--- type: Whitepaper title: "Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH" description: Key exchange protocols hash their handshake transcript with MD5 or SHA-1, so an attacker who computes a chosen-prefix collision between two transcripts can make a client and a server sign the same hash. This yields credential forwarding against TLS client and server authentication and channel bindings, plus impersonation and downgrade attacks on TLS 1.1, IKEv2 and SSH-2. resource: "https://www.ndss-symposium.org/wp-content/uploads/2017/09/transcript-collision-attacks-breaking-authentication-tls-ike-ssh.pdf" tags: [whitepaper, webseclist-reference, auth-bypass, tls, https, cve, owasp-a01-2021, owasp-a02-2021] generated: by: webseclist-refs/1 at: "2026-08-11T17:43:21+00:00" status: stable stale_after: 2027-08-11 sources: - id: original resource: "https://www.ndss-symposium.org/wp-content/uploads/2017/09/transcript-collision-attacks-breaking-authentication-tls-ike-ssh.pdf" title: "Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH" author: Karthikeyan Bhargavan, Gaëtan Leurent also_at: [] authors: - Karthikeyan Bhargavan - Gaëtan Leurent canonical_url: "" cited_by: - "2016-17.md:63" commit: "" content_sha256: 46ef63b53c1ab8296ba28f5fb20f1e3402c586e9b0954190c3281cbbfbb156a2 depth: full depth_reason: default kind: whitepaper language: "" licence: unknown original_url: "https://www.ndss-symposium.org/wp-content/uploads/2017/09/transcript-collision-attacks-breaking-authentication-tls-ike-ssh.pdf" published: "" publisher: "" publisher_english: "" raw_sha256: 51583877f50f668113184ca1be50b0aafb69b2bca761eacfa57eac4f004dea36 retrieved_from: "https://www.ndss-symposium.org/wp-content/uploads/2017/09/transcript-collision-attacks-breaking-authentication-tls-ike-ssh.pdf" retrieved_kind: stored retrieved_utc: "2026-08-11T17:43:21+00:00" slug: transcript-collision-attacks-breaking-authentication-tls-ike-ssh snapshot: "" title_english: "" translation_file: "" translation_of: "" --- # Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH **Transcript Collision Attacks: Breaking Authentication in TLS, IKE and SSH** - Karthikeyan Bhargavan, Gaëtan Leurent, Publisher not stated. - Published: date not stated - Original: - Preserved from: https://www.ndss-symposium.org/wp-content/uploads/2017/09/transcript-collision-attacks-breaking-authentication-tls-ike-ssh.pdf (stored) on 2026-08-11 - Licence: unknown Rights remain with the original author and publisher. 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Transcript Collision Attacks: Breaking Authentication in TLS, IKE, and SSH Karthikeyan Bhargavan Gaëtan Leurent INRIA INRIA karthikeyan.bhargavan@inria.fr gaetan.leurent@normalesup.org Abstract—In response to high-profile attacks that ex- However, recent practical attacks on MD5 and almost- ploit hash function collisions, software vendors have practical attacks on SHA-1 have led researchers and started to phase out the use of MD5 and SHA-1 in practitioners to question whether these uses of hash third-party digital signature applications such as X.509 functions in popular protocols are still secure. certificates. However, weak hash constructions continue to be used in various cryptographic constructions within The first collision on MD5 was demonstrated in mainstream protocols such as TLS, IKE, and SSH, because 2005 [38], and since then, collision-finding algorithms practitioners argue that their use in these protocols relies have gotten much better. Simple MD5 collisions can only on second preimage resistance, and hence is unaf- now be found in seconds on a standard desktop. In re- fected by collisions. This paper systematically investigates sponse, protocol experts reviewed the use of MD5 in In- and debunks this argument. ternet protocols such as Transport Layer Security (TLS) We identify a new class of transcript collision attacks and IPsec [16], [15], [3]. Despite some disagreement on key exchange protocols that rely on efficient collision- on the long-term impact of collisions, they concluded finding algorithms on the underlying hash construc- that most uses of hash functions in these protocols tions. We implement and demonstrate concrete credential- were not affected by collisions. Consequently, MD5 forwarding attacks on TLS 1.2 client authentication, TLS continues to be supported (alongside newer, stronger 1.3 server authentication, and TLS channel bindings. We describe almost-practical impersonation and downgrade hash algorithms) in protocols like TLS and IPsec. attacks in TLS 1.1, IKEv2 and SSH-2. As far as we know, In 2009, an MD5 collision was used to create a these are the first collision-based attacks on the crypto- rogue CA certificate [36], hence breaking the security graphic constructions used in these popular protocols. of certificate-based authentication in many protocols. A Our practical attacks on TLS were responsibly dis- variant of this attack was used by the Flame malware closed (under the name SLOTH) and have resulted in to disguise itself as a valid Windows Update security security updates to several TLS libraries. Our analysis patch [34]. Due to these high-profile attacks, there demonstrates the urgent need for disabling all uses of is now consensus among certification authorities and weak hash functions in mainstream protocols, and our software vendors to stop issuing and accepting new recommendations have been incorporated in the upcoming MD5 certificates. Learning from the MD5 experience, Token Binding and TLS 1.3 protocols. software vendors are also pro-actively phasing out SHA- 1 certificates, since collisions on SHA-1 are believed to I. I NTRODUCTION be almost practical [35]. Hash functions, such as MD5 and SHA-1, are widely This leaves open the question of what to do about used to build authentication and integrity mechanisms other uses of MD5 and SHA-1 in popular crypto- in cryptographic protocols. They are used within public- graphic protocols. Practitioners commonly believe that key certificates, digital signatures, message authentica- collisions only affect non-repudiable signatures (like tion codes (MAC), and key derivation functions (KDF). certificates), but that signatures and MACs used within protocols are safe as long as they include unpredictable Permission to freely reproduce all or part of this paper for noncommer- contents, such as nonces [16], [15].In these cases, cial purposes is granted provided that copies bear this notice and the full citation on the first page. Reproduction for commercial purposes protocol folklore says that a second preimage attack is strictly prohibited without the prior written consent of the Internet would be required to break these protocols, and such Society, the first-named author (for reproduction of an entire paper attacks are still considered hard, even for MD5. only), and the author’s employer if the paper was prepared within the scope of employment. Conversely, theoretical cryptographers routinely as- NDSS ’16, 21-24 February 2016, San Diego, CA, USA sume collision-resistance in proofs of security for Copyright 2016 Internet Society, ISBN 1-891562-41-X these protocols. For example, various recent proofs of http://dx.doi.org/10.14722/ndss.2016.23418 TLS [17], [22], [11] assume collision-resistance even though the most popular hash functions used in TLS are MD5 and SHA-1. Whom shall we believe? Either it is the case that cryptographic proofs of these protocols are based on too-strong (i.e. false) assumptions that should be weakened, or that practitioners are wrong and collision resistance is required for protocol security. This paper seeks to clarify this situation by systemat- ically investigating the use of hash functions in the key Fig. 1. SIGMA’: A mutually-authenticated key exchange protocol exchanges underlying various versions of TLS, IPsec, and SSH. We demonstrate that, contrary to common belief, collisions can be used to break fundamental secu- of the basic SIGMA (sign-and-mac) protocol from [21] rity guarantees of these protocols. We describe a generic which served as the inspiration for the key exchanges class of attacks called transcript collision attacks, and used in many protocols including IKE, OTR, and JFK. detail concrete instances of these attacks against real- world applications. In particular, we demonstrate how In SIGMA’, the initiator A first sends a message a man-in-the-middle attacker can impersonate TLS 1.2 m1 to B, consisting of Diffie-Hellman public value g x , clients, TLS 1.3 servers, and IKEv2 initiators. We also along with some protocol-specific parameters info A that show how a network attacker can downgrade TLS 1.1 may include, for example, a nonce, a protocol version, and SSH-2 [39] connections to use weak ciphers. We a proposed ciphersuite, etc. B responds with a message implement proofs-of-concept exploit demos for three m2 containing its own Diffie-Hellman public value g y of these attacks to demonstrate their practicality, and and some parameters info B . A and B have now com- provide attack complexities for the others. We believe pleted an anonymous Diffie-Hellman exchange and can that ours are the first hash collision-based attacks on the compute the shared secret g xy and use it to derive the cryptographic constructions within these protocols. session key. However, before using the session key, they authenticate each other by exchanging digital signatures We do not claim to have found all transcript col- over the protocol transcript hash(m1 |m2 ) using their lision attacks in these protocols; nor do we think that long-term signing keys (sk A , sk B ). (Digital signature our attack implementations are the most efficient. Still, algorithms typically hash their arguments before sign- our results already provide enough evidence for us ing them, and we have chosen to make this hashing to strongly recommend that weak hash functions like explict in our presentation of SIGMA’.) By signing the MD5 and SHA-1 should be immediately disabled from transcript, A and B verify that they agree upon all the Internet protocols. Partly due to recommendations by elements of the key exchange, and in particular, that a us and other researchers, these hash functions and other network attacker has not tampered with the messages. weak constructions