2192:
25:
1115:- Bishop Fox (formerly Stach & Liu). Create MD4 and MD5 hash collisions using groundbreaking new code that improves upon the techniques originally developed by Xiaoyun Wang. Using a 1.6 GHz Pentium 4, MD5 collisions can be generated in an average of 45 minutes, and MD4 collisions can be generated in an average of 5 seconds. Originally released on 22Jun2006.
449:. The rogue certificate may not be revokable by real authorities, and could also have an arbitrary forged expiry time. Even though MD5 was known to be very weak in 2004, certificate authorities were still willing to sign MD5-verified certificates in December 2008, and at least one Microsoft code-signing certificate was still using MD5 in May 2012.
336:. In this case, the attacker can choose two arbitrarily different documents, and then append different calculated values that result in the whole documents having an equal hash value. This attack is normally harder, a hash of n bits can be broken in 2 time steps, but is much more powerful than a classical collision attack.
293:
However, workarounds are possible by abusing dynamic constructs present in many formats. In this way, two documents would be created which are as similar as possible in order to have the same hash value. One document would be shown to an authority to be signed, and then the signature could be copied
566:
lookups. It was originally described in 2003. To execute such an attack, the attacker sends the server multiple pieces of data that hash to the same value and then tries to get the server to perform slow lookups. As the main focus of hash functions used in hash tables was speed instead of security,
495:
algorithms cannot sign a large amount of data efficiently, most implementations use a hash function to reduce ("compress") the amount of data that needs to be signed down to a constant size. Digital signature schemes often become vulnerable to hash collisions as soon as the underlying hash function
290:. The collision attacks against MD5 have improved so much that, as of 2007, it takes just a few seconds on a regular computer. Hash collisions created this way are usually constant length and largely unstructured, so cannot directly be applied to attack widespread document formats or protocols.
322:
files are vulnerable to collision attacks by using color value (such that text of one message is displayed with a white color that blends into the background, and text of the other message is displayed with a dark color) which can then be altered to change the signed document's
543:, one of which appeared legitimate and was submitted for signing by the RapidSSL certificate authority. The second version, which had the same MD5 hash, contained flags which signal web browsers to accept it as a legitimate authority for issuing arbitrary other certificates.
574:
are introduced, with the security objective that collisions are hard to find as long as the key is unknown. They may be slower than previous hashes, but are still much easier to compute than cryptographic hashes. As of 2021, Jean-Philippe
Aumasson and
1054:
Scott A. Crosby and Dan S. Wallach. 2003. Denial of service via algorithmic complexity attacks. In
Proceedings of the 12th conference on USENIX Security Symposium - Volume 12 (SSYM'03), Vol. 12. USENIX Association, Berkeley, CA, USA,
824:
583:(2012) is the most widely-used hash function in this class. (Non-keyed "simple" hashes remain safe to use as long as the application's hash table is not controllable from the outside.)
422:
could be asked to sign a certificate for one domain, and then that certificate (specially its signature) could be used to create a new rogue certificate to impersonate another domain.
467:
with computing complexity between 2 and 2 and cost less than 100,000 US dollars. In 2020, researchers reduced the complexity of a chosen-prefix collision attack against SHA-1 to 2.
294:
to the other file. Such a malicious document would contain two different messages in the same document, but conditionally display one or the other through subtle changes to the file:
507:
Mallory creates two different documents A and B that have an identical hash value, i.e., a collision. Mallory seeks to deceive Bob into accepting document B, ostensibly from Alice.
414:
to specific hash functions. In 2007, a chosen-prefix collision attack was found against MD5, requiring roughly 2 evaluations of the MD5 function. The paper also demonstrates two
278:
to specific hash functions. When a collision attack is discovered and is found to be faster than a birthday attack, a hash function is often denounced as "broken". The
2172:
2002:
310:, have conditional constructs. (if-then-else) that allow testing whether a location in the file has one value or another in order to control what is displayed.
1107:
832:
271:. In a classical collision attack, the attacker has no control over the content of either message, but they are arbitrarily chosen by the algorithm.
43:
993:
Falkenberg, Andreas; Mainka, Christian; Somorovsky, Juraj; Schwenk, Jörg (2013). "A New
Approach towards DoS Penetration Testing on Web Services".
