550:, an expert in quantum computing: "The time needed to factor an RSA integer is the same order as the time needed to use that same integer as modulus for a single RSA encryption. In other words, it takes no more time to break RSA on a quantum computer (up to a multiplicative constant) than to use it legitimately on a classical computer." The general consensus is that these public key algorithms are insecure at any key size if sufficiently large quantum computers capable of running Shor's algorithm become available. The implication of this attack is that all data encrypted using current standards based security systems such as the ubiquitous
597:"A sufficiently large quantum computer, if built, would be capable of undermining all widely-deployed public key algorithms used for key establishment and digital signatures. It is generally accepted that quantum computing techniques are much less effective against symmetric algorithms than against current widely used public key algorithms. While public key cryptography requires changes in the fundamental design to protect against a potential future quantum computer, symmetric key algorithms are believed to be secure provided a sufficiently large key size is used. The public-key algorithms (
617:, and NSA is not specifying any commercial quantum resistant standards at this time. NSA expects that NIST will play a leading role in the effort to develop a widely accepted, standardized set of quantum resistant algorithms. Given the level of interest in the cryptographic community, we hope that there will be quantum resistant algorithms widely available in the next decade. The AES-256 and SHA-384 algorithms are symmetric, and believed to be safe from attack by a large quantum computer."
1963:
625:"A cryptanalytically-relevant quantum computer (CRQC) would have the potential to break public-key systems (sometimes referred to as asymmetric cryptography) that are used today. Given foreign pursuits in quantum computing, now is the time to plan, prepare and budget for a transition to QR algorithms to assure sustained protection of NSS and related assets in the event a CRQC becomes an achievable reality."
233:
590:/2 bits of security. Quantum brute force is easily defeated by doubling the key length, which has little extra computational cost in ordinary use. This implies that at least a 256-bit symmetric key is required to achieve 128-bit security rating against a quantum computer. As mentioned above, the NSA announced in 2015 that it plans to transition to quantum-resistant algorithms.
116:
and so it is only the difficulty of obtaining the key that determines security of the system, provided that there is no analytic attack (i.e. a "structural weakness" in the algorithms or protocols used), and assuming that the key is not otherwise available (such as via theft, extortion, or compromise
80:
was designed to have a 168-bit key, but an attack of complexity 2 is now known (i.e. Triple DES now only has 112 bits of security, and of the 168 bits in the key the attack has rendered 56 'ineffective' towards security). Nevertheless, as long as the security (understood as "the amount of effort it
196:
The actual degree of security achieved over time varies, as more computational power and more powerful mathematical analytic methods become available. For this reason, cryptologists tend to look at indicators that an algorithm or key length shows signs of potential vulnerability, to move to longer
582:. Bennett, Bernstein, Brassard, and Vazirani proved in 1996 that a brute-force key search on a quantum computer cannot be faster than roughly 2 invocations of the underlying cryptographic algorithm, compared with roughly 2 in the classical case. Thus in the presence of large quantum computers an
218:
revealed additional dangers in using Diffie-Hellman key exchange when only one or a few common 1024-bit or smaller prime moduli are in use. This practice, somewhat common at the time, allows large amounts of communications to be compromised at the expense of attacking a small number of primes.
201:
using 400 computers over 11 months. The factored number was of a special form; the special number field sieve cannot be used on RSA keys. The computation is roughly equivalent to breaking a 700 bit RSA key. However, this might be an advance warning that 1024 bit RSA keys used in secure online
982:
Adrian, David; Bhargavan, Karthikeyan; Durumeric, Zakir; Gaudry, Pierrick; Green, Matthew; Halderman, J. Alex; Heninger, Nadia; Springall, Drew; Thomé, Emmanuel; Valenta, Luke; VanderSloot, Benjamin; Wustrow, Eric; Zanella-Béguelin, Santiago; Zimmermann, Paul (October 2015).
514:
previously recommended 256-bit ECC for protecting classified information up to the SECRET level, and 384-bit for TOP SECRET; In 2015 it announced plans to transition to quantum-resistant algorithms by 2024, and until then recommends 384-bit for all classified information.
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observed that "Last time, it took nine years for us to generalize from a special to a nonspecial, hard-to-factor number" and when asked whether 1024-bit RSA keys are dead, said: "The answer to that question is an unqualified yes."