based on them have been removed Finally, A and B also prove to each other that they know from the draft version of the TLS 1.3 protocol. the session key g xy by exchanging MACs computed with this key over their own identities. Outline Section II introduces transcript collision at- tacks on authenticated key exchange protocols. Sec- Like other AKE protocols, SIGMA’ aims to prevent tion III outlines the state-of-the-art in collision-finding message tampering, peer impersonation, and session algorithms for MD5, SHA-1, and their concatenation. key leakage, even if the network and other clients and Section IV describe the TLS protocol, and Section V servers are under the control of the adversary. Formally, describes concrete attacks on various versions of TLS authenticating the transcript guarantees matching con- and three proof-of-concept demos. Section VI describes versations, that is, that the two parties agree on each concrete attacks on IKE and SSH. Section VII summa- others identity and other important protocol parameters. rizes the impact of our attacks and disclosure status. Section VIII concludes. Transcript Collision Attacks The alert reader will notice that SIGMA’ does not in fact guarantee that A II. T RANSCRIPT C OLLISION ATTACKS ON and B agree on the message sequence m1 |m2 ; it only AUTHENTICATED K EY E XCHANGE guarantees that they agree on the hash of this sequence. What if a network attacker were to tamper with the mes- Authenticated Key Exchange (AKE) protocols are sages, so that A and B see different message sequences executed between two parties, usually called client and but the hashes of the two sequences is the same? In that server or initiator and responder, in order to establish case, the protocol will proceed to completion but the a shared session key that can be used to encrypt sub- integrity and authentication guarantees no longer hold. sequent messages. A typical example is the SIGMA’ protocol depicted in Figure 1. This protocol is a variant Figure 2 illustrates such an attack. The man-in-the- 2 a transcript collision by finding x0 , y 0 , info 0A , info 0B such that hash(m1 |m02 ) = hash(m01 |m2 ). The amount of work required to find such a collision depends on the hash function. As we will see in the next section, such collisions require 2N/2 work for hash functions that produce N bits. Hence, for MD5, such a collision would require the MitM to compute 264 MD5 hashes, which may well be achievable by powerful adversaries. A Chosen-Prefix Transcript Collision We now con- sider a more efficient attack that works even when B sends an unpredictable m2 containing a fresh Fig. 2. Man-in-the-middle credential forwarding attack on SIGMA’. (ephemeral) Diffie-Hellman value g y and a previously The attacker creates a transcript collision by tampering with the unknown info B . However, we assume that the length messages shown in red. At the end of the protocol, the client and of m2 (M ) is fixed and known to MitM. Moreover, server have seemingly authenticated each other, but the attacker knows both connection keys, and hence can read or write any data. suppose that in the second message of SIGMA’, info B is allowed to have arbitrary length and arbitrary con- tents. That is, even if info B has junk data at the end, middle (MitM) intercepts messages sent between A and A will accept the message. Specifically, suppose that 0 B. It sends its own message m01 = g x |info 0A to B and info B = len B |data B where data B is opaque data that 0 it sends it own response m02 = g y |info 0B to A. Suppose will be ignored by A. (We will see several examples it can choose these messages such that the authenticated of such “collision-friendly” messages in TLS, IKE, and transcripts match: SSH.) Finally, we assume that the hash function uses the Merkle-Damgård construction [29], [7], so that it obeys hash(m1 |m02 ) = hash(m01 |m2 ) the length extension property: if hash(x) = hash(y) then hash(x|z) = hash(y|z). (Strictly speaking, this We call this a transcript collision. Now, MitM can property only holds when the lengths of x, y are equal simply forward A’s signature over this transcript to B and a multiple of the hash function block size.) and vice versa. A and B will accept the signatures since the hashed transcripts match and the signing keys Under all these conditions, MitM can compute a are 0correct.0 However, the MitM knows the session keys transcript collision by finding two collision bitstrings (g x y , g xy ) on both connections (since it knows x0 , y 0 ). C1 , C2 of L1 and L2 bytes respectively, such that: Hence, the MitM has fully hijacked both connections and can now send messages to B pretending to be A info 0 info A 0 z }|B { 0 and to A pretending to be B. This is an impersonation x0 z}|{ y 0 hash(m1 | [g | len B |C1 |−]) = hash([g | C2 ]) attack that breaks peer authentication. | {z } | {z } m02 m01 If the boundaries between the messages m1 and m2 are not clearly demarcated, there are a number of trivial where len 0B = L1 + M . Note that we have left empty attacks that can ensure that m1 |m02 = m01 |m2 with no space (written −) of size M bytes that still needs to need for hash collisions. In the examples of this paper, be filled after C1 in info 0B . As we will see in the next we will assume that each message (and each message section, this kind of collision is called a chosen-prefix field) is prefixed with its length, so that we can focus collision and is typically achievable with far less work on attacks that rely on weaknesses in the hash function. than a generic collision attack. For example, a chosen- prefix collision in MD5 requires the MitM to compute A Generic Transcript Collision The main challenge about 239 MD5 hashes, which takes only a few CPU in implementing the attack in Figure 2 is that the MitM hours. has to compute the messages m01 and m02 after receiving m1 but before the responder has sent its response m2 . After receiving m1 from A and computing C1 , C2 , The feasibility of the attack depends on the contents and MitM now sends m01 to B. When B responds with m2 formats of these messages. (of size M bytes), MitM now stuffs m2 at the end of info 0B (in place of −) and sends m02 to A. Due to the Suppose the responder B always sends the same length extension property, we have: message m2 for every request; that is, it uses the same (static) Diffie-Hellman value g y and same parameters info 0 info A 0 info B . (This situation occurs, for example in protocols z }|B { y0 x0 z}|{ 0 like QUIC, where the server uses a static configuration.) hash(m1 | [g | len B |C1 |m2 ]) = hash([g | C2 ] |m2 ) | {z } | {z } In that case, after receiving m1 , the MitM can compute m02 m01 3 That is, the MitM has obtained a transcript collision and search: an adversary has to try about 2N random inputs the impersonation attack succeeds. in order to find a preimage. However, for collisions, there is a generic attack with complexity 2N/2 because The attack here exploits hash collisions in combi- of the birthday paradox. If an adversary computes the nation with flexible protocol-specific message formats, images of a set of 2N/2 inputs, this defines about 2N and as we will see, this is one of the main novel tricks pairs of inputs, and there is a high probability that one that we use to mount various attacks in this paper. of these pairs is a collision. Other Transcript Collisions The transcript collisions Generic collision attacks While a naive collision at- described above are not the only attacks possible on tack requires to store 2N/2 images of the hash function, such protocols. In some cases, MitM may not be able 0 0 it is possible to mount a parallel and memory-less attack to use its own Diffie-Hellman values g x , g y but it may with a very small overhead [37]. This generic collision still be able to tamper with the protocol parameters (e.g. attack is very powerful: it can use meaningful messages, ciphersuites) in info 0A , info 0B . In such cases, the MitM and can easily be used for chosen-prefix collisions (see does not have full control over either connection (i.e. it details in Appendix). cannot impersonate A or B) because it does know the session keys, but it may still be able to downgrade the Concatenation To strengthen protocols against colli- protocol parameters to use weak, breakable ciphers. sions in any one hash function, it may be tempting to In other cases, the message format may lend itself to use a combination of two independent hash functions. simpler common-prefix collisions that require even less For example, TLS versions up to 1.1 use a concatenation work than chosen-prefix collisions. Such collisions on of MD5 and SHA-1. While the output length of this MD5 can be found in seconds even on standard desk- construction is 288 bits, it does not offer the security tops. In the next section, we will discuss these different of a 288-bit hash function. In particular, Joux described types of collisions in more detail (some technical details a multi-collision attack that breaks the concatenation of previous results are given in the Appendix), and in the of two hash functions with roughly the same effort as remainder of the paper, we will exploit them to mount breaking the strongest one of the two [18]. transcript collision attacks on real-world protocols. Shortcut collision attacks In the last decade, hash function cryptanalysis has been a very active research III. H ASH F UNCTION C RYPTANALYSIS area, and more efficient attacks have been discovered on ∗ N A hash function H : {0, 1} → {0, 1} maps arbi- widely used hash functions. The (estimated) complexity trary length binary strings to strings of N bits. Broadly of the best attacks currently known against MD5 and speaking, a cryptographic hash function is expected SHA-1 are the following: to behave like a randomly selected function from the ∗ N set of all functions from {0, 1} to {0, 1} ; building MD5 Common-prefix collision: 216 [36] input/output values with specific properties should be as Chosen-prefix collision: 239 [36] hard for H as for a random function. More concretely, SHA-1 Common-prefix collision: 261 [35] a cryptographic hash functions should meet four goals: Chosen-prefix collision: 277 [35] MD5 | SHA-1 Common-prefix collision: 267 [18] 1) Preimage resistance: Given a target value H, Chosen-prefix collision: 277 [18] it should be hard to find x such that H(x) = H 2) Second-preimage resistance: Given an input Shortcut collision attack usually return messages with x, it should be hard to find a second input random-looking blocks that are not controlled by the x0 6= x such that H(x0 ) = H(x) adversary. This makes it harder to use these messages 3) Chosen-prefix collision resistance: Given in a real attack, but we will see that in many cases prefixes P and P 0 , it should be hard to find we can still have meaningful messages by stuffing the a pair of values x, x0 such that H(P 0 |x0 ) = random blocks in non-significant sections. H(P |x). 