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== Attacks == |
== Attacks == |
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Multiple attacks were discovered against PKCS #1 v1.5 |
Multiple attacks were discovered against PKCS #1 v1.5, specifically its padding scheme.<ref name="Coron">{{cite book|author=Jean-Sébastien Coron, Marc Joye, [[David Naccache]], and Pascal Paillier|title=Advances in Cryptology — EUROCRYPT 2000 |volume=1807|publisher=[[EUROCRYPT]]|year=2000|pages=369–381|url=https://www.iacr.org/archive/eurocrypt2000/1807/18070374-new.pdf|doi=10.1007/3-540-45539-6|isbn=978-3-540-67517-4|series=Lecture Notes in Computer Science|s2cid=8447520}}</ref><ref name="Bard12"/> |
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In 1998, [[Daniel Bleichenbacher]] published a seminal paper on what became known as [[Adaptive chosen-ciphertext attack#Practical attacks|Bleichenbacher's attack]] (also known as "million message attack").<ref name="Bard12">{{cite thesis |
In 1998, [[Daniel Bleichenbacher]] published a seminal paper on what became known as [[Adaptive chosen-ciphertext attack#Practical attacks|Bleichenbacher's attack]] (also known as "million message attack"). The attack uses the padding as an oracle.<ref name="Bard12">{{cite thesis |
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| url=https://hal.inria.fr/hal-00691958v3 |
| url=https://hal.inria.fr/hal-00691958v3 |
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| title=Efficient Padding Oracle Attacks on Cryptographic Hardware |
| title=Efficient Padding Oracle Attacks on Cryptographic Hardware |
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| page=19| type=report |
| page=19| type=report |
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}}</ref><ref>{{IETF RFC|3218}} – Preventing the Million Message Attack on Cryptographic Message Syntax</ref> PKCS #1 was subsequently updated in the release 2.0 and patches were issued to users wishing to continue using the old version of the standard.<ref name="Coron"/> However, the vulnerable padding scheme remains in use and has resulted in subsequent attacks: |
}}</ref><ref>{{IETF RFC|3218}} – Preventing the Million Message Attack on Cryptographic Message Syntax</ref> PKCS #1 was subsequently updated in the release 2.0 and patches were issued to users wishing to continue using the old version of the standard.<ref name="Coron"/> However, the vulnerable padding scheme remains in use and has resulted in subsequent attacks: |
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* Bardou ''et al.'' (2012) find that several models of [[PKCS 11]] tokens still use the v1.5 padding scheme for RSA |
* Bardou ''et al.'' (2012) find that several models of [[PKCS 11]] tokens still use the v1.5 padding scheme for RSA. They propose an improved version of Bleichenbacher's attack that requires fewer messages. As a result of this improvement, they managed to extract the secret key from several models in under an hour. They also show that the AES-CBC scheme is vulnerable to a different [[padding oracle attack]].<ref name="Bard12"/><ref>{{cite web |title=A bad couple of years for the cryptographic token industry |url=https://blog.cryptographyengineering.com/2012/06/21/bad-couple-of-years-for-cryptographic/ |website=A Few Thoughts on Cryptographic Engineering |language=en |date=21 June 2012 |first=Matthew |last=Green }}</ref> |
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* Böck ''et al.'' (2018) report that many modern [[HTTPS]] servers are vulnerable to a variation of the attack. TLS 1.2 contains anti-Bleichenbacher countermeasures, but the workarounds are not correctly implemented in many software due to their sheer complexity.<ref>{{Cite web |url = https://robotattack.org |title = ROBOT attack: Return Of Bleichenbacher's Oracle Threat |author=Hanno Böck |author2=Juraj Somorovsky |author3=Craig Young |access-date = February 27, 2018 }}</ref> |
* Böck ''et al.'' (2018) report that many modern [[HTTPS]] servers are vulnerable to a variation of the attack. TLS 1.2 contains anti-Bleichenbacher countermeasures, but the workarounds are not correctly implemented in many software due to their sheer complexity.<ref>{{Cite web |url = https://robotattack.org |title = ROBOT attack: Return Of Bleichenbacher's Oracle Threat |author=Hanno Böck |author2=Juraj Somorovsky |author3=Craig Young |access-date = February 27, 2018 }}</ref> |
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| doi=10.1109/ARES.2007.38| isbn=978-0-7695-2775-8 |
| doi=10.1109/ARES.2007.38| isbn=978-0-7695-2775-8 |
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| s2cid=2459509 |
| s2cid=2459509 |