558:
used to protect access to sensitive computing systems is at risk. Encrypted data protected using public-key algorithms can be archived and may be broken at a later time, commonly known as retroactive/retrospective decryption or
473:
1024-bit RSA keys are equivalent in strength to 80-bit symmetric keys, 2048-bit RSA keys to 112-bit symmetric keys, 3072-bit RSA keys to 128-bit symmetric keys, and 15360-bit RSA keys to 256-bit symmetric keys. In 2003,
613:) are all vulnerable to attack by a sufficiently large quantum computer. While a number of interesting quantum resistant public key algorithms have been proposed external to NSA, nothing has been standardized by
295:
of keys in what is known as a brute-force attack. Because longer symmetric keys require exponentially more work to brute force search, a sufficiently long symmetric key makes this line of attack impractical.
149:). In light of this, and the practical difficulty of managing such long keys, modern cryptographic practice has discarded the notion of perfect secrecy as a requirement for encryption, and instead focuses on
132:
A key should, therefore, be large enough that a brute-force attack (possible against any encryption algorithm) is infeasible – i.e. would take too long and/or would take too much memory to execute.
478:
claimed that 1024-bit keys were likely to become crackable sometime between 2006 and 2010, while 2048-bit keys are sufficient until 2030. As of 2020 the largest RSA key publicly known to be cracked is
69:. Ideally, the lower-bound on an algorithm's security is by design equal to the key length (that is, the algorithm's design does not detract from the degree of security inherent in the key length).
366:
However, by the late 90s, it became clear that DES could be cracked in a few days' time-frame with custom-built hardware such as could be purchased by a large corporation or government. The book
499:(ECC) is an alternative set of asymmetric algorithms that is equivalently secure with shorter keys, requiring only approximately twice the bits as the equivalent symmetric algorithm. A 256-bit
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1491:
1943:
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493:, which is related to the integer factorization problem on which RSA's strength is based. Thus, a 2048-bit Diffie-Hellman key has about the same strength as a 2048-bit RSA key.
370:(O'Reilly and Associates) tells of the successful ability in 1998 to break 56-bit DES by a brute-force attack mounted by a cyber civil rights group with limited resources; see
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351:
and NIST argued was sufficient for non-governmental protection at the time. The NSA has major computing resources and a large budget; some cryptographers including
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614:
409:
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633:(now referred to as CNSA 1.0), originally launched in January 2016, to the Commercial National Security Algorithm Suite 2.0 (CNSA 2.0), both summarized below:
459:
must be longer for equivalent resistance to attack than symmetric algorithm keys. The most common methods are assumed to be weak against sufficiently powerful
319:
would be able to search the possible keys more efficiently. If a suitably sized quantum computer would reduce a 128-bit key down to 64-bit security, roughly a
1579:
858:
630:
389:
published in 2001 uses key sizes of 128, 192 or 256 bits. Many observers consider 128 bits sufficient for the foreseeable future for symmetric algorithms of
1558:
Blaze, Matt; Diffie, Whitfield; Rivest, Ronald L.; et al. "Minimal Key
Lengths for Symmetric Ciphers to Provide Adequate Commercial Security". January, 1996
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402:
81:
would take to gain access") is sufficient for a particular application, then it does not matter if key length and security coincide. This is important for
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610:
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Even if a symmetric cipher is currently unbreakable by exploiting structural weaknesses in its algorithm, it may be possible to run through the entire
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of computer systems). The widely accepted notion that the security of the system should depend on the key alone has been explicitly formulated by
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65:(i.e. a logarithmic measure of the fastest known attack against an algorithm), because the security of all algorithms can be violated by
578:) are widely conjectured to offer greater security against known quantum computing attacks. They are widely thought most vulnerable to
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algorithm has roughly the same key strength as RSA for the same key sizes. The work factor for breaking Diffie-Hellman is based on the
500:
1619:
272:
993:
401:
has issued guidance that it plans to switch to quantum computing resistant algorithms and now requires 256-bit AES keys for data
185:). Because each of these has a different level of cryptographic complexity, it is usual to have different key sizes for the same
76:
are designed to have security equal to their key length. However, after design, a new attack might be discovered. For instance,
534:
Derivatives of Shor's algorithm are widely conjectured to be effective against all mainstream public-key algorithms including
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complained that this made the cipher so weak that NSA computers would be able to break a DES key in a day through brute force
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1034:
888:"Transitions: Recommendation for Transitioning the Use of Cryptographic Algorithms and Key Lengths, NIST SP-800-131A Rev 2"
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455:. These problems are time-consuming to solve, but usually faster than trying all possible keys by brute force. Thus,
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key sizes or more difficult algorithms. For example, as of May 2007, a 1039-bit integer was factored with the
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Arjen K. Lenstra, Eric R. Verheul: Selecting
Cryptographic Key Sizes. J. Cryptology 14(4): 255-293 (2001) —
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189:, depending upon the algorithm used. For example, the security available with a 1024-bit key using asymmetric
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increases. The large number of operations (2) required to try all possible 128-bit keys is widely considered
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145:', the key length must be at least as large as the message and only used once (this algorithm is called the
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1517:"Announcing the Commercial National Security Algorithm Suite 2.0, U/OO/194427-22, PP-22-1338, Ver. 1.0"
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depends on the intractability (computational and theoretical) of certain mathematical problems such as
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are used to control the operation of a cipher so that only the correct key can convert encrypted text (
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for key agreement is now disallowed." NIST approved symmetric encryption algorithms include three-key
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key. A message encrypted with an elliptic key algorithm using a 109-bit long key was broken in 2004.