4) Collision resistance: For a hash function H, it Implementation of attacks Since generic collision should be hard to find a pair of inputs x 6= x0 attacks can be easily parallelized and require little such that H(x0 ) = H(x). memory, they can efficiently be implemented in GPUs. In particular, an attack against MD5 require 264 com- The expected security of a hash function is defined putations. This is well within reach for a motivated as the complexity of the best generic attack, i.e. the adversary: it would cost around $165 000 on Amazon best attack that works on any hash function, without EC2 (using a spot price of 8 ¢/h for a g2.2xlarge instance using any specific property of the design. For preimages doing 2.5 GH/s). Dedicated hardware would be signifi- or second-preimages, the best attack is a brute-force cantly more efficient, but require a large investment. As 4 a point of comparison, the current Bitcoin network is able to compute up to 259 SHA-256 hashes per second. We have implemented this attack against the 96-bit MAC used for the Finished message of TLS 1.1. Our demo took 20 days using four Tesla K20Xm GPUs, which is comparable to the expected time we can derive from hash function benchmarks. For a chosen-prefix collision, an important part of the computation is spend constructed differential paths, and this is much harder to parallelize on GPU. We used the HashClash software [33] by Marc Stevens to perform this computation. Stevens et al.’s estimate that the chosen-collision attack should require 239 hash com- putations, or 35 core-hours [36]. In order to build the collision as fast as possible, we modified the software to Fig. 3. TLS 1.2: A mutually-authenticated DHE handshake. Fields take better advantage of parallelism. The hashclash soft- shown in red indicate parts of the handshake that can contain arbitrary- ware spends most of its time building differential paths, length opaque data (useful for stuffing collision blocks). Handshake with a forward step, a backward step, and a connection transcripts (log 1 , log 2 , log 3 ) refer to the concatenation of all mes- step. We realized that the backward step uses a limited sages up to (and including) the current one. Messages SCR, CC, CCV are optional and only appear when client certificate authentication is used. number of potential starting points, and we precomputed NPN is optional and only appears when the client and server support the results for all possible starting points. In addition, the next-protocol-negotiation extension. The tls-unique channel we merged the forward and connection steps, in order to binding is a connection identifier that may be used by applications avoid the serialization and deserialization of the result. to bind user authentication tokens, such as cookies and passwords, to With these optimisations, we can build a chosen-prefix the underlying TLS channel to prevent credential forwarding. collision in one hour with a 48 cores machine, using a few gigabytes of RAM (the original code required key exchange message SKE that contains an ephemeral at least 3 hours). We believe the time can be further public value g y along with a description of the Diffie- reduced, but this will require a significant rewrite of the Hellman group chosen by the server, including the prime hashclash software to allow parallelism across several p and generator g. The server signs these values to machines, or to rewrite it for GPUs. protect then from tampering and to prove that it knows the private key (sk S ) for the certificate: IV. T HE TLS H ANDSHAKE P ROTOCOL sign(sk S , hash(nc |ns |p|g|g y )) The Transport Layer Security protocol (TLS) [8] is perhaps the most widely used secure channel protocol. The signature and hash algorithm used for this signature Many versions of TLS are used on the Internet; the latest is chosen by the server based on its certificate as well released version is TLS 1.2 [8], while TLS 1.3 [9] is as the supported algorithms indicated by the client currently undergoing standardization at the IETF. within an optional signature-algorithms extension in the client hello. In TLS versions before 1.2, the hash Figure 3 depicts a typical handshake in TLS (in algorithm was fixed to be MD5 | SHA-1 but TLS 1.2 versions 1.0 to 1.2). The client first sends a hello allows clients and servers to choose any hash algorithm message CH that contains a fresh random client nonce they both support (MD5, SHA-1, SHA-256, etc.) Hence nc and various protocol parameters exc , including the in TLS 1.2, each digital signature is prefixed with protocol version, supported list of ciphersuites, and identifiers for the chosen signature and hash algorithm. various protocol extensions. Each extension is prefixed by its length and can contain a payload of up to 216 If the server wants the client to authenticate itself bytes. Notably, the client hello may include extensions with a public-key certificate, it then sends a certificate that the server does not understand or support, and the request message SCR indicating the certificate types and server will ignore them. signature algorithms it supports, as well as an optional list of distinguished names dn for the client certification The server responds to the client hello with a series authorities that it trusts. As with hello extensions, each of messages (from SH to SHD). The server hello SH distinguished name can be 216 bytes long and can contains a fresh server nonce ns and parameters exs , contain arbitrary data that the client will ignore if it does including the server’s chosen version, ciphersuite, and not recognize the name. The server’s message flight then protocol extensions. In most ciphersuites, the server then ends with the server hello done message SHD. sends its public-key certificate SC. In Ephemeral Diffie- Hellman (DHE) ciphersuites, SC is followed by a server The client then sends its own certificate CC if the 5 server asked for it, and its own Diffie-Hellman key a general class of credential forwarding attacks unless share g x in a client key exchange message CKE. If the the application-level credential is channel bound to the client sent a certificate, it must prove that it knows the TLS connection (e.g. see [5]. In such attacks, a client private key sk C by sending a client certificate verify C connects to a malicious server M and authenticates CCV message with a signature over the full message log with some credential over TLS, but M forwards the up to this point in the protocol: authentication message over another TLS channel to S, thereby logging in as C at S. The attack is prevented if sign(sk C , hash(CH|SH|SC|SKE|SCR|SHD|CC|CKE)) the authentication protocol embeds a unique identifier | {z } log 1 for the underlying TLS channel, so that a message sent over one channel cannot be forwarded over another. One At this point, the client and server both derive a session such identifier, called tls-unique, defined in [2], uses master secret ms and authenticated encryption keys the contents of the CFIN message as a unique identifier for both directions (k1 , k2 ). The client sends a change for the TLS connection. This tls-unique channel cipher spec message to indicate that the subsequent mes- binding is used by a number of emerging application- sages it sends will be encrypted (with k1 .) This message level authentication protocols, such as SCRAM [28], is not technically part of the handshake protocol and FIDO [14], and Token Binding [32], specifically to does not appear in the authenticated transcript, and so avoid credential-forwarding attacks. it is not shown in Figure 3. If the client and server both indicate support for the V. T RANSCRIPT C OLLISION ATTACKS ON TLS next-protocol-negotiation extension [24] in their hello As we saw in the previous section, TLS uses a messages, the client then sends an encrypted extensions variety of hash constructions to implement key security message NPN containing a selected application layer mechanisms like client and server authentication, hand- protocol (e.g. http/1.1 or spdy/3). The protocol shake integrity, and channel binding. We now demon- name is ASCII-encoded and then padded to the nearest strate weaknesses in these constructions and show how multiple of 32 bytes (to avoid leaking information via they can be exploited to mount practical transcript the encrypted message length.) collision attacks on real-world clients and servers. The client then sends an encrypted finished message CFIN containing a MAC of the full handshake log log 2 A. Breaking TLS 1.2 Client Authentication using the master secret ms. In TLS 1.0 and 1.1, this using a Chosen-Prefix Transcript Collision MAC is computed using a combination of HMAC-MD5 and HMAC-SHA-1, whereas in TLS 1.2, it uses HMAC- Suppose a client C uses the same certificate to SHA-256. In all these versions, the result of the MAC connect to two different servers A and S. We show that is then truncated to 12 bytes (96 bits): if A is malicious, it can force C to create a signature (in CCV) that A can use to impersonate C at S, as mac96 (ms, hash(CH|SH|SC|SKE|SCR|SHD|CC|CKE|CCV|NPN)) depicted in Figure 4. Here, A acts as a man-in-the- | {z log 2 } middle between C and S. Note, however, that A uses its own certificate cert a and does not rely on knowing When a server receives CFIN, it verifies that the client any long-term secrets belonging to C or S. agrees with it on the full message log and on the master secret. It responds by sending its own change cipher Recall that the client signs the transcript hash(log c1 ); spec