567:
most major programming languages were affected, with new vulnerabilities of this class still showing up a decade after the original presentation.
855:
682:
1840:
524:, claiming that Alice signed B. Because the digital signature matches document B's hash, Bob's software is unable to detect the substitution.
1760:
1148:
878:
644:
we are able to find collisions for MD5 in about 2 compressions for recommended IHVs which takes approx. 6 seconds on a 2.6GHz
Pentium 4.
1177:
907:
972:
Alexander
Sotirov; Marc Stevens; Jacob Appelbaum; Arjen Lenstra; David Molnar; Dag Arne Osvik; Benne de Weger (30 December 2008).
433:, taking advantage of a prefix collision attack against the MD5 hash function. This meant that an attacker could impersonate any
2225:
1776:
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Because of the way hash functions are used in the HMAC construction, the techniques used in these recent attacks do not apply
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636:
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A real-world collision attack was published in
December 2008 when a group of security researchers published a forged
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files can contain cropped images, with a different part of an image being displayed without affecting the hash value.
61:
483:
are not vulnerable. For the attack to be useful, the attacker must be in control of the input to the hash function.
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is practically broken; techniques like randomized (salted) hashing will buy extra time by requiring the harder
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625:, Cryptology ePrint Archive Report 2004/199, 16 Aug 2004, revised 17 Aug 2004. Retrieved July 27, 2008.
916:"SHA-1 is a Shambles - First Chosen-Prefix Collision on SHA-1 and Application to the PGP Web of Trust"
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was largely induced by published collision attacks against two very commonly used hash functions,
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of its components by a
Microsoft root certificate that still used the compromised MD5 algorithm.
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An extension of the collision attack is the chosen-prefix collision attack, which is specific to
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753:"Chosen-Prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities"
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514:, who agrees to what the document says, signs its hash, and sends the signature to Mallory.
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2010:
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malware successfully used a new variation of a chosen-prefix collision attack to spoof
418:
certificates for different domain names, with colliding hash values. This means that a
233:
83:
1108:"Meaningful Collisions", attack scenarios for exploiting cryptographic hash collisions
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attack that uses hash collisions to exploit the worst-case (linear probe) runtime of
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1020:
2021:
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1410:
998:
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856:"CWI Cryptanalist Discovers New Cryptographic Attack Variant in Flame Spy Malware"
714:"A Note on the Practical Value of Single Hash Collisions for Special File Formats"
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91:
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To prevent hash flooding without making the hash function overly complex, newer
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879:"SHA-1 collision attacks are now actually practical and a looming danger"
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711:
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1992:
915:
898:"From Collisions to Chosen-Prefix Collisions Application to Full SHA-1"
897:
750:
563:
299:
255:
Mathematically stated, a collision attack finds two different messages
252:
bits can be broken in 2 time steps (evaluations of the hash function).
248:, these attacks are much faster than a brute force would be. A hash of
1088:
2056:
1456:
1335:
828:
687:
1243:
1087:
Gerbet, Thomas; Kumar, Amrit; Lauradoux, Cédric (12 November 2014).
1037:
479:, thus collision attacks do not affect their security. For example,
463:
In 2019, researchers found a chosen-prefix collision attack against
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In 2008, researchers used a chosen-prefix collision attack against
34:
provides insufficient context for those unfamiliar with the subject
622:
1571:
1527:
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992:
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Many applications of cryptographic hash functions do not rely on
759:. Lecture Notes in Computer Science. Vol. 4515. p. 1.
1977:
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1275:
712:
Max
Gebhardt; Georg Illies; Werner Schindler (4 January 2017).
441:, thereby subverting the certificate validation built in every
86:
tries to find two inputs producing the same hash value, i.e. a
1466:
1355:
1310:
1258:
1215:
1210:
1204:
517:
Mallory attaches the signature from document A to document B.
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426:
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623:
Collisions for Hash
Functions MD4, MD5, HAVAL-128 and RIPEMD
1581:
1576:
1547:
1542:
1506:
1038:"About that hash flooding vulnerability in Node.js... · V8"
913:
895:
480:
313:
751:
Marc
Stevens; Arjen Lenstra; Benne de Weger (2007-11-30).