363:. The NSA disputed this, claiming that brute-forcing DES would take them "something like 91 years".
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Encryption systems are often grouped into families. Common families include symmetric systems (e.g.
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1492:"NSA Releases Future Quantum-Resistant (QR) Algorithm Requirements for National Security Systems"
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470:, an update to the widely accepted recommendation of a 1024-bit minimum since at least 2002.
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proposed phasing out 80-bit keys by 2015. At 2005, 80-bit keys were allowed only until 2010.
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1530:. September 2022. Table IV: CNSA 2.0 algorithms, p. 9.; Table V: CNSA 1.0 algorithms, p. 10
547:
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467:
371:
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142:
1206:"Recommendation for Key Management; Part 3: Application-Specific Key Management Guidance"
1153:
Barker, Elaine; Barker, William; Burr, William; Polk, William; Smid, Miles (2005-08-01).
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keys for general use. Because of this, DES was replaced in most security applications by
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is considered approximately equal in security to an 80-bit key in a symmetric algorithm.
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Since 2015, NIST guidance says that "the use of keys that provide less than 112 bits of
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992:. 22nd ACM Conference on Computer and Communications Security (CCS '15). Denver, CO.
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for conventional digital computing techniques for the foreseeable future. However, a
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206:, since they may become breakable in the foreseeable future. Cryptography professor
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1084:"Minimal key lengths for symmetric ciphers to provide adequate commercial security"
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374:. Even before that demonstration, 56 bits was considered insufficient length for
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comes the closest with an effective security of roughly half its key length.
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109:
105:
531:. Of the two, Shor's offers the greater risk to current security systems.
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1832:
1585:
436:
1464:"Commercial National Security Algorithm Suite and Quantum Computing FAQ"
1253:"A Cost-Based Security Analysis of Symmetric and Asymmetric Key Lengths"
571:
479:
382:, which has 112 bits of security when using 168-bit keys (triple key).
257: in this section. Unsourced material may be challenged and removed.
1753:
55:
408:
In 2003, the U.S. National
Institute for Standards and Technology,
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bits, there are 2 possible keys. This number grows very rapidly as
777:
Algorithm for computing a condensed representation of information
691:
Algorithm for computing a condensed representation of information
1387:"Certicom Announces Elliptic Curve Cryptography Challenge Winner"
713:
Asymmetric algorithm for digitally signing firmware and software
702:
Asymmetric algorithm for digitally signing firmware and software
503:(ECDH) key has approximately the same safety factor as a 128-bit
1109:, Cato Institute Briefing Paper no. 51, Arnold G. Reinhold, 1999
606:
1608:
986:
Imperfect
Forward Secrecy: How Diffie-Hellman Fails in Practice
844:
See the discussion on the relationship between key lengths and
85:, because no such algorithm is known to satisfy this property;
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Since
September 2022, the NSA has been transitioning from the
432:
226:
43:
1574:
466:
Since 2015, NIST recommends a minimum of 2048-bit keys for
339:
was selected in 1974 as the base for what would become the
1552:
Recommendation for Key
Management — Part 1: general,
523:
The two best known quantum computing attacks are based on
1580:
Articles discussing the implications of quantum computing
1035:"DES Stanford-NBS-NSA meeting recording & transcript"
941:"Researchers: 307-digit key crack endangers 1024-bit RSA"
27:
Number of bits in a key used by a cryptographic algorithm
848:
attacks at the bottom of this page for more information.
108:. All commonly-used ciphers are based on publicly known
857:
See the complete tables and the transition timeline at
1774:
Cryptographically secure pseudorandom number generator
1443:
Bennett C.H., Bernstein E., Brassard G., Vazirani U.,
1283:"Recommendation for Key Management: Part 1 – General"
1155:"Recommendation for Key Management – Part 1: General"
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61:
Key length defines the upper-bound on an algorithm's
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used to protect e-commerce and
Internet banking and
343:. Lucifer's key length was reduced from 128 bits to
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1642:
1446:
The strengths and weaknesses of quantum computation
763:Elliptic Curve Digital Signature Algorithm (ECDSA)
593:In a 2016 Quantum Computing FAQ, the NSA affirmed:
519:
Effect of quantum computing attacks on key strength
1082:; Thompson, Eric; Wiener, Michael (January 1996).