message to turn on encryption and a server finished so the key idea of the attack is to compute a collision message SFIN that contains a 96-bit MAC over the full between this client-side transcript and the server-side handshake log log 3 using the master secret ms. transcript hash(log s1 ), even though the two connections see different message sequences. When the MitM A At the end of the handshake, both client and server receives a client hello from C, it responds with its have authenticated each other, proved knowledge of the own hello SH0 , certificate SC0 , key exchange SKE0 . It master secret, and agreed upon the message log. They then initiates a connection with the server S by sending can now start encrypting application data to each other a carefully crafted client hello CH0 . A now runs both using the connection keys (k1 , k2 ). connections in parallel. It will receive a hello SH, certifi- cate SC, key exchange SKE, and certificate request SCR In most common TLS usage scenarios, clients are from S. We assume that the length of these messages not authenticated using certificates. The handshake au- SH|SC|SKE|SCR is fixed (= M ) and is known in advance. thenticates only the server and the client-side user is authenticated within the application using a challenge- Note that A needs to choose CH0 before it receives response protocol based on a password or some other any messages from S. A can compute CH0 and SCR0 as bearer token (e.g. HTTP cookie). Such application-level follows. A uses a chosen-prefix collision to find two bit- authentication protocols are known to be vulnerable to strings (C1 , C2 ) of length L1 and L2 bytes respectively 6 hash(log1s ). A simply forwards these messages to S, pretending to be C, and S accepts these messages. Controlling the master secret Even though S has accept C’s certificate on its connection with A, A cannot complete the connection unless it knows the master secret on its connection with S. The master secret is computed from g xy so A needs to know the x corresponding the g x that C sent in its key exchange message CKE. In order to accomplish this task, we rely on a key forcing attack in the DHE handshake. When A sends SKE0 to C, it does not send a valid Diffie-Hellman group (p, g). Instead, it chooses an 0 arbitrary public value k = g x and sets p = k 2 − k and g = k. This p value is clearly not a prime, and it has the property that no matter what private value x is generated by C, we will have g x mod p = k. Hence, by choosing such a bogus Diffie-Hellman group, A can force C to send a CKE with a public value that it controls. Fig. 4. Man-in-the-middle client signature forwarding attack on TLS To complete the attack, we assume that S always 1.2. The client C connects to a malicious server A and offers to uses the same Diffie-Hellman group (p, g). A chooses authenticate with its certificate cert C . The attacker A computes a 0 chosen-prefix collision on the client signature transcript hash(log 1 ), some x0 and sets k = g x mod p. It then sends SKE0 and uses it to impersonate the client at a different server S. Messages to C with the bogus group (k 2 − k, k) and the public that the attacker controls are labeled in red. A sends a bogus Diffie- value k. Now, the CKE sent by C will contain k, and A Hellman group (k2 − k, k) to C; we use k = g here for simplicity. will forward it to S. A will then forward C’s signature CCV as usual. The master 0 secret between A and S will be derived from g x y mod p, but A knows x0 and hence such that C1 appears within the last distinguished name can compute this value. Consequently, A can complete dn0 in SCR0 and C2 appears within the last extension the handshake and impersonate C at S. ex0c in CH0 : We observe that the attack here relies on the client hash(CH|SH0 |SC0 |SKE0 |SCR0 (C1 |−)) not validating the Diffie-Hellman groups it receives = hash(CH0 (nc , C2 )) | {z } |{z} dn0 from the server. From our experiments, we find that ex0c most TLS libraries do not validate the groups they Furthermore, we set the length of dn0 in SCR0 to be receive in the server key exchange, probably because L1 + M , so that it still has M bytes (denoted by −) checking for primality is expensive. In some libraries, that need to be filled in after C1 . the value k 2 −k is rejected because it is an even number. In those cases, we find that we can use p = k 2 − 1 and Now, A sends CH0 to S, receives SH|SC|SKE|SCR in with 50% probability, the client will compute g x = k, response, and stuffs these messages into the remaining allowing the attack to succeed. This weakness in TLS- M bytes in SCR0 and sends it to C. At this point the DHE has been noted before [6] and a new protocol hash of the message transcripts in the two connections extension aims to fix it by allowing only well-known coincide, assuming that the hash function satisfies the Diffie-Hellman groups [12]. However, an optional ex- length extension property: tension cannot prevent our attack scenario, since A could always pretend to not support the extension and hash(CH|SH|SC0 |SKE0 |SCR0 (C1 |SH|SC|SKE|SCR)) | {z } mount the attack anyway. dn0 = hash(CH0 (nc , C2 )|SH|SC|SKE|SCR) Note that the attack only relies on DHE between |{z} ex0c C and A; the connection between A and S can use ECDHE or RSA and the attack would still work. In From this message onwards, the hash of the handshake other words, such transcript collisions can also be used log in both connections will remain the same. A then to mount cross-protocol attacks in the sense of [26]. forwards the sever hello done SHD to C. In response, C sends a certificate CC, a key exchange CKE, and Attack Complexity The transcript collision attack a certificate verify CCV that contains a signature over requires A to compute a chosen-prefix collision for the transcript hash(log c1 ) which is now the same as the hash function used in the client signature. In TLS 7 versions before 1.2, the default hash function is a software [33]. In our demo, A accepts the client hello concatenation of MD5 and SHA-1 and hence requires and then keeps the client-side TLS connection alive computing 277 MD5 and SHA-1 hashes. In TLS 1.2, until a collision has been found. Most TLS connections if the signature uses SHA-1, the cost is 277 hashes. can be kept alive by sending regular warning alerts; Remarkably, TLS 1.2 also allows RSA-MD5 signatures, Java clients are willing to keep the connection open and for such signatures, the cost of the collision is indefinitely. Keeping the client waiting for an hour is not only 239 MD5 hashes. Below, we describe our proof- always practical, but we note that some unsupervised of-concept implementation that relies on RSA-MD5. TLS clients (such as git) are used to perform long- running connections to web APIs, and long connection Note that these cost estimates are per-connection be- times may not be noticed. In any case, the collision cause the collision needs to be computed once for each search scales well with computational power and can client nonce nc . Usually, these nonces are generated be significantly sped up by a powerful adversary. with a strong random number generator. However, in some cases the client random can become predictable Once the collision has been found, A connects to S due to implementation bugs (e.g. see CVE-2015-0285 to completes the attack and is able to impersonate C in OpenSSL). We also observe that it is commonly at S and read and write data that only C should have believed that these nonces only need to be unique, not access to. Hence, the demo shows that A is able to unpredictable. For example, the OpenSSL library uses break TLS 1.2 client authentication between mainstream RAND_pseudo_bytes to generate the client and server TLS clients and servers. The precise handshake traces random, whereas it uses RAND_bytes to generate other exhibiting the collision are available from our website. key material; the former succeeds even when there is not enough entropy in the system. If the client nonce were predictable, or if it were to be repeated with B. Breaking TLS 1.2 Server Authentication high frequency, the collision can be computed offline at using a Generic Transcript Collision leisure, making SHA-1 collisions almost feasible. Even though our attack below does not rely on predictable The key to our attack above on TLS 1.2 client nonces, it offers yet another justification for the need authentication is that the client is willing to sign the hash for strongly random nonces in TLS. of the full message log, and the format of various TLS messages is flexible enough to allow the attacker to stuff Implementing a Proof-Of-Concept To implement the meaningless collision blocks and server-side messages attack, we need a client that is willing to sign with into them. A similar chosen-prefix transcript collision RSA-MD5 and a server that is willing to accept such attack would not work on TLS 1.2 server authentication signatures. We found a number of TLS libraries that because the server signature transcript does not contain support RSA-MD5 client signatures, including certain flexible-size elements. versions of OpenSSL, GnuTLS, Oracle and IBM Java, In DHE handshakes, the signature covers only the and BouncyCastle. (See Section VII for more details.) client and server nonces and the server’s Diffie-Hellman In particular, all major Java web application servers and key share: sign(sk S , hash(nc |ns |p|g|g y )). So, the only the default TLS servers on Red Hat Enterprise Linux (6 part of the signed value that the attacker may control and 7) accept RSA-MD5 signatures. is the client nonce nc which is fixed-length (32 bytes), For our demo, we set up a man-in-the-middle attack half the size of one MD5 block. between a standard Java HTTPS client and a Java This prevents the use of shortcut collision attacks HTTPS server (with default configurations.) The MitM against MD5, but generic attacks based on the small implements Figure 4. In order to setup the collision 128-bit MD5 hash length are still possible, and not too while preserving the TLS message formats, the attacker far from being practical. needs to carefully set the length fields in various places in CH0 and SCR0 . For example, in CH0 it needs to set consistent lengths for the full hello message, for the Collecting and storing signatures. To mount a tran- extensions field, and for the last extension. Furthermore, script collision attack on TLS 1.2 server authentication, the MitM needs to make sure that the two prefixes have an attacker first has to collect a large number, say a length that is a multiple of the MD5 block size (512 2x , of RSA-MD5 signatures signed by the server. The bits). To achieve this, we fill up the last extension in attacker may do this by passively observing RSA-MD5 CH0 and the last distinguished name in SCR0 with enough connections to the server, but since such connections zero bytes until the prefixes are block-aligned. may be rare, it may have to actively connect to the server to obtain a sufficient number of signatures. Once As explained in Section III, the chosen-prefix col- these signatures (and the corresponding hashes) have lision can be be computed in one hour on a 48 core been collected and stored, the attacker can impersonate workstation using a modified version of the hashclash the server to any client. 