Editing Chosen-ciphertext attack

{{Short description|Attack model for cryptanalysis}}
{{more footnotes needed|date=January 2011}}
A '''chosen-ciphertext attack''' ('''CCA''') is an [[attack model]] for [[cryptanalysis]] where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the secret key used for decryption.

For formal definitions of security against chosen-ciphertext attacks, see for example:  [[Michael Luby]]<ref name="luby">{{cite book|last1=Luby|first1=Michael|title=Pseudorandomness and Cryptographic Applications|date=1996|publisher=Princeton University Press}}</ref> and [[Mihir Bellare]] et al.<ref name=BDJR>{{cite book|last1=Bellare|first1=M.|last2=Desai|first2=A.|last3=Jokipii|first3=E.|last4=Rogaway|first4=P.|title=Proceedings 38th Annual Symposium on Foundations of Computer Science |chapter=A concrete security treatment of symmetric encryption |date=1997|pages=394–403|doi=10.1109/SFCS.1997.646128|isbn=0-8186-8197-7|s2cid=42604387}}</ref>

==Introduction==
A number of otherwise secure schemes can be defeated under chosen-ciphertext attack.  For example, the [[El Gamal]] cryptosystem is [[semantic security|semantically secure]] under [[chosen-plaintext attack]], but this semantic security can be trivially defeated under a chosen-ciphertext attack.  Early versions of [[RSA (algorithm)|RSA]] padding used in the [[Secure Sockets Layer|SSL]] protocol were vulnerable to a sophisticated [[adaptive chosen-ciphertext attack]] which revealed SSL session keys.  Chosen-ciphertext attacks have implications for some self-synchronizing [[stream cipher]]s as well.  Designers of tamper-resistant cryptographic [[smart card]]s must be particularly cognizant of these attacks, as these devices may be completely under the control of an adversary, who can issue a large number of chosen-ciphertexts in an attempt to recover the hidden secret key.

It was not clear at all whether public key cryptosystems could withstand the chosen ciphertext attack until the initial breakthrough work of [[Moni Naor]] and [[Moti Yung]] in 1990, which suggested a mode of dual encryption with [[Data integrity|integrity]] proof (now known as the "Naor-Yung" encryption paradigm).<ref name=naor-yung>{{cite journal|title=Moni Naor and Moti Yung, Public-key cryptosystems provably secure against chosen ciphertext attacks|journal=Proceedings 21st Annual ACM Symposium on Theory of Computing|date=1990|pages=427–437}}</ref> This work made understanding of the notion of security against chosen ciphertext attack much clearer than before and open the research direction of constructing systems with various protections against variants of the attack.

When a cryptosystem is vulnerable to chosen-ciphertext attack, implementers must be careful to avoid situations in which an adversary might be able to decrypt chosen-ciphertexts (i.e., avoid providing a decryption oracle).  This can be more difficult than it appears, as even partially chosen ciphertexts can permit subtle attacks.  Additionally, other issues exist and some cryptosystems (such as [[RSA (algorithm)|RSA]]) use the same mechanism to sign messages and to decrypt them.  This permits attacks when [[cryptographic hash function|hashing]] is not used on the message to be signed.  A better approach is to use a cryptosystem which is [[provable security|provably secure]] under chosen-ciphertext attack, including (among others) [[Optimal Asymmetric Encryption Padding|RSA-OAEP]] secure under the random oracle heuristics, [[Cramer-Shoup system|Cramer-Shoup]] which was the first public key practical system to be secure. For symmetric encryption schemes it is known that  [[authenticated encryption]] which is a primitive based on  [[symmetric encryption]] gives security against chosen ciphertext attacks, as was first shown by [[Jonathan Katz (computer scientist)|Jonathan Katz]] and [[Moti Yung]].<ref name=katz-yung>{{cite journal|title=Jonathan Katz and Moti Yung, Unforgeable Encryption and Chosen Ciphertext Secure Modes of Operation. FSE 2000: 284-299}}</ref>

==Varieties==
Chosen-ciphertext attacks, like other attacks, may be adaptive or non-adaptive. In an adaptive chosen-ciphertext attack, the attacker can use the results from prior decryptions to inform their choices of which ciphertexts to have decrypted. In a non-adaptive attack, the attacker chooses the ciphertexts to have decrypted without seeing any of the resulting plaintexts. After seeing the plaintexts, the attacker can no longer obtain the decryption of additional ciphertexts.