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}}</ref> Variants of this attack are reported in 2008<ref>Kühn, Ulrich; Pyshkin, Andrei; Tews, Erik; Weinmann, Ralf-Philipp (2008): [https://dl.gi.de/items/91d7c4b0-c254-4fbb-b45c-190479a052b3 Variants of Bleichenbacher’s Low-Exponent Attack on PKCS#1 RSA Signatures.] SICHERHEIT 2008 – Sicherheit, Schutz und Zuverlässigkeit. Beiträge der 4. Jahrestagung des Fachbereichs Sicherheit der Gesellschaft für Informatik e.V. (GI). Bonn: Gesellschaft für Informatik e. V.. PISSN 1617-5468. {{ISBN|978-3-88579-222-2}}. pp. 97–109. Regular Research Papers. Saarbrücken. 2.- 4. April 2008</ref> and 2014.<ref>{{cite web |title=Advanced Threat Research {{!}} Intel Security |url=http://www.intelsecurity.com/advanced-threat-research/berserk.html |date=1 April 2015|archive-url=https://web.archive.org/web/20150401143322/http://www.intelsecurity.com/advanced-threat-research/berserk.html |archive-date=2015-04-01 }}</ref> This class of attack exploits a flawed implementation of the signature verification; a proper implementation would not be vulnerable.<ref name=jager18/> |
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}}</ref> His attack exploits a flawed implementation of the signature verification; a proper implementation would not be vulnerable.<ref name=jager18/> |
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==See also== |
==See also== |
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Incryptography, PKCS #1 is the first of a family of standards called Public-Key Cryptography Standards (PKCS), published by RSA Laboratories. It provides the basic definitions of and recommendations for implementing the RSA algorithm for public-key cryptography. It defines the mathematical properties of public and private keys, primitive operations for encryption and signatures, secure cryptographic schemes, and related ASN.1 syntax representations.
The current version is 2.2 (2012-10-27). Compared to 2.1 (2002-06-14), which was republished as RFC 3447, version 2.2 updates the list of allowed hashing algorithms to align them with FIPS 180-4, therefore adding SHA-224, SHA-512/224 and SHA-512/256.
The PKCS #1 standard defines the mathematical definitions and properties that RSA public and private keys must have. The traditional key pair is based on a modulus, n, that is the product of two distinct large prime numbers, p and q, such that .
Starting with version 2.1, this definition was generalized to allow for multi-prime keys, where the number of distinct primes may be two or more. When dealing with multi-prime keys, the prime factors are all generally labeled as for some i, such that:
As a notational convenience, and
.
The RSA public key is represented as the tuple , where the integer e is the public exponent.
The RSA private key may have two representations. The first compact form is the tuple , where d is the private exponent. The second form has at least five terms
, or more for multi-prime keys. Although mathematically redundant to the compact form, the additional terms allow for certain computational optimizations when using the key. In particular, the second format allows to derive the public key.[1]
The standard defines several basic primitives. The primitive operations provide the fundamental instructions for turning the raw mathematical formulas into computable algorithms.
By themselves the primitive operations do not necessarily provide any security. The concept of a cryptographic scheme is to define higher level algorithms or uses of the primitives so they achieve certain security goals.
There are two schemes for encryption and decryption:
There are also two schemes for dealing with signatures:
The two signature schemes make use of separately defined encoding methods:
The signature schemes are actually signatures with appendix, which means that rather than signing some input data directly, a hash function is used first to produce an intermediary representation of the data, and then the result of the hash is signed. This technique is almost always used with RSA because the amount of data that can be directly signed is proportional to the size of the keys; which is almost always much smaller than the amount of data an application may wish to sign.
Below is a list of cryptography libraries that provide support for PKCS#1:
Multiple attacks were discovered against PKCS #1 v1.5, specifically its padding scheme.[3][4]
In 1998, Daniel Bleichenbacher published a seminal paper on what became known as Bleichenbacher's attack (also known as "million message attack"). The attack uses the padding as an oracle.[4][5] PKCS #1 was subsequently updated in the release 2.0 and patches were issued to users wishing to continue using the old version of the standard.[3] However, the vulnerable padding scheme remains in use and has resulted in subsequent attacks:
In 2006, Bleichenbacher presented a new forgery attack against the signature scheme RSASSA-PKCS1-v1_5.[8] Variants of this attack are reported in 2008[9] and 2014.[10] This class of attack exploits a flawed implementation of the signature verification; a proper implementation would not be vulnerable.[2]
{{cite book}}
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