8 Upon receiving a client hello message including the client nonce nc , the attacker chooses a DH secret y 0 and computes 0 the MD5 hashes of the transcripts nc |ns |p|g|g y for a series of random server nonces ns , until the hash matches a value that was collected previously. Finding this collision requires the attacker to compute about 2128−x MD5 hashes and then look them up in the stored signature database. When a match is found, the stored signature can be used by the attacker to forge the server’s SKE message for the current connection, and hence impersonate the server. The complexity of this attack on TLS 1.2 server authentication is therefore 2128−x MD5 hashes per connection, in addition to 2x connections performed before-hand, and 2x storage. The attacker can trade-off between these costs—the more signatures he can collect, the less he has to compute per connection. For example, if it is feasible to collect, store, and search through 264 Fig. 5. TLS 1.3: A server-authenticated 1-RTT (EC)DHE handshake signatures, then the per-connection cost is 264 hashes. based on draft 10 of the specification. The client and server send their Although we have described the attack in terms of MD5, key shares within the hello messages and all subsequent handshake messages are encrypted. The server signs the current handshake a similar but more expensive attack can be mounted transcript hash(log 2 ) in a new SCV message. on RSA-SHA1 server signatures, which would require 2160−x computation per-connection. Practical Impact of the Attack. Both the precompu- of TLS clients would be affected. To err on the safe side, tation and per-connection cost of the attack is currently we recommend that TLS libraries should immediately out of reach for academic researchers, but might be disable all MD5-based signatures. within the capabilities of well-resourced adversaries. Exploiting predictable nonces and keys. We observe A prerequisite for the attack is to find servers that that the precomputation in the above attack can be would be willing to sign their SKE messages with avoided if the server uses a predictable nonce ns and RSA-MD5. Internet-wide scans show that about 31% predictable DH parameters p, g, g y . In this case, the of the Alexa top 1 million websites support RSA- attacker only has to perform 264 computations online. MD5 signatures.1 This subset includes popular websites How realistic is this assumption? Many TLS imple- hosted by Akamai, such as microsoft.com. mentations allow DH keys to be reused; in OpenSSL, for example, keys are reused by default unless the A second question is whether TLS clients would ac- application sets the SSL_OP_SINGLE_DH_USE flag. For cept RSA-MD5 signatures. Most popular web browsers such servers, the parameters are clearly predictable. and TLS libraries do not offer RSA-MD5 as one of the supported signature algorithm in the client hello. That leaves the server nonce, and as we noted for This might lead one to believe that they would not clients, a bug in the use of the random number gen- accept RSA-MD5 server signatures. However, we found erator could lead to predictable nonces. Alternatively, and reported security bugs in NSS (the library used the server may support a recent TLS variant called by Firefox and some versions of Chrome), GnuTLS Snap-Start [23] that allows the client (and hence the (used in curl and git), and BouncyCastle; these libraries attacker) to choose the server nonce. That said, we do (and applications that rely on them) incorrectly accept not know of any deployed TLS 1.2 implementation that RSA-MD5 signatures even if they have been explicitly uses predictable nonces, but this section serves as a disabled. For example, Firefox will accept an RSA-MD5 warning to implementors that strongly random nonces signature from a website, even though it is not supposed are needed in TLS, and not just for preventing replays. to. Furthermore, other TLS libraries such as versions of OpenSSL (up to version 1.0.1e), mbedTLS, and Java C. Breaking TLS 1.3 Client and Server Authentication routinely offer and accept RSA-MD5 signatures. using a Chosen-Prefix Transcript Collision Conseqently, if an attacker has the resources to achieve the server impersonation attack, a large number From the viewpoint of transcript collisions, TLS 1.2 server signatures may seem stronger than client signa- 1 https://securitypitfalls.wordpress.com/2015/12/07/november- tures, but not signing enough leads to other security 2015-scan-results/ problems. For example, the server becomes vulnerable 9 to cross-protocol attacks [26] and to downgrade attacks the length extension property of the hash function, all like Logjam [1]. In response to such attacks, the new subsequent handshake hashes collide. So, A can forward design of TLS 1.3 requires the server to sign the full S’s signature in SCV to C and C’s signature in CCV to handshake log, including the negotiated parameters. S, and both will be accepted, even though the DH keys have been tampered with by a man-in-the-middle. Figure 5 illustrates the standard one-round-trip (1- RTT) message flow in the current draft (version 10) of Implementing a Proof-Of-Concept Up to draft 7, the TLS 1.3 specification. In comparison to TLS 1.2, the TLS 1.3 specification explicitly allowed RSA-MD5 this protocol flips the order in which the DH key shares signatures. We wrote a proof-of-concept attack demo are sent, so that the handshake can complete in one based on our own simple prototype implementation round trip. The key shares are sent within extensions of TLS 1.3 that signs with RSA-MD5. As with TLS in the hello messages CH and SH. The server no longer 1.2 client authentication, we found the chosen-prefix sends an SKE message. Instead, it sends a new server collision in roughly one hour on a single workstation. certificate verify message SCV just before the finished message. The SCV contains a signature over the hash As we observed when discussing TLS 1.2, a large of the full message log up to this point (log 2 ). Another number of TLS servers and clients support RSA-MD5 departure from TLS 1.2 is that all handshake messages signatures. Consequently, we believe that if TLS 1.3 after SH are encrypted, in order to protect the privacy of draft 7 were to be implemented today, it is quite likely the client and server certificates from passive attackers. that many of its clients and servers would be vulnerable to our man-in-the-middle attack. However, this attack We demonstrate a chosen-prefix transcript collision vector was removed from TLS 1.3, at least partly due on TLS 1.3 that breaks both client and server signatures, to our findings, when draft 8 of the protocol explicitly enabling a full man-in-the-middle attack on the protocol. deprecated MD5-based signatures. The attack is similar in spirit to the one on TLS 1.2 client signatures; we use the flexible formats of the client and server hello messages to create a trascript D. Downgrading TLS 1.0-1.1 to Weak Ciphersuites collision immediately after the server hello SH. using a Chosen-Prefix Transcript Collision The client C wants to connect to S, but its mes- In TLS, the integrity of the handshake depends sages are intercepted by a network attacker A. After upon the MACs exchanged in the Finished messages. If A receives the client’s CH, it sends its own CH0 to these MACs were broken, the attacker would be free to the server, receives the servers SH, and sends its own modify the hello messages to downgrade the connection SH0 to the client. A now knows the Diffie-Hellman to an old protocol version or weak ciphersuite, or to shared secrets on both connections, and it has chosen delete important extensions such as the renegotiation CH0 and SH0 such that hash(CH|SH0 ) = hash(CH0 |SH). indication countermeasure [11]. Consequently, A can now simply forward all hanshake Recall that the Finished MACs are computed over messages between C and S, and both client and server the hash of the full handshake trascript (hash(log 2 ) and authentication will succeed. A will need to decrypt and hash(log 3 ) in Figure 3). In TLS 1.0 and 1.1, this hash reencrypt these messages, but it can do so because it function is the concatenation of MD5 and SHA-1. As knows the encryption keys on both connections. More we saw in Section III, a chosen-prefix collision on this importantly, once the handshake is complete, A can read construction can be computed with 277 work. We find a and tamper with application data in both directions. man-in-the-middle transcript collision attack on server- To compute CH0 and SH0 , A needs to find a chosen- authenticated TLS 1.1 that is similar to the TLS 1.3 prefix collision C1 , C2 of length L1 and L2 bytes re- attack. A network attacker modifies the client and server spectively such that C1 appears within the last extension hellos so that the handshake hashes collide immediately of of SH0 and C2 appears as the last extension of CH0 : after these two messages; the rest of the handshake 0 0 is left unchanged. The client authenticates the server hash(CH|SH0 (ns , g y , C1 |−)) = hash(CH0 (nc , g x , C2 )) and the handshake completes successfully, and although | {z } |{z} ex0s ex0c the attacker does