===Lunchtime attacks===
A specially noted variant of the chosen-ciphertext attack is the "lunchtime", "midnight", or "indifferent" attack, in which an attacker may make adaptive chosen-ciphertext queries but only up until a certain point, after which the attacker must demonstrate some improved ability to attack the system.<ref name="CS">[[Ronald Cramer]] and [[Victor Shoup]], "[https://dx.doi.org/10.1007/BFb0055717 A Practical Public Key Cryptosystem Provably Secure against Adaptive Chosen Ciphertext Attack]", in Advances in Cryptology – [[CRYPTO]] '98 proceedings, [[Santa Barbara, California]], 1998, pp. 13-25. ([[Cramer-Shoup system|article]])</ref>  The term "lunchtime attack" refers to the idea that a user's computer, with the ability to decrypt, is available to an attacker while the user is out to lunch.  This form of the attack was the first one commonly discussed: obviously, if the attacker has the ability to make adaptive chosen ciphertext queries, no encrypted message would be safe, at least until that ability is taken away.  This attack is sometimes called the "non-adaptive chosen ciphertext attack";<ref name="BDPR">[[Mihir Bellare]], [[Anand Desai]], [[David Pointcheval]], and [[Phillip Rogaway]], [https://www.di.ens.fr/david.pointcheval/Documents/Papers/1998_crypto.pdf Relations among Notions of Security for Public-Key Encryption Schemes], in Advances in Cryptology – CRYPTO '98,  Santa Barbara, California, pp. 549-570.</ref> here, "non-adaptive" refers to the fact that the attacker cannot adapt their queries in response to the challenge, which is given after the ability to make chosen ciphertext queries has expired.

===Adaptive chosen-ciphertext attack===
{{main|Adaptive chosen-ciphertext attack}}
A (full) adaptive chosen-ciphertext attack is an attack in which ciphertexts may be chosen adaptively before and after a challenge ciphertext is given to the attacker, with only the stipulation that the challenge ciphertext may not itself be queried.  This is a stronger attack notion than the lunchtime attack, and is commonly referred to as a CCA2 attack, as compared to a CCA1 (lunchtime) attack.<ref name="BDPR" />  Few practical attacks are of this form.  Rather, this model is important for its use in proofs of security against chosen-ciphertext attacks.  A proof that attacks in this model are impossible implies that any realistic chosen-ciphertext attack cannot be performed.

A practical adaptive chosen-ciphertext attack is the Bleichenbacher attack against [[PKCS1|PKCS#1]].<ref>D. Bleichenbacher. [http://www.bell-labs.com/user/bleichen/papers/pkcs.ps Chosen Ciphertext Attacks against Protocols Based on RSA Encryption Standard PKCS #1] {{webarchive|url=https://web.archive.org/web/20120204040056/http://www.bell-labs.com/user/bleichen/papers/pkcs.ps |date=2012-02-04 }}. In Advances in Cryptology – CRYPTO'98, LNCS vol. 1462, pages: 1&ndash;12, 1998</ref>

Numerous cryptosystems are proven secure against adaptive chosen-ciphertext attacks, some proving this security property based only on algebraic assumptions, some additionally requiring an idealized random oracle assumption. For example, the [[Cramer-Shoup system]]<ref name="CS" /> is secure based on number theoretic assumptions and no idealization, and after a number of subtle investigations it was also established that the practical scheme [[RSA-OAEP]] is secure under the RSA assumption in the idealized random oracle model.<ref>[[Mihir Bellare|M. Bellare]], [[Phillip Rogaway|P. Rogaway]]  ''Optimal Asymmetric Encryption -- How to encrypt with RSA'' extended abstract in Advances in Cryptology – [[Eurocrypt]] '94 Proceedings, Lecture Notes in Computer Science Vol. 950, A. De Santis ed, [[Springer-Verlag]], 1995.  [http://www-cse.ucsd.edu/users/mihir/papers/oae.pdf full version (pdf)] {{Webarchive|url=https://web.archive.org/web/20080708233234/http://www-cse.ucsd.edu/users/mihir/papers/oae.pdf |date=2008-07-08 }}</ref>

==See also==
* [[RCCA security]]

==References==
{{reflist}}

==Further reading==
* [https://www.usenix.org/system/files/conference/usenixsecurity16/sec16_paper_garman.pdf Dancing on the Lip of the Volcano: Chosen Ciphertext Attacks on Apple iMessage (Usenix 2016)]

{{Attack models in cryptanalysis}}

{{DEFAULTSORT:Chosen-Ciphertext Attack}}
[[Category:Cryptographic attacks]]