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Achosen-plaintext attack (CPA) is anattack model forcryptanalysis which presumes that the attacker can obtain theciphertexts for arbitraryplaintexts.^[1] The goal of the attack is to gain information that reduces the security of theencryption scheme.^[2]

Modern ciphers aim to providesemantic security, also known asciphertext indistinguishability under chosen-plaintext attack, and they are therefore, by design, generally immune to chosen-plaintext attacks if correctly implemented.

In a chosen-plaintext attack theadversary can (possiblyadaptively) ask for the ciphertexts of arbitrary plaintext messages. This is formalized by allowing the adversary to interact with an encryptionoracle, viewed as ablack 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 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 alsoIn practice). Chosen-plaintext attacks become extremely important in the context ofpublic 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:

• Batch chosen-plaintext attack, where the adversary chooses all of the plaintexts before seeing any of the corresponding ciphertexts. This is often the meaning intended by "chosen-plaintext attack" when this is not qualified.
• Adaptive chosen-plaintext attack (CPA2), where the adversary can request the ciphertexts of additional plaintexts after seeing the ciphertexts for some plaintexts.

A general batch chosen-plaintext attack is carried out as follows^{[failed verification]}:

1. The attacker may choosen plaintexts. (This parametern is specified as part of theattack model, it may or may not be bounded.)
2. The attacker then sends thesen plaintexts to the encryption oracle.
3. The encryption oracle will then encrypt the attacker's plaintexts and send them back to the attacker.
4. The attacker receivesn ciphertexts back from the oracle, in such a way that the attacker knows which ciphertext corresponds to each plaintext.
5. Based on the plaintext–ciphertext pairs, the attacker can attempt to extract the key used by the oracle to encode the plaintexts. Since the attacker in this type of attack is free to craft the plaintext to match his needs, the attack complexity may be reduced.

Consider the following extension of the above situation. After the last step,

1. The adversary outputs two plaintextsm₀ andm₁.
2. A bitb is chosen uniformly at random${\displaystyle b\leftarrow \{0,1\}}$.
3. The adversary receives the encryption ofm_b, and attempts to "guess" which plaintext it received, and outputs a bitb'.

A cipher hasindistinguishable 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.^[3]

The following examples demonstrate how some ciphers that meet other security definitions may be broken with a chosen-plaintext attack.

The following attack on theCaesar cipher allows full recovery of the secret key:

1. Suppose the adversary sends the message:Attack at dawn,
2. and the oracle returnsNggnpx ng qnja.
3. The adversary can then work through to recover the key in the same way as a Caesar cipher. The adversary could deduce the substitutionsA →N,T →G and so on. This would lead the adversary to determine that 13 was the key used in the Caesar cipher.

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 aone-time pad allows full recovery of the secret key. Suppose the message length and key length are equal ton.

1. The adversary sends a string consisting ofn zeroes to the oracle.
2. The oracle returns thebitwiseexclusive-or of the key with the string of zeroes.
3. The string returned by the oracleis the secret key.

While the one-time pad is used as an example of aninformation-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 the name "one-time" pad).

InWorld War II US Navy cryptanalysts discovered that Japan was planning to attack a location referred to as "AF". They believed that "AF" might beMidway Island, because other locations in theHawaiian 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 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 thebattle.^[3][4]

Also duringWorld War II, Allied codebreakers atBletchley Park would sometimes ask theRoyal 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 was that the Germans, seeing the mines, would use anEnigma 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 ofplanting a known-plaintext was calledgardening.^[5] Allied codebreakers also helped craft messages sent by double agentJuan Pujol García, whose encrypted radio reports were received in Madrid, manually decrypted, and then re-encrypted with anEnigma machine for transmission to Berlin.^[6] This helped the codebreakers decrypt the code used on the second leg, having supplied the originaltext.^[7]

In modern day, chosen-plaintext attacks (CPAs) are often used to breaksymmetric 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 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 thanknown-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 is also secure againstknown-plaintext andciphertext-only attacks.

However, a chosen-plaintext attack is less powerful than achosen-ciphertext attack, where the attacker can obtain the plaintexts of arbitrary ciphertexts. A CCA-attacker can sometimes break a CPA-secure system.^[3] For example, theEl Gamal cipher is secure against chosen plaintext attacks, but vulnerable to chosen ciphertext attacks because it isunconditionally malleable.

• GMR (cryptography)

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