send to the server. When the server receives a secret with 3.0 embedded in it from a 2.0 client, it can determine that there has been an attack on the client's Hello message in which the client's true version number (3.0) was rolled back to 2.0.
However, this defense does not work in the case of session resumption. Mur discovered a version rollback attack on the resumption protocol. The attack succeeds since in the resumption protocol, the client does not send a secret to the server, and the intruder's alteration of version numbers in the Hello messages goes undetected.
Strictly speaking, this attack is not a violation of the specification , since the latter implicitly allows an SSL session that was established using the 3.0 protocol to be resumed using the 2.0 protocol. However, this attack makes implementations of SSL 3.0 potentially vulnerable to SSL 2.0 weaknesses. Wagner and Schneier  reach a similar conclusion in their informal analysis of SSL 3.0.
Following is the definition of the SSL 3.0 handshake protocol according to . When several messages from the same party follow each other in the original definition, they have been collapsed into a single protocol step (e.g., Certificate, ClientKeyExchange, and CertificateVerify were joined into ClientVerify). The underlined pieces of SSL 3.0 are not in Protocol Z.
Assuming that the cryptographic functions are perfect, the underlined pieces can be removed from the SSL 3.0 handshake protocol without jeopardizing its security. However, they do serve a useful purpose by strengthening cryptography and making brute-force attacks on the protocol less feasible.
For example, recall that the shared secret is not used directly as the symmetric key between C and S. Instead, it is used as input to a (pseudorandom) function that computes the actual shared secret. Therefore, breaking the symmetric cipher will not necessarily compromise the shared secret as it would require inverting two hash functions. To obtain the shared secret, the intruder would have to break public-key encryption in the ClientKeyExchange message.
The construction of the keyed hash in ClientVerify, ServerFinished, and ClientFinished messages as follows the HMAC method proposed by Krawczyk , who proved that adding a secret key to the function makes it significantly more secure even if the actual hash function is relatively weak.
In general, we would like to emphasize that SSL 3.0 contains many security measures that are designed to protect the protocol against cryptographic attacks. Since we modeled an idealized protocol in Mur under the perfect cryptography assumption, we found SSL 3.0 secure even without these features.
While one goal of our analysis was ``rational reconstruction'' of the SSL 3.0 handshake protocol, we were also interested in lessons to be learned about using finite-state analysis to verify large protocols. We were particularly concerned about the potentially very large number of reachable states, given that the SSL handshake protocol consists of 7 steps, and each message sent in a particular step includes several components, each of which can be changed by the intruder under certain conditions.
Our model of the intruder is very simple and straightforward. There is no intrinsic knowledge of the protocol embedded in the intruder, nor does the design of the intruder involve any prior knowledge of any form of attack. The intruder may monitor communication between the protocol participants, intercept and generate messages, split intercepted messages into components and recombine them in arbitrary order. No clues are given, however, as to which of these techniques should be used at any given moment. Therefore, the effort involved in implementing the model of the intruder is mostly mechanical.
The following simple techniques proved useful in reducing the number of states to be explored:
Running under Linux on a Pentium-120 with 32MB of RAM, the verifier requires approximately 1.5 minutes to check for the case of 1 client, 1 server, 1 open session, and no resumptions. Less than 5000 states are explored.
The largest instance of our model that we verified included 2 clients, 1 server, no more than 2 simultaneous open sessions per server, and no more than 1 resumption per session. Checking took slightly under 8 hours, with 193,000 states explored.
Our study shows that the finite-state enumeration tool Mur can be successfully applied to complex security protocols like SSL. The analysis uncovered some anomalies in SSL 3.0. (None of these anomalies, however, poses a direct threat to the security of SSL 3.0.) Of these anomalies at least one had slipped through expert human analysis, confirming the usefulness of computer assistance in protocol design.
We are seeking to improve on the current limitations of our approach in three ways. First, modeling a complex cryptographic protocol in the Mur language is a relatively time-consuming (but straightforward) task. Automatic translation from a high-level protocol description language like CAPSL to Mur could significantly reduce the human effort for the analysis. Second, often the protocols have very large numbers of reachable states. Thus, we plan to develop techniques that reduce the number of states that have to be explored when analyzing cryptographic protocols. Finally, ``low level'' properties of the cryptographic functions used in a protocol often cause the protocol to fail, even if it appears to be correct at the high level. We plan to extend our modeling approach to allow detection of such protocol failures by developing more detailed protocol models.
We are grateful to the members of our research group for discussions of the SSL protocol, which resulted in a better understanding thereof. We would also like to thank the anonymous reviewers for comments that helped to clarify further details of the SSL protocol.
This appendix outlines the SSL 2.0 protocol. In the protocol description below, is a number that identifies a particular session. When the server starts a new session with the client, it assigns it a fresh . When the client wants to resume a previous session, it includes its in the Hello message, and the server returns which is the same session number with the ``session found'' bit set.
Notice that the basic SSL 2.0 protocol shown above does not protect plaintext transmitted in the Hello messages, making the protocol vulnerable to version rollback and cryptographic preferences attacks described in Section 4.5 above.
A description of other weaknesses in SSL 2.0 can be found in SSL-Talk FAQ .
In the SSL 2.0 resumption protocol with authentication shown below, is the means of authentication desired by the server, is the server's challenge, is the type of the certificate provided by the client, is the actual certificate (e.g., a CA-signed certificate for the client's verification key), and is the data that authenticates the client (e.g., signed challenge ).
The SSL 3.0 master secret is computed using
where . In most of this paper, the master secret is denoted simply as .
Finite-State Analysis of SSL 3.0
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