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35-404: The vulnerability exploited is a combination of chosen plaintext attack and inadvertent information leakage through data compression, similar to that described in 2002 by the cryptographer John Kelsey . It relies on the attacker being able to observe the size of the ciphertext sent by the browser while at the same time inducing the browser to make multiple carefully crafted web connections to

70-405: A random oracle answers each query randomly but consistently; the oracle is assumed to be available to all parties including the attacker, as the hash function is. Such a proof shows that unless the attacker solves the hard problem at the heart of the security reduction, they must make use of some interesting property of the hash function to break the protocol; they cannot treat the hash function as

105-407: A " black box " that is able to produce a solution for any instance of a given computational problem: An oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle to obtain a solution to any instance of the computational problem for that oracle. For example, if the problem is a decision problem for a set A of natural numbers, the oracle machine supplies

140-444: A chosen-plaintext attack the adversary can (possibly adaptively ) ask for the ciphertexts of arbitrary plaintext messages. This is formalized by allowing the adversary to interact with an encryption oracle , viewed as a black box . The attacker’s goal is to reveal all or a part of the secret encryption key. It may seem infeasible in practice that an attacker could obtain ciphertexts for given plaintexts. However, modern cryptography

175-482: A chosen-plaintext attack. The following attack on the Caesar cipher allows full recovery of the secret key: With more intricate or complex encryption methodologies the decryption method becomes more resource-intensive, however, the core concept is still relatively the same. The following attack on a one-time pad allows full recovery of the secret key. Suppose the message length and key length are equal to n . While

210-413: A hierarchy of machines, each with a more powerful halting oracle and an even harder halting problem. This hierarchy of machines can be used to define the arithmetical hierarchy . In cryptography , oracles are used to make arguments for the security of cryptographic protocols where a hash function is used. A security reduction for the protocol is given in the case where, instead of a hash function,

245-443: A small part of the plaintext may need to be chosen by the attacker; such attacks are known as plaintext injection attacks. A chosen-plaintext attack is more powerful than known-plaintext attack , because the attacker can directly target specific terms or patterns without having to wait for these to appear naturally, allowing faster gathering of data relevant to cryptanalysis. Therefore, any cipher that prevents chosen-plaintext attacks

280-420: Is unconditionally malleable . Oracle machine In complexity theory and computability theory , an oracle machine is an abstract machine used to study decision problems . It can be visualized as a Turing machine with a black box , called an oracle , which is able to solve certain problems in a single operation. The problem can be of any complexity class . Even undecidable problems , such as

315-472: Is also secure against known-plaintext and ciphertext-only attacks. However, a chosen-plaintext attack is less powerful than a chosen-ciphertext attack , where the attacker can obtain the plaintexts of arbitrary ciphertexts. A CCA-attacker can sometimes break a CPA-secure system. For example, the El Gamal cipher is secure against chosen plaintext attacks, but vulnerable to chosen ciphertext attacks because it

350-473: Is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts . The goal of the attack is to gain information that reduces the security of the encryption scheme. Modern ciphers aim to provide semantic security, also known as ciphertext indistinguishability under chosen-plaintext attack , and they are therefore, by design, generally immune to chosen-plaintext attacks if correctly implemented. In

385-439: Is carried out as follows : Consider the following extension of the above situation. After the last step, A cipher has indistinguishable encryptions under a chosen-plaintext attack if after running the above experiment the adversary can't guess correctly ( b = b' ) with probability non- negligibly better than 1/2. The following examples demonstrate how some ciphers that meet other security definitions may be broken with

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420-458: Is implemented in software or hardware and is used for a diverse range of applications; for many cases, a chosen-plaintext attack is often very feasible (see also In practice ). Chosen-plaintext attacks become extremely important in the context of public key cryptography where the encryption key is public and so attackers can encrypt any plaintext they choose. There are two forms of chosen-plaintext attacks: A general batch chosen-plaintext attack