1350:
1345:
1198:
586:
It is possible to perform an analogous attack to fill up
529:
319:
283:
429:
signing certificate that could be used to impersonate a
995:
2013 IEEE 20th International Conference on Web Services
935:. Cryptography Research Inc. 2005-02-15. Archived from
2003:
Cryptographically secure pseudorandom number generator
707:
705:
703:
410:
More efficient attacks are also possible by employing
1118:
1086:
339:
Mathematically stated, given two different prefixes
700:
676:
621:Xiaoyun Wang, Dengguo Feng, Xuejia Lai, Hongbo Yu:
97:There are roughly two types of collision attacks:
797:
327:
274:More efficient attacks are possible by employing
94:where a specific target hash value is specified.
2212:
876:
683:"Hash Collisions (The Poisoned Message Attack)"
240:is inherently vulnerable to collisions using a
825:"Microsoft releases Security Advisory 2718704"
744:
634:
1834:
1142:
925:
798:Alexander Sotirov; et al. (2008-12-30).
223:
914:Gaëtan Leurent; Thomas Peyrin (2020-01-05).
896:Gaëtan Leurent; Thomas Peyrin (2019-05-06).
853:
536:certificate. They created two versions of a
1841:
1827:
1149:
1135:
1090:The Power of Evil Choices in Bloom Filters
617:
615:
503:The usual attack scenario goes like this:
954:Randomized Hashing and Digital Signatures
772:
522:sends the signature and document B to Bob
62:Learn how and when to remove this message
532:using this scenario, to produce a rogue
1058:
757:Advances in Cryptology - EUROCRYPT 2007
612:
2213:
1822:
1130:
1113:Fast MD5 and MD4 Collision Generators
1032:
1030:
486:
44:providing more context for the reader
858:. Centrum Wiskunde & Informatica
18:
590:using a (partial) preimage attack.
470:
13:
1027:
14:
2237:
1101:
1071:"SipHash: a fast short-input PRF"
800:"Creating a rogue CA certificate"
2191:
2190:
1848:
546:
353:, the attack finds two suffixes
23:
1080:
1048:
986:
965:
952:Shai Halevi and Hugo Krawczyk,
946:
2052:Information-theoretic security
1746:NIST hash function competition
877:Catalin Cimpanu (2019-05-13).
847:
817:
791:
670:
628:
328:Chosen-prefix collision attack
280:NIST hash function competition
148:Chosen-prefix collision attack
1:
1065:Jean-Philippe Aumasson &
831:. 3 June 2012. Archived from
605:
334:Merkle–Damgård hash functions
151:Given two different prefixes
2226:Cryptographic hash functions
1751:Password Hashing Competition
1162:message authentication codes
1158:Cryptographic hash functions
980:Chaos Communication Congress
975:MD5 considered harmful today
854:Marc Stevens (7 June 2012).
635:M.M.J. Stevens (June 2007).
104:Find two different messages
7:
2168:Message authentication code
2123:Cryptographic hash function
1926:Cryptographic hash function
1705:Merkle–Damgård construction
774:10.1007/978-3-540-72540-4_1
593:
298:Some document formats like
238:cryptographic hash function
90:. This is in contrast to a
10:
2242:
2047:Harvest now, decrypt later
224:Classical collision attack
101:Classical collision attack
2186:
2163:Post-quantum cryptography
2115:
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1093:(report). INRIA Grenoble.
512:sends document A to Alice
2153:Quantum key distribution
2143:Authenticated encryption
1998:Random number generation
1499:key derivation functions
933:"Hash Collision Q&A"
2148:Public-key cryptography
2138:Symmetric-key algorithm
1931:Key derivation function
1891:Cryptographic primitive
1884:Authentication protocol
1869:Outline of cryptography
1864:History of cryptography
1777:Hash-based cryptography
1679:Length extension attack
637:"On Collisions for MD5"
215:), where ∥ denotes the
1936:Secure Hash Algorithms
1879:Cryptographic protocol
1787:Message authentication
732:Cite journal requires
658:Cite journal requires
541:public key certificate
437:-secured website as a
2221:Cryptographic attacks
2042:End-to-end encryption
1988:Cryptojacking malware
534:certificate authority
431:certificate authority
420:certificate authority
230:symmetric-key ciphers
2158:Quantum cryptography
2082:Trusted timestamping
1003:10.1109/ICWS.2013.72
997:. pp. 491–498.