not know the master secret, it can downgrade the connection to use any weak algorithm Suppose we know that the server S will respond to that both the client and server support, but prefer not CH0 with a server hello message SH of known length to use, such as an EXPORT ciphersuite [1], or a weak M . Then in SH0 , we set the length of ex0s to L1 + M encryption algorithm like RC4. so that there is room for M more bytes after C1 . Once A receives SH from S, it stuffs this message A similar transcript collision attack appears in DTLS within this extra space in SH0 and sends it to C. Hence, 1.0, a UDP-based variant of TLS 1.1. In DTLS, the after the server hello, the handshake transcripts at the attack can be made even more efficient by exploiting client and server have the same hash. Moreover, due to its cookie mechanism. In response to a client hello CH, 10 The goal of the attacker is to make sure that the contents of the client finished message (i.e. the tls-unique) coincide on both connections: mac96 (msc , log c2 ) = mac96 (mss , log s2 ) The attacker can use any controlled part of the tran- script, but we will set things up carefully so that he can compute the collision as late as possible, in order to reduce the size of the messages to hash. More precisely, we use the certificate request SCR0 on the client-side and the NPN message on the server side, which are sent when all other messages in the transcript are already fixed. The attacker uses C1 as the last distinguished name in SCR0 and C2 as the padding in the NPN message (after the protocol name “http/1.1”), and computes (C1 , C2 ) such that the MAC coincides. Once this collision is found, the MitM sends these Fig. 6. Man-in-the-middle credential forwarding attack on two messages on the corresponding connections and tls-unique channel binding. The attack uses a transcript collision completes the handshakes. A can then impersonate C to impersonate the client to the server. at S by forwarding any application-level channel-bound credentials sent by C (for A) to S. a DTLS server can send a hello verify request message Implementing a Proof-Of-Concept We implemented HVR containing a cookie. The client is meant to restart a man-in-the-middle attacker to demonstrate the attack. the handshake by sending the exact same client hello We used an OpenSSL client as C and the main Google message but with this cookie included in it. Since the website as S, since this website supports the next- HVR is not authenticated, the arbitrary-length cookie protocol-negotiation protocol extension. After receiving field allows any network attacker to inject data into the the client hello CH from the client and the server hello transcript, after a known prefix of a fixed length. This done SHD from the server-side, the MitM runs a generic allows the chosen-prefix attack to be transformed to collision search to compute SCR0 and NPN. an almost common prefix attack, similar to the cookie- based attack on IKEv2 in Section VI-A. For the collision search, we implemented the TLS PRF mac96 function using the CUDA framework for NVIDIA GPUs. In TLS versions up to 1.1, this con- E. Breaking the tls-unique Channel Binding struction is built using MD5 and SHA-1; in TLS 1.2 using a Generic Transcript Collision the construction uses SHA-256. However, the strength Suppose an application-level authentication protocol of the hash function is immaterial because what we are at C binds its login credential to the tls-unique attacking is the truncated 96-bit MAC. The underlying channel binding [2], so that when the credential is hash function does not matter. Following the analysis sent from C to A, it cannot be used by A at S. We explain in Section III, it should require about 248 demonstrate how the attacker A could use a generic computations on average to get a collision. collision attack to break this protection. Our implementation run at 160 MH/s for TLS 1.1 Figure 6 depicts the attack. It follows the general and 113 MH/s for TLS 1.2 on a Tesla K20Xm GPU. pattern of the TLS 1.2 client authentication attack, This is comparable to the expected speed we can derive except that it relies on a collision on the transcript from benchmarks of MD5, SHA-1 and SHA-256 on this MAC in the client finished message, rather than a GPU.It took 20 days to find a collision for TLS 1.1, collision in the hash function. The client C connects using four Tesla K20Xm GPUs. Our demo evaluated to the MitM A who then opens a new connection to S. the PRF about 249.9 times, which is rather unlucky: it The attacker sends a SKE0 to C that contains a bogus should take half that number on average. We note that group (k 2 − 1, k), thereby forcing the client to send the generic collision attack is completely parallelizable k x mod (k 2 − 1) = k in its client key exchange CKE. and hence the time for finding a collision can be brought On the server side, the attacker can send its own CKE0 down to an arbitrarily small number by throwing enough containing any Diffie-Hellman value. Hence, the MitM computational power at it. Using Amazon EC2, this knows the master secrets ms c , ms s and connection keys should cost about $140 for TLS 1.1, and $200 for TLS on both connections. 1.2. The transcripts are available on our website. 11 Figure 11 in Appendix depicts an attack on IKEv2 ini- tiator authentication that relies on a transcript collision on this signature. The network attacker intercepts the SA INIT request from I to R and responds with a cookie ck. The initiator I restarts the key exchange by including ck in the new SA INIT request (m1 ). However, the attacker has chosen ck in a way that the hash of m1 is the same as the hash of a tampered SA INIT request m01 that contains the attacker’s Diffie- 0 Hellman public value g x . The attacker sends this tam- Fig. 7. IKEv2: A mutually-authenticated key exchange. Message pered request m01 to the responder and upon receiving parts colored in red can have arbitrary length. a response, it tampers with the response to 0replace R’s Diffie-Hellman key g y with its own key g y . Note that the attacker does not tamper with the nonces ni , nr . Truncated HMAC is not collision-resistant A more general lesson to be taken from our attack on 0 At this 0 point, the attacker knows the shared secrets tls-unique is that there are many uses of HMAC g x y , g xy and encryption keys on the two connections. in cryptographic protocols that are not protected from Moreover the hash used in the signature transcript collisions in the underlying hash function. For example, collides all the way to the mac(ki , IDi ). To complete although HMAC-MD5 may be a good MAC, it is not the attack, the attacker must ensure that ki is that same collision-resistant when the key is known to the attacker. at I and R. It 0can ensure this by choosing x0 , y 0 such x0 y Similarly, when HMAC-SHA256 is truncated to 96 bits, that g = g xy (as discussed below). Thereafter, it can it may still be a good MAC, but it is certainly not a good forward I’s signature to R and hence impersonate I. hash function (since collisions can still be found in 248 steps). Consequently, when inspecting the use of hash Implementing the Attack To implement the attack, functions in Internet protocols, it would be a mistake to we must first find a collision between m1 and m01 . assume that all uses of HMAC are safe; it is important We observe that in IKEv2 the length of the cookie is to look both at the mechanism and its intended security supposed to be at most 64 octets but we found that many goal. In some cases, we may need HMAC to be both a implementations allow cookies of up to 216 bytes. We MAC and a collision-resistant hash function. can use this flexibility in computing long collisions. The attacker finds two length-prefixed bitstrings VI. T RANSCRIPT C OLLISIONS IN IKE AND SSH (C1 , C2 ) of L bytes each such that Although the bulk of this paper has focused on colli- hash(SA INIT([C1 |−]|−)) = hash(SA INIT( C2 |−)) sions in TLS, similar attacks apply to other mainstream | {z } |{z} ck ck0 protocols like IKEv1, IKEv2, and SSH. We describe two exemplary attacks here. where the length of ck is set to L+M , that is, ck has M empty bytes ready to 0 fill in. We set M to the length of A. Breaking IKEv2 Initiator Authentication using a the bitstring SA0i |g x |ni that the attacker wants to send Precomputed Common-Prefix Transcript Collision to R in its tampered SA INIT request m01 . The idea is that the attacker can now stuff the tampered message Figure 7 depicts the IKEv2 authenticated key ex- into ck, and can stuff the original message into info 0i to change protocol, which is similar to the SIGMA’ pro- obtain a transcript collision: tocol discussed in Section II. The initiator first sends 0 an SA INIT request containing its Diffie-Hellman value hash(SA INIT([C1 |SA0i |g x |ni ]|SAi |g x |ni |info i )|−) = g x , nonce ni , and proposed cryptographic parameters | {z ck } SAi , info i . The responder replies with its own public 0 hash(SA INIT([C2 ]|SA0i |g x |ni |[SAi |g x |ni |info i ])|−) value g y , nonce nr and parameters SAr , info r . Alter- |{z} | {z } ck info 0i natively, the responder may send a cookie ck, thereby asking the initiator to restart the protocol by sending the The collision (C1 , C2 ) can be found easily as a chosen- same SA INIT request but with ck included in it. prefix collision attack. Since the collision occurs be- After the SA INIT exchange, the initiator and re- fore any unpredictable value has been included in the sponder authenticate each other by signing a portion of message, it can be computed offline; that is, it does the message transcript. Notably the initiator signs: not have to be computed while a connection is live. The collision can then be used to break any number hash(SA INIT(ck|SAi |g x |ni |info i )|nr |mac(ki , IDi )) of connections between I and R. Such collisions are easy to compute for MD5, but we found that even | {z } m1 12 though MD5 signatures are allowed by the standard, they are not commonly supported by IKEv2 imple- mentations. However, SHA-1 signatures are mandatory for all IKEv2 implementations, so an offline chosen- prefix collision on SHA-1 is enough to mount the attack. The best known complexity of such collisions is