455-494: Is not completely standard. In some contexts, such as the proof of the time and space hierarchy theorems , it is more useful to assume that the abstract machine defining class A {\displaystyle A} only has access to a single oracle for one language. In this context, A B {\displaystyle A^{B}} is not defined if the complexity class B {\displaystyle B} does not have any complete problems with respect to

490-437: Is only weak evidence that P≠NP, since a statement may be true for a random oracle but false for ordinary Turing machines; for example, IP ≠PSPACE for a random oracle A but IP = PSPACE . A machine with an oracle for the halting problem can determine whether particular Turing machines will halt on particular inputs, but it cannot determine, in general, whether machines equivalent to itself will halt. This creates

525-458: Is required in general. The complexity class of decision problems solvable by an algorithm in class A with an oracle for a language L is called A . For example, P is the class of problems solvable in polynomial time by a deterministic Turing machine with an oracle for the Boolean satisfiability problem . The notation A can be extended to a set of languages B (or a complexity class B), by using

560-455: The BEAST exploit. The exploit was due to be revealed in full at the 2012 ekoparty security conference. Rizzo and Duong presented CRIME as a general attack that works effectively against a large number of protocols, including but not limited to SPDY (which always compresses request headers), TLS (which may compress records) and HTTP (which may compress responses). CRIME can be defeated by preventing

595-401: The halting problem , can be used. An oracle machine can be conceived as a Turing machine connected to an oracle . The oracle, in this context, is an entity capable of solving some problem, which for example may be a decision problem or a function problem . The problem does not have to be computable; the oracle is not assumed to be a Turing machine or computer program. The oracle is simply

630-541: The August 2013 Black Hat conference, researchers Gluck, Harris and Prado announced a variant of the CRIME exploit against HTTP compression called BREACH (short for Browser Reconnaissance and Exfiltration via Adaptive Compression of Hypertext). It uncovers HTTPS secrets by attacking the inbuilt HTTP data compression used by webservers to reduce network traffic. Chosen plaintext attack A chosen-plaintext attack ( CPA )

665-437: The case where an oracle is chosen randomly from among all possible oracles (an infinite set). It has been shown in this case, that with probability 1, P ≠NP . When a question is true for almost all oracles, it is said to be true for a random oracle . This choice of terminology is justified by the fact that random oracles support a statement with probability 0 or 1 only. (This follows from Kolmogorov's zero–one law .) This

700-487: The codebreakers decrypt the code used on the second leg, having supplied the original text . In modern day, chosen-plaintext attacks (CPAs) are often used to break symmetric ciphers . To be considered CPA-secure, the symmetric cipher must not be vulnerable to chosen-plaintext attacks. Thus, it is important for symmetric cipher implementors to understand how an attacker would attempt to break their cipher and make relevant improvements. For some chosen-plaintext attacks, only

735-428: The following definition: When a language L is complete for some class B, then A =A provided that machines in A can execute reductions used in the completeness definition of class B. In particular, since SAT is NP-complete with respect to polynomial time reductions, P =P . However, if A = DLOGTIME , then A may not equal A . (The definition of A B {\displaystyle A^{B}} given above

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770-578: The message and immediately reported to their superiors that "AF" was low on water, confirming the Navy's hypothesis and allowing them to position their force to win the battle . Also during World War II , Allied codebreakers at Bletchley Park would sometimes ask the Royal Air Force to lay mines at a position that didn't have any abbreviations or alternatives in the German naval system's grid reference. The hope

805-558: The name "one-time" pad). In World War II US Navy cryptanalysts discovered that Japan was planning to attack a location referred to as "AF". They believed that "AF" might be Midway Island , because other locations in the Hawaiian Islands had codewords that began with "A". To prove their hypothesis that "AF" corresponded to "Midway Island" they asked the US forces at Midway to send a plaintext message about low supplies. The Japanese intercepted

840-416: The one-time pad is used as an example of an information-theoretically secure cryptosystem, this security only holds under security definitions weaker than CPA security. This is because under the formal definition of CPA security the encryption oracle has no state. This vulnerability may not be applicable to all practical implementations – the one-time pad can still be made secure if key reuse is avoided (hence