572:keyed hash functions
477:collision resistance
165:, find two suffixes
16:Cryptographic attack
1911:Cryptographic nonce
1674:Side-channel attack
1067:Daniel J. Bernstein
765:2007LNCS.4515....1S
600:Puzzle friendliness
577:Daniel J. Bernstein
447:electronic commerce
234:brute force attacks
40:improve the article
2027:Subliminal channel
2011:Pseudorandom noise
1953:Key (cryptography)
1731:CAESAR Competition
1715:HAIFA construction
1664:Brute-force attack
959:2009-06-20 at the
487:Digital signatures
403:) (where ∥ is the
232:are vulnerable to
84:cryptographic hash
2208:
2207:
2204:
2203:
2087:Key-based routing
2077:Trapdoor function
1943:Digital signature
1814:
1813:
1810:
1809:
1608:ChaCha20-Poly1305
1425:Password hashing/
1012:978-0-7695-5025-1
784:978-3-540-72539-8
690:2005 rump session
560:denial of service
493:digital signature
439:man-in-the-middle
72:
71:
64:
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2022:Insecure channel
1874:Classical cipher
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1695:Avalanche effect
1649:Collision attack
1192:Common functions
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802:. Archived from
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692:. Archived from
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471:Attack scenarios
246:birthday problem
144:More generally:
80:collision attack
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1724:Standardization
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1710:Sponge function
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1659:Birthday attack
1654:Preimage attack
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1593:
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1496:General purpose
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1269:Other functions
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1231:SHA-3 finalists
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961:Wayback Machine
951:
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939:on 2008-07-17.
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554:(also known as
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242:birthday attack
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1102:External links
1100:
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1069:(2012-09-18).
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1011:
985:
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945:
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869:
846:
835:on 7 June 2012
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734:|journal=
699:
696:on 2010-03-27.
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525:
518:
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508:
488:
485:
472:
469:
400:
393:
382:
375:
364:
357:
350:
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329:
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324:
317:
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308:Microsoft Word
225:
222:
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194:
187:
176:
169:
162:
155:
149:
142:
141:
137:
126:
115:
108:
102:
88:hash collision
70:
69:
31:
29:
22:
15:
9:
6:
4:
3:
2:
2238:
2227:
2224:
2222:
2219:
2218:
2216:
2197:
2189:
2188:
2185:
2179:
2178:Steganography
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2134:
2133:Stream cipher
2131:
2129:
2126:
2124:
2121:
2120:
2118:
2114:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2092:Onion routing
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2072:Shared secret
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2043:
2040:
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2035:
2033:
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2028:
2025:
2023:
2020:
2018:
2015:
2012:
2009:
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2001:
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1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
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1971:
1969:
1966:
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1963:Key generator
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1937:
1934:
1932:
1929:
1927:
1924:
1923:
1922:
1921:Hash function
1919:
1917:
1914:
1912:
1909:
1907:
1904:
1902:
1899:
1897:
1896:Cryptanalysis
1894:
1892:
1889:
1885:
1882:
1881:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
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1837:
1832:
1830:
1825:
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1803:
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1798:
1795:
1793:
1792:Proof of work
1790:
1788:
1785:
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1780:
1778:
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1768:
1762:
1759:
1757:
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1716:
1713:
1711:
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1703:
1701:
1698:
1696:
1693:
1692:
1690:
1686:
1680:
1677:
1675:
1672:
1670:
1669:Rainbow table
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1646:
1644:
1640:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1600:
1598:
1595:
1592:Authenticated
1589:
1583:
1580:
1578:
1575:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1554:
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1546:
1544:
1541:
1539:
1536:
1534:
1531:
1529:
1526:
1525:
1523:
1521:
1520:MAC functions
1517:
1510:
1508:
1505:
1504:
1502:
1500:
1494:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1458:
1455:
1453:
1450:
1448:
1445:
1443:
1440:
1438:
1435:
1434:
1432:
1429:
1423:
1417:
1414:
1412:
1409:
1407:
1404:
1402:
1399:
1397:
1394:
1392:
1389:
1387:
1384:
1382:
1379:
1377:
1374:
1372:
1369:
1367:
1364:
1362:
1359:
1357:
1354:
1352:
1349:
1347:
1344:
1342:
1339:
1337:
1334:
1332:
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1273:
1271:
1267:
1260:
1257:
1255:
1252:
1250:
1247:
1245:
1242:
1240:
1237:
1236:
1234:
1232:
1228:
1222:
1219:
1217:
1214:
1212:
1209:
1207:(compromised)
1206:
1203:
1201:(compromised)
1200:
1197:
1196:
1194:
1190:
1184:
1183:Known attacks
1181:
1179:
1176:
1174:
1171:
1170:
1167:
1163:
1159:
1152:
1147:
1145:
1140:
1138:
1133:
1132:
1129:
1125:
1121:
1114:
1111:
1109:
1106:
1105:
1092:
1091:
1083:
1072:
1068:
1061:
1051:
1043:
1039:
1033:
1031:
1022:
1018:
1014:
1008:
1004:
1000:
996:
989:
981:
977:
976:
968:
962:
958:
955:
949:
942:
938:
934:
928:
917:
910:
899:
892:
884:
880:
873:
857:
850:
834:
830:
826:
820:
806:on 2012-04-18
805:
801:
794:
786:
780:
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770:
766:
762:
758:
754:
747:
739:
726:
715:
708:
706:
704:
695:
691:
689:
684:
680:
677:Magnus Daum;
673:
665:
652:
645:
638:
631:
624:
618:
616:
611:
601:
598:
597:
591:
589:
588:Bloom filters
584:
582:
578:
573:
568:
565:
561:
557:
553:
552:Hash flooding
547:Hash flooding
544:
542:
539:
535:
531:
523:
520:Mallory then
519:
516:
513:
509:
506:
505:
504:
501:
499:
494:
484:
482:
478:
468:
466:
461:
459:
455:
450:
448:
444:
440:
436:
432:
428:
423:
421:
417:
413:
412:cryptanalysis
408:
406:
405:concatenation
399:
392:
388:
381:
374:
370:
363:
356:
349:
342:
337:
335:
321:
318:
315:
312:
309:
305:
301:
297:
296:
295:
291:
289:
285:
281:
277:
276:cryptanalysis
272:
270:
266:
262:
258:
253:
251:
247:
244:. Due to the
243:
239:
235:
231:
218:
217:concatenation
211:
204:
200:
193:
186:
182:
175:
168:
161:
154:
150:
147:
146:
145:
136:
132:
125:
121:
114:
107:
103:
100:
99:
98:
95:
93:
89:
85:
81:
77:
66:
63:
55:
52:February 2020
45:
41:
35:
32:This article
30:
21:
20:
2128:Block cipher
1968:Key schedule
1958:Key exchange
1948:Kleptography
1906:Cryptosystem
1850:Cryptography
1648:
1089:
1082:
1060:
1050:
1041:
994:
988:
974:
967:
948:
940:
937:the original
927:
909:
891:
882:
872:
860:. Retrieved
849:
837:. Retrieved
833:the original
819:
808:. Retrieved
804:the original
793:
756:
746:
725:cite journal
694:the original
686:
679:Stefan Lucks
672:
651:cite journal
643:
630:
585:
569:
555:
551:
550:
527:
521:
511:
502:
490:
474:
462:
458:code signing
451:
424:
409:
407:operation).
397:
390:
386:
379:
372:
368:
361:
354:
347:
340:
338:
331:
292:
273:
268:
264:
263:, such that
260:
256:
254:
249:
227:
209:
202:
198:
191:
184:
180:
173:
166:
159:
152:
143:
134:
130:
123:
119:
112:
105:
96:
79:
76:cryptography
73:
58:
49:
38:Please help
33:
2116:Mathematics
2107:Mix network
1782:Merkle tree
1770:Utilization
1756:NSA Suite B
445:to protect
443:web browser
2215:Categories
2067:Ciphertext
2037:Decryption
2032:Encryption
1993:Ransomware
1594:encryption
1371:RadioGatún
1178:Comparison
810:2009-10-07
606:References
564:hash table
367:such that
300:PostScript
228:Much like
219:operation.