currently 277 , which may be feasible for a powerful adversary (especially if better shortcut attacks on SHA- 1 are discovered). We also observe that the two prefixes are very simi- lar: we only need the length of the cookie to be different. Following the format of IKE message, the length field is on bytes 22 and 23 of the hashed transcript, and all previous bytes must have a fixed value. Hence, we can almost use a common-prefix collision attack, if the collision algorithm introduces a difference in bytes 22- 23, and no difference in preceding bytes. For MD5, the Fig. 8. SSH-2: Key exchange and user authentication. most efficient collision attacks do not have a compatible message difference, but it seems possible to build a dedicated attack with complexity below 239 . However, (embedded in) ID0i on the server side, until the PRF for SHA-1, all known collision attacks use differences values on the two sides collide. It can then forward in every message words, and are thus unsuitable. I’s signature to R, even though it knows the Diffie- The 0final step to implement the attack is to ensure Hellman shared secret. When the PRF is HMAC-MD5, 0 that g xy = g x y . To achieve this, we rely on a small this generic collision attack costs about 2 ∗ 264 HMAC subgroup confinement attack. To see a simple example, computations per connection. suppose the attacker chose x0 = y 0 = 0; then the two shared secrets would have the value 1. This specific so- C. Downgrading SSH-2 to Weak Ciphersuites lution would not work in practice because most IKEv2 with a Chosen-Prefix Transcript Collision implementations validate the received Diffie-Hellman public value to ensure that it is larger than 1 and smaller Figure 8 depicts the SSH-2 [39] protocol, which than p − 1. However, many IKEv2 implementations implements yet another variation of an authenticated support the Diffie-Hellman groups 22-24 that are known Diffie-Hellman protocol. The client and server exchange to have many small subgroups. These implementations identification strings Vc , Vs , negotiate protocol param- do not validate the incoming public value, and hence eters Ic , Is , and perform a Diffie-Hellman exchange are susceptible to similar small subgroup confinement g x , g y . To authenticate the exchange, clients and servers attacks, as discussed in [5]. To complete our transcript sign a session hash, defined as: collision attack, the MitM can use one such small H = hash(Vc |Vs |Ic |Is |pk S |g x |g y |g xy ) subgroup to ensure that the shared values on the two connections are the same with high probability. We show that a target collision on this hash value can allow downgrade attaks. B. Breaking IKEv1 Initiator Authentication Figure 12 in Appendix depicts a downgrade attack with a Generic Transcript Collision on SSH-2. The network attacker tampers with the key IKEv1, the predecessor of IKEv2, and is also vul- exchange message Ic in one direction and with Is in nerable to transcript collision attacks. We briefly outline the other. It chooses their values in a way such that the one attack, without giving more details for lack of space. following hashes coincide The initiator’s signature in IKEv1 is computed as: hash(Vc |Vs |Ic | C1 |−) = hash(Vc |Vs | C2 ) xy x y |{z} sign(sk I , prf(prf(ni |nr , g ), g |g |ci |cr |SAi |IDi )) | {z } Is0 Ic0 A commonly-used PRF function in IKEv1 is HMAC- Using this collision, we leave enough space empty in MD5, and we find a generic transcript collision attack Is0 to stuff the real Is inside. Consequently the session on the outer PRF value that allows initiator imperson- hashes on the two sides coincide and the connection ation. A man-in-the-middle attacker intercepts a con- is completed. In this attack, the MitM does not tamper nection 0 between I and R; it tries out many random with the Diffie-Hellman values and hence it does not g y values on the client-side, and many random values know the connection keys. However, it manages to 13 tamper with both Ic and Is , and can therefore down- 5) Red Hat issued backported patches RHEL 6 grade the negotiate ciphersuite to a weak cryptographic and 7 to disable MD5 signatures in their ver- algorithm that the attacker knows how to break. sion of OpenSSL version 1.0.1e. 6) NSS 3.21 (FireFox 43) disabled support for Implementing the target collision for SSH-2 requires MD5 server signatures; MD5-based client sig- a chosen-prefix attack on SHA-1 which is still consid- natures were already disabled. ered impractical (at least 277 work). Moreover, since the 7) GnuTLS 3.3.15 disabled MD5 signatures in two tampered fields Ic and Is are meant to be strings the default configuration. (not bitstrings), we cannot use arbitrary collisions. Still, 8) BouncyCastle Java 1.54 (C# 1.8.1) disabled we find this attack to be an interesting illustration of MD5 signatures in the default configuration. the use of transcipt collisions for downgrade attacks. 9) Oracle and IBM are updating the TLS im- SSH-2 has a peculiar session hash construction, with plementation in their Java runtimes to disable the shared secret g xy placed at the end. This makes MD5 signatures in the default configuration. certain kinds of collision attacks more difficult, but we 10) mbedTLS is being updated to disable MD5 note that this construction is not particularly secure; server signatures; MD5 client signatures were since it includes the shared secret, the session hash already disabled. needs to be non-leaking in addition to being collision- These changes impact the Firefox and Android resistant [4]. Moreover, if the SSH server reuses its browsers, about 31% of web servers, most Java Diffie-Hellman public value, this secret suffix becomes application servers and their clients, and many vulnerable to key recovery attacks like on APOP [25]. other custom applications that use less well-known Other variations of SSH allow for more tampering, TLS libraries. We are maintaining a website with which may enable new attacks. The SSH Diffie-Hellman the currently known attacks, affected software, and Group Exchange protocol [10] allows SSH servers to disclosure status at our website: choose any Diffie-Hellman group for use in the key http://sloth-attack.org . exchange. So, like in our TLS attacks, a man-in-the- middle attacker can send a bogus or weak group to the VIII. C ONCLUSIONS client, and use it to control more fields in the session We have demonstrated that the use of MD5 and hash and mount new transcript collision attacks. truncated HMACs for authenticating transcripts in vari- ous Internet protocols leads to exploitable chosen-prefix VII. SLOTH: R ESPONSIBLE D ISCLOSURE AND and generic collision attacks. We also showed several I MPACT unsafe uses of SHA-1 that will become dangerous when more efficient collision-finding algorithms for SHA- Table I summarizes the attacks discussed in this 1 are discovered. In all cases, the complexity of our paper. Three of our attacks on TLS are already practical; transcript collision attacks are significantly lower than others are within the reach of powerful adversaries. the estimated work for a second preimage attack on the underlying hash function. This definitively settles Our attacks on TLS were publicly disclosed under the debate on whether the security of mainstream the acronym SLOTH (security losses from obsolete cryptographic protocols depend on collision resistance. and truncated transcript hashes) and were assigned a The answer is yes, cryptographers were right. Except protocol-level CVE-2015-7575. We informed the au- in rare cases, mainstream protocols do require colli- thors of affected protocol specifications and developers sion resistance for protection against man-in-the-middle for various TLS libraries. We recommended that pro- transcript collision attacks. Consequently, we strongly tocols and implementations should stop using MD5- recommend that weak hash functions like MD5 and based signatures and other weak hash constructions. SHA-1 should not just be deprecated; they should be Our disclosure and recommendations resulted in the forcefully disabled in existing protocols. following security updates: An open research question is whether it is possible 1) TLS 1.3 draft 7 stopped truncating the Fin- to design key exchange protocols that will be resilient ished MACs and started using the full HMAC to new collision attacks. One strategy is to use a output. commitment scheme (like ZRTP [40]) that would make 2) TLS 1.3 draft 8 deprecated MD5 signatures. it more difficult for a man-in-the-middle to tamper 3) The Token Binding Protocol draft 2 removed with the transcript. However, such schemes may still tls-unique and moved to a stronger channel be vulnerable to certain shortcut collisions [19]. For binding. signatures, randomized hashing [13] provides a different 4) Akamai servers disabled support or RSA-MD5 way forward but its integration into a complex protocol client and server signatures. like TLS would need to be carefully analyzed. 14 Protocol Property Mechanism Attack Collision Type Precomp. Work/conn. Preimage Wall-clock time TLS 1.2 Client Auth RSA-MD5 Impersonation Chosen Prefix 239 2128 48 core hours TLS 1.3 Server Auth RSA-MD5 Impersonation Chosen Prefix 239 2128 48 core hours TLS 1.0-1.2 Channel Binding HMAC (96 bits) Impersonation Generic 248 296 80 GPU days TLS 1.2 Server Auth RSA-MD5 Impersonation Generic 2X conn. 2128−X 2128 TLS 1.0-1.1 Handshake Integrity MD5 | SHA-1 Downgrade Chosen Prefix 277 2160 IKE v1 Initiator Auth HMAC-MD5 Impersonation Generic 265 2128 IKE v2 Initiator Auth RSA-SHA-1 Impersonation Chosen Prefix 277 0 2160 SSH-2 Exchange Integrity SHA-1 Downgrade Chosen Prefix 277 2160 TABLE I. S UMMARY OF T RANSCRIPT C OLLISION ATTACKS ON I NTERNET P ROTOCOLS R EFERENCES [20] D. Knuth. Seminumerical algorithms, volume 2 of the art of computer programming, 1981. [1] D. Adrian, K. Bhargavan, Z. Durumeric, P. Gaudry, M. Green, [21] H. Krawczyk. SIGMA: The SIGn-and-MAc approach to J. A. Halderman, N. Heninger, D. Springall, E. Thomé, L. Va- authenticated Diffie-Hellman and its use in the IKE protocols. lenta, B. VanderSloot, E. Wustrow, S. Zanella-Béguelin, , In CRYPTO. 