Editing Adaptive chosen-ciphertext attack

{{Short description|Cryptographic attack}}
{{More footnotes needed|date=January 2011}}
An '''adaptive chosen-ciphertext attack''' (abbreviated as '''CCA2''') is an interactive form of [[chosen-ciphertext attack]] in which an attacker first sends a number of [[ciphertext]]s to be decrypted chosen adaptively, and then uses the results to distinguish a target ciphertext without consulting the oracle on the challenge ciphertext. In an adaptive attack, the attacker is further allowed adaptive queries to be asked after the target is revealed (but the target query is disallowed). It is extending the [[chosen-ciphertext attack|indifferent (non-adaptive) chosen-ciphertext attack]] (CCA1) where the second stage of adaptive queries is not allowed. [[Charles Rackoff]] and Dan Simon defined CCA2 and suggested a system building on the non-adaptive CCA1 definition and system of [[Moni Naor]] and [[Moti Yung]] (which was the first treatment of chosen ciphertext attack immunity of public key systems).

In certain practical settings, the goal of this attack is to gradually reveal information about an encrypted message, or about the decryption key itself. For [[public-key cryptography|public-key systems]], adaptive-chosen-ciphertexts are generally applicable only when they have the property of [[malleability (cryptography)|ciphertext malleability]] &mdash; that is, a ciphertext can be modified in specific ways that will have a predictable effect on the decryption of that message.

==Practical attacks==
Adaptive-chosen-ciphertext attacks were perhaps considered to be a theoretical concern, but not to have been be manifested in practice, until 1998, when [[Daniel Bleichenbacher]] (then of [[Bell Laboratories]]) demonstrated a practical attack against systems using RSA encryption in concert with the [[PKCS 1|PKCS#1 v1.5]] encoding function, including a version of the [[Secure Sockets Layer]] (SSL) protocol used by thousands of [[web server]]s at the time.<ref>{{cite conference |conference=CRYPTO '98 |conference-url=https://link.springer.com/book/10.1007/BFb0055715 |date=August 23–27, 1998 |first=Daniel |last=Bleichenbacher |title=Chosen Ciphertext Attacks Against Protocols Based on the RSA Encryption Standard PKCS #1 |publisher=Springer Berlin Heidelberg |place=Santa Barbara, California |pages=1–12 |doi=10.1007/BFb0055716 |url=https://link.springer.com/content/pdf/10.1007%2FBFb0055716.pdf |isbn=978-3-540-64892-5 |doi-access=free}}</ref>

The Bleichenbacher attacks, also known as the million message attack, took advantage of flaws within the PKCS #1 v1.5 padding function to gradually reveal the content of an RSA encrypted message. Under this padding function, padded plaintexts have a fixed format that it should follow. If the decryption device  (e.g. SSL-equipped web server) somehow reveals whether the padding is valid, it also serves as an "oracle" that reveals information on the secret key. Finding the whole key requires sending several million test ciphertexts to the target.<ref>{{cite web |last=Pornin |first=Thomas |year=2014 |title=Can you explain Bleichenbacher's CCA attack on PKCS#1 v1.5? |url=https://crypto.stackexchange.com/a/12706 |website=Cryptography Stack Exchange |language=en}}</ref> In practical terms, this means that an SSL session key can be exposed in a reasonable amount of time, perhaps a day or less.

With slight variations, this vulnerability was still exploitable in many servers in 2018, under the new name "Return Of Bleichenbacher's Oracle Threat" (ROBOT).<ref>{{cite web |url=https://robotattack.org |title=ROBOT attack |author=Hanno Böck |author2=Juraj Somorovsky |author3=Craig Young |access-date=February 27, 2018}}</ref>

==Preventing attacks==
In order to prevent adaptive-chosen-ciphertext attacks, it is necessary to use an encryption or encoding scheme that limits ciphertext [[malleability (cryptography)|malleability]] and a proof of security of the system. After the theoretical and foundation level development of CCA secure systems, a number of systems have been proposed in the Random Oracle model: the most common standard for RSA encryption is [[Optimal Asymmetric Encryption Padding]] (OAEP). Unlike improvised schemes such as the padding used in the early versions of PKCS#1, OAEP has been proven secure in the [[random oracle]] model,<ref>{{cite journal
|last1=Fujisaki
|first1=Eiichiro
|authorlink1=
|last2=Okamoto
|first2=Tatsuaki
|last3=Pointcheval
|first3=David
|last4=Stern
|first4=Jacques
|title=RSA-OAEP Is Secure under the RSA Assumption
|journal=Journal of Cryptology
|volume=17
|issue=2
|pages=81–104
|year=2004
|url=https://www.di.ens.fr/~pointche/Documents/Papers/2004_joc.pdf
|doi=10.1007/s00145-002-0204-y
|id=
|accessdate=2009-01-12|citeseerx=10.1.1.11.7519
|s2cid=218582909
}}</ref> OAEP was incorporated into PKCS#1 as of version 2.0 published in 1998 as the now-recommended encoding scheme, with the older scheme still supported but not recommended for new applications.<ref>{{cite IETF |title=PKCS #1: RSA Cryptography Specifications Version 2.0 |rfc=2437 |last1=Kaliski |first1=B. |last2=Staddon |first2=J. |date=October 1998 |publisher=[[Internet Engineering Task Force |IETF]] |accessdate=February 20, 2019 |doi=10.17487/RFC2437}}</ref> However, the golden standard for security is to show the system secure without relying on the Random Oracle idealization.<ref name="katz">{{cite book |last1=Katz |first1=Jonathan |last2=Lindell |first2=Yehuda |title=Introduction to Modern Cryptography |date=2015 |publisher=Chapman & Hall/CRC |location=Boca Raton |isbn=978-1-4665-7027-6 |pages=174–175, 179–181 |edition=2}}</ref>

==Mathematical model==
In complexity-theoretic cryptography, security against adaptive chosen-ciphertext attacks is commonly modeled using [[ciphertext indistinguishability]] (IND-CCA2).

==References==
{{Reflist}}

{{Attack models in cryptanalysis|state=expanded}}

[[Category:Cryptographic attacks]]