179:such that
118:such that
2057:Plaintext
1511:KDF1/KDF2
1430:functions
1416:Whirlpool
829:Microsoft
688:Eurocrypt
2196:Category
2102:Kademlia
2062:Codetext
2005:(CSPRNG)
1983:Machines
1736:CRYPTREC
1567:Poly1305
1487:yescrypt
1401:Streebog
1281:CubeHash
1261:(winner)
1021:17805370
957:Archived
594:See also
510:Mallory
491:Because
323:content.
269:hash(m2)
265:hash(m1)
236:, every
1857:General
1642:Attacks
1572:SipHash
1528:CBC-MAC
1462:LM hash
1442:Balloon
1306:HAS-160
761:Bibcode
581:SipHash
558:) is a
556:HashDoS
1978:Keygen
1802:Pepper
1741:NESSIE
1688:Design
1482:scrypt
1477:PBKDF2
1452:Catena
1447:bcrypt
1437:Argon2
1396:Snefru
1391:Shabal
1386:SWIFFT
1366:RIPEMD
1361:N-hash
1336:MASH-2
1331:MASH-1
1316:Kupyna
1276:BLAKE3
1259:Keccak
1244:Grøstl
1221:BLAKE2
1042:v8.dev
1019:
1009:
862:9 June
839:4 June
781:
304:macros
2013:(PRN)
1596:modes
1472:Makwa
1467:Lyra2
1457:crypt
1406:Tiger
1356:MDC-2
1311:HAVAL
1296:Fugue
1254:Skein
1239:BLAKE
1216:SHA-3
1211:SHA-2
1205:SHA-1
1074:(PDF)
1017:S2CID
982:2008.
919:(PDF)
901:(PDF)
883:ZDNet
717:(PDF)
640:(PDF)
481:HMACs
465:SHA-1
454:Flame
427:X.509
416:X.509
302:, or
288:SHA-1
82:on a
1797:Salt
1761:CNSA
1628:IAPM
1582:VMAC
1577:UMAC
1562:PMAC
1557:CMAC
1553:OMAC
1548:NMAC
1543:HMAC
1538:GMAC
1507:HKDF
1376:SIMD
1326:Lane
1301:GOST
1286:ECOH
1173:List
1160:and
1055:3-3.
1007:ISBN
864:2012
841:2012
779:ISBN
738:help
664:help
452:The
387:hash
385:) =
369:hash
360:and
314:TIFF
286:and
259:and
199:hash
197:) =
181:hash
172:and
158:and
131:hash
129:) =
120:hash
111:and
78:, a
1633:OCB
1623:GCM
1618:EAX
1613:CWC
1603:CCM
1533:DAA
1411:VSH
1381:SM3
1351:MD6
1346:MD4
1341:MD2
1321:LSH
1291:FSB
1199:MD5
999:doi
769:doi
579:'s
538:TLS
530:MD5
435:SSL
320:PDF
306:in
284:MD5
74:In
42:by
2217::
1249:JH
1040:.
1029:^
1015:.
1005:.
978:.
881:.
827:.
777:.
767:.
755:.
729::
727:}}
723:{{
702:^
685:.
681:.
655::
653:}}
649:{{
642:.
614:^
500:.
396:∥
378:∥
346:,
267:=
261:m2
257:m1
208:∥
190:∥
140:).
1842:e
1835:t
1828:v
1555:/
1150:e
1143:t
1136:v
1076:.
1044:.
1023:.
1001::
921:.
903:.
885:.
866:.
843:.
813:.
787:.
771::
763::
740:)
736:(
719:.
666:)
662:(
401:2
398:s
394:2
391:p
389:(
383:1
380:s
376:1
373:p
371:(
365:2
362:s
358:1
355:s
351:2
348:p
344:1
341:p
250:n
213:2
210:s
206:2
203:p
201:(
195:1
192:s
188:1
185:p
183:(
177:2
174:s
170:1
167:s
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160:p
156:1
153:p
138:2
135:m
133:(
127:1
124:m
122:(
116:2
113:m
109:1
106:m
65:)
59:(
54:)
50:(
46:.
36:.
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