2003. and P. Zimmermann. Imperfect forward secrecy: How diffie- hellman fails in practice. In ACM CCS, 2015. [22] H. Krawczyk, K. G. Paterson, and H. Wee. On the security of the TLS protocol: A systematic analysis. In CRYPTO, 2013. [2] J. Altman, N. Williams, and L. Zhu. Channel bindings for TLS. IETF RFC 5929, 2010. [23] A. Langley. Transport Layer Security (TLS) Snap Start. Internet Draft, 2010. [3] S. Bellovin and E. Rescorla. Deploying a new hash algorithm. In NDSS, 2006. [24] A. Langley. Transport Layer Security (TLS) Next Protocol Negotiation Extension. Internet Draft, 2012. [4] F. Bergsma, B. Dowling, F. Kohlar, J. Schwenk, and D. Stebila. [25] G. Leurent. Practical key-recovery attack against APOP, an Multi-ciphersuite security of the secure shell (ssh) protocol. In MD5-based challenge-response authentication. IJACT, 1(1):32– ACM CCS, pages 369–381, 2014. 46, 2008. [5] K. Bhargavan, A. Delignat-Lavaud, and A. Pironti. Verified [26] N. Mavrogiannopoulos, F. Vercauteren, V. Velichkov, and contributive channel bindings for compound authentication. In B. Preneel. A cross-protocol attack on the TLS protocol. In NDSS, 2015. ACM CCS, 2012. [6] K. Bhargavan, A. D. Lavaud, C. Fournet, A. Pironti, and P.- [27] F. Mendel, C. Rechberger, and M. Schläffer. MD5 is weaker Y. Strub. Triple handshakes and cookie cutters: Breaking and than weak: Attacks on concatenated combiners. In ASIACRYPT, fixing authentication over TLS. In IEEE S&P (Oakland), 2014. 2009. [7] I. B. Damgård. A design principle for hash functions. In [28] A. Menon-Sen, N. Williams, A. Melnikov, and C. New- CRYPTO’89, 1990. man. Salted Challenge Response Authentication Mechanism [8] T. Dierks and E. Rescorla. The Transport Layer Security (TLS) (SCRAM) SASL and GSS-API Mechanisms. IETF RFC 5802, Protocol Version 1.2. IETF RFC 5246, 2008. 2010. [9] T. Dierks and E. Rescorla. The Transport Layer Security (TLS) [29] R. C. Merkle. A certified digital signature. In CRYPTO’89, Protocol Version 1.3. Internet Draft, 2014. 1990. [10] M. Friedl, N. Provos, and W. Simpson. Diffie-Hellman Group [30] J. M. Pollard. A monte carlo method for factorization. BIT Exchange for the Secure Shell (SSH) Transport Layer Protocol. Numerical Mathematics, 15(3):331–334, 1975. IETF RFC 4419, 2006. [31] J. M. Pollard. Monte carlo methods for index computation. [11] F. Giesen, F. Kohlar, and D. Stebila. On the security of TLS Mathematics of computation, 32(143):918–924, 1978. renegotiation. In ACM CCS, 2013. [32] A. Popov, M. Nystroem, D. Balfanz, and A. Langley. The [12] D. Gillmor. Negotiated Finite Field Diffie-Hellman Ephemeral Token Binding Protocol Version 1.0. Internet Draft, 2015. Parameters for TLS. Internet Draft, 2015. [33] M. Stevens. Hashclash. https://marc-stevens.nl/p/hashclash/. [13] S. Halevi and H. Krawczyk. Strengthening digital signatures [34] M. Stevens. Counter-cryptanalysis. In CRYPTO, 2013. via randomized hashing. In CRYPTO, 2006. [35] M. Stevens. New collision attacks on SHA-1 based on optimal [14] B. Hill, D. Baghdasaryan, B. Blanke, R. Lindemann, and joint local-collision analysis. In EUROCRYPT, 2013. J. Hodges. FIDO UAF Application API and Transport Binding [36] M. Stevens, A. K. Lenstra, and B. de Weger. Chosen-prefix Specification v1.0. Draft Specification, 2015. collisions for MD5 and applications. IJACT, 2(4):322–359, [15] P. Hoffman. Use of Hash Algorithms in Internet Key Exchange 2012. (IKE) and IPsec. IETF RFC 4894, 2007. [37] P. C. van Oorschot and M. J. Wiener. Parallel collision search [16] P. Hoffman and B. Schneier. Attacks on Cryptographic Hashes with cryptanalytic applications. J. Cryptology, 12(1):1–28, in Internet Protocols. IETF RFC 4270, 2005. 1999. [17] T. Jager, F. Kohlar, S. Schäge, and J. Schwenk. On the security [38] X. Wang and H. Yu. How to break MD5 and other hash of TLS-DHE in the standard model. In CRYPTO, 2012. functions. In EUROCRYPT, 2005. [18] A. Joux. Multicollisions in iterated hash functions. application [39] T. Ylonen and C. Lonvick. The Secure Shell (SSH) Transport to cascaded constructions. In CRYPTO, 2004. Layer Protocol. RFC 4253 (Proposed Standard), 2006. [19] J. Kelsey and T. Kohno. Herding hash functions and the [40] P. Zimmermann. ZRTP: Media Path Key Agreement for Unicast nostradamus attack. In EUROCRYPT, 2006. Secure RTP. IETF RFC 6189, 2012. 15 H Collision CPC x0 x1 x2 x3 x4 x5 Generic 2N/2 2N/2 H1 IV1 h1 H1 |H2 2N1 /2 N2 /2 + 2N2 /2 2N1 /2 N2 /2 + 2N2 /2 x00 x01 x02 x03 x04 x05 MD5 216 239 SHA-1 261 277 MD5 | SHA-1 267 277 M H2 TABLE II. C OMPLEXITY OF FINDING COLLISIONS IN VARIOUS IV2 h2 HASH CONSTRUCTIONS M0 Fig. 9. Multi-collision attack A PPENDIX A. Attacks against Hash Functions x00 IV10 We now give more details about attacks against hash SHA-1 h1 function, considering both generic attacks and dedicated IV1 attacks against widely-used functions MD5 and SHA-1. x0 The main results are summarizex in Table II. x00 M0 MD5 IV20 Generic collision attacks While a basic collision h2 attack requires to compute and store 2N/2 images of the hash function, it is possible to mount a parallel and IV2 x0 M memory-less attack with a very small overhead. The main idea was introduced by Pollard as the Rho algo- Fig. 10. CPC attack against MD5 | SHA-1 rithm for factorization [30] and discrete logarithms [31], and was later generalized to collision search. The hash function is first restricted from {0, 1}∗ → {0, 1}N to order to locate the collision. This attack requires about {0, 1}N → {0, 1}N , so that it can be iterated. After 2N/2 evaluations of H, and a memory of αc when using some number of steps, a chain of iterations reaches a c CPUs. cycle, and the graph will have the shape of the greek letter ρ. On average, the cycle has length O(2N/2 ) and This attack can be tweaked for a chosen-prefix col- is reached after O(2N/2 ) steps. The point where the lision attack using an auxiliary function g : {0, 1}N → tail of the meets with the cycle reveals a collision in {0, 1}N defined as: the hash function. It can be detected in time O(2N/2 ) H(P |x) if x is even with little or no memory, using various cycle detection g(x) = methods, such as Floyd’s algorithm [20] (also known as H(P 0 |x) if x is odd. tortoise and hare). Collisions in g can be found with the previous Some variants of this attack using distinguished techniques. With probability 1/2 a collision is g is points can be parallelized efficiently. We now describe between an even x and an odd x0 (or vice versa), this a parallel version of Pollard’s Lambda algorithm, as implies a chosen-prefix collision H(P |x) = H(P 0 |x0 ). described by van Oorschot and Wiener [37], using c An accurate complexity analysis is providedpin [37]: CPUs. Each CPU will compute iteration chains of the a collision is expected to be found after π2N /2 function H, and stop when reaching a distinguished evaluations. For a chosen-prefix point, that is a point with some easy to test property. For √ collision, we expect to find two collisions in g after π2N evaluations. instance, we stop a computation when the ending point satisfies x < 2N/2 αc for some small constant α, so that Concatenation Collisions in the concatenation of two the expected length of a chain is 2N/2 /αc. When a chain hash functions H1 |H2 can be found with roughly the is finished, we store the starting point, the length, and same effort as breaking the strongest one of the two, the ending point. We generate αc chains in this way, so using the multi-collision technique of Joux [18]. that the function has been evaluated about 2N/2 times, and there is a high probability that there was a collision. The adversary first finds a collision pair (x0 , x00 ) The important idea of this attack is that if a given point for H1 , starting from the initialization value of H1 . is reached by two different chains, both chain will stop Then it finds a collision pair (x1 , x01 ) starting from at the same distinguished point. Therefore, we look at H1 (x0 ) = H1 (x00 ). This defines 4 messages with the the ending points of the chains, and when a collision is same H1 -digest: x0 |x1 , x0 |x01 , x00 |x1 , x00 |x01 . After N2 /2 detected, we restart the chains from the starting point in steps, this defines a set of 2N2 /2 messages with the 16 same H1 -digest. With high probability, two of these B. Transcript Collision Attacks on IKEv2 and SSH-2 messages have the same H2 -digest as well (see Fig- ure 9). Therefore, one can find a collision in H1 |H2 with a complexity only N2 /2 × 2N1 /2 + 2N2 /2 . For MD5 | SHA-1, this translates to 280 , roughly as much as a generic collision attack on SHA-1. Better attacks against MD5 | SHA-1 result from the combination of Joux’s multicollision technique with shortcut attacks against SHA-1. A collision attack can be build for a cost of 64 × 261 + 264 ≈ 267 (building sequentially 64 collisions for MD5). For a chosen- prefix collision, we first perform a chosen-prefix col- lision against SHA-1, to generate messages (x, x0 ) such that SHA-1(P |x) = SHA-1(P 0 |x0 ). Then we build a multicollision in SHA-1 starting from this value, and we evaluate MD5 over a set of 264 messages in order to find a collision. The total cost is about Fig. 11. Man-in-the-middle initiator impersonation attack on IKEv2. The initiator I connects to the responder R but a man-in-the-middle 277 + 64 × 261 + 264 ≈ 277 (see Figure 10). attacker A intercepts and tampers with some messages (shown in red). A pecomputes a collision (C1 , C2 ) between the prefixes of two Moreover it has been shown that it is possible to SA INIT messages that both begin with a cookie payload. Then by combine cryptanalytic shortcuts both on SHA-1 and sending a carefully crafted cookie to I, A can trigger a transcript MD5, assuming that collision attacks against SHA-1 collision on the initiator signature, which it can then forward to R, improve in the future [27]. This may allow collision thereby impersonating I on a connection that it controls. attacks against MD5 | SHA-1 with less than 264 work. Table II summarizes the currently-known complexities for computing various hash collisions. Fig. 12. Man-in-the-middle downgrade attack on SSH-2. The client C connects to a server S, but a network attacker A tampers with the key exchange messages (shown in red) to downgrade them to a weak ciphersuite. To succeed, A must compute a chosen-prefix collision on the session hash H after receiving C’s key exchange message. 17