875-445: The oracle machine may enter the ASK state. When this happens, the following actions are performed in a single computational step: The effect of changing to the ASK state is thus to receive, in a single step, a solution to the problem instance that is written on the oracle tape. There are many alternative definitions to the one presented above. Many of these are specialized for the case where

910-461: The oracle solves a decision problem. In this case: These definitions are equivalent from the point of view of Turing computability: a function is oracle-computable from a given oracle under all of these definitions if it is oracle-computable under any of them. The definitions are not equivalent, however, from the point of view of computational complexity. A definition such as the one by van Melkebeek, using an oracle tape which may have its own alphabet,

945-423: The oracle with a natural number, and the oracle responds with "yes" or "no" stating whether that number is an element of A . There are many equivalent definitions of oracle Turing machines, as discussed below. The one presented here is from van Melkebeek (2003 , p. 43). An oracle machine, like a Turing machine, includes: In addition to these components, an oracle machine also includes: From time to time,

980-415: The reductions available to A {\displaystyle A} .) It is understood that NP ⊆ P , but the question of whether NP , P , NP, and P are equal remains tentative at best. It is believed they are different, and this leads to the definition of the polynomial hierarchy . Oracle machines are useful for investigating the relationship between complexity classes P and NP , by considering

1015-451: The relationship between P and NP for an oracle A. In particular, it has been shown there exist languages A and B such that P =NP and P ≠NP . The fact the P = NP question relativizes both ways is taken as evidence that answering this question is difficult, because a proof technique that relativizes (i.e., unaffected by the addition of an oracle) will not answer the P = NP question. Most proof techniques relativize. One may consider

1050-437: The server picks one of them and sends it back in its ServerHello message. The server can only choose a compression method the client has offered, so if the client only offers 'none' (no compression), the data will not be compressed. Similarly, since 'no compression' must be allowed by all TLS clients, a server can always refuse to use compression. As of September 2012, the CRIME exploit against SPDY and TLS-level compression

1085-442: The source, which includes the secret content that the attacker desires to discover. Divide and conquer techniques can then be used to home in on the true secret content in a relatively small number of probe attempts that is a small multiple of the number of secret bytes to be recovered. The CRIME exploit was hypothesized by Adam Langley, and first demonstrated by the security researchers Juliano Rizzo and Thai Duong, who also created

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1120-421: The target site. The attacker then observes the change in size of the compressed request payload, which contains both the secret cookie that is sent by the browser only to the target site, and variable content created by the attacker, as the variable content is altered. When the size of the compressed content is reduced, it can be inferred that it is probable that some part of the injected content matches some part of

1155-519: The use of compression, either at the client end, by the browser disabling the compression of SPDY requests, or by the website preventing the use of data compression on such transactions using the protocol negotiation features of the TLS protocol. As detailed in The Transport Layer Security (TLS) Protocol Version 1.2 , the client sends a list of compression algorithms in its ClientHello message, and

1190-625: Was described as mitigated in the then-latest versions of the Chrome and Firefox web browsers. Some websites have applied countermeasures at their end. The nginx web-server was not vulnerable to CRIME since 1.0.9/1.1.6 (October/November 2011) using OpenSSL 1.0.0+, and since 1.2.2/1.3.2 (June / July 2012) using all versions of OpenSSL. Note that as of December 2013 the CRIME exploit against HTTP compression has not been mitigated at all. Rizzo and Duong have warned that this vulnerability might be even more widespread than SPDY and TLS compression combined. At

1225-679: Was that the Germans, seeing the mines, would use an Enigma machine to encrypt a warning message about the mines and an "all clear" message after they were removed, giving the allies enough information about the message to break the German naval Enigma. This process of planting a known-plaintext was called gardening . Allied codebreakers also helped craft messages sent by double agent Juan Pujol García , whose encrypted radio reports were received in Madrid, manually decrypted, and then re-encrypted with an Enigma machine for transmission to Berlin. This helped

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