881:
879:
877:
752:Elliptic Curve Diffie-Hellman (ECDH) Key Exchange
744:Symmetric block cipher for information protection
658:Symmetric block cipher for information protection
574:) and collision resistant hash functions (such as
1575:www.keylength.com: An online keylength calculator
705:All parameters approved. SHA256/192 recommended.
1199:
1197:
1011:"How secure is AES against brute force attacks?"
915:"Researcher: RSA 1024-bit Encryption not Enough"
397:become available. However, as of 2015, the U.S.
173:). They may be grouped according to the central
623:
595:
1416:"Commercial National Security Algorithm Suite"
1294:National Institute of Standards and Technology
1217:National Institute of Standards and Technology
1166:National Institute of Standards and Technology
886:Barker, Elaine; Roginsky, Allen (March 2019).
1620:
1107:Strong Cryptography The Global Tide of Change
327:supports key lengths of 256 bits and longer.
8:
1555:NIST Special Publication 800-57. March, 2007
859:Commercial National Security Algorithm Suite
810:Asymmetric algorithm for digital signatures
766:Asymmetric algorithm for digital signatures
680:Asymmetric algorithm for digital signatures
631:Commercial National Security Algorithm Suite
125:(in the 1940s); the statements are known as
965:"Weak Diffie-Hellman and the Logjam Attack"
799:Asymmetric algorithm for key establishment
788:Asymmetric algorithm for key establishment
755:Asymmetric algorithm for key establishment
669:Asymmetric algorithm for key establishment
621:In a 2022 press release, the NSA notified:
323:equivalent. This is one of the reasons why
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1613:
1605:
1601:
1204:Barker, Elaine; Dang, Quynh (2015-01-22).
273:Learn how and when to remove this message
726:
640:
873:
837:
710:Xtended Merkle Signature Scheme (XMSS)
427:. Approvals for two-key Triple DES and
566:Mainstream symmetric ciphers (such as
7:
255:adding citations to reliable sources
741:Advanced Encryption Standard (AES)
655:Advanced Encryption Standard (AES)
1364:. Cado-nfs-discuss. Archived from
435:'s Skipjack algorithm used in its
141:showed that to achieve so-called '
129:and Shannon's Maxim respectively.
25:
785:Diffie-Hellman (DH) Key Exchange
1962:
1961:
1319:from the original on 2020-05-09.
999:from the original on 2022-10-10.
699:Leighton-Micali Signature (LMS)
546:. According to Professor Gilles
443:Asymmetric algorithm key lengths
231:
1360:Zimmermann, Paul (2020-02-28).
1234:from the original on 2015-02-26
1183:from the original on 2016-12-13
331:Symmetric algorithm key lengths
242:needs additional citations for
165:) and asymmetric systems (e.g.
1823:Information-theoretic security
586:-bit key can provide at least
157:Key size and encryption system
1:
501:Elliptic-curve Diffie–Hellman
439:program employs 80-bit keys.
1422:. 2015-08-09. Archived from
1393:. 2004-04-27. Archived from
1330:Kaliski, Burt (2003-05-06).
1131:. 2009-01-15. Archived from
939:Cheng, Jacqui (2007-05-23).
774:Secure Hash Algorithm (SHA)
688:Secure Hash Algorithm (SHA)
431:were withdrawn in 2015; the
387:Advanced Encryption Standard
1939:Message authentication code
1894:Cryptographic hash function
1707:Cryptographic hash function
1302:10.6028/NIST.SP.800-57pt1r5
1281:Barker, Elaine (May 2020).
1225:10.6028/NIST.SP.800-57pt3r1
544:elliptic curve cryptography
497:Elliptic-curve cryptography
403:classified up to Top Secret
171:Elliptic-curve cryptography
87:elliptic curve cryptography
2008:
1818:Harvest now, decrypt later
1473:. 2016-01-01. pp. 6–8
1362:"Factorization of RSA-250"
1125:"NSA Suite B Cryptography"
561:harvest now, decrypt later
491:discrete logarithm problem
284:
199:special number field sieve
1957:
1934:Post-quantum cryptography
1604:
1451:SIAM Journal on Computing
813:Minimum 3072-bit modulus
802:Minimum 3072-bit modulus
791:Minimum 3072-bit modulus
83:asymmetric-key algorithms
1924:Quantum key distribution
1914:Authenticated encryption
1769:Random number generation
1528:National Security Agency
1496:National Security Agency
1471:National Security Agency
1453:26(5): 1510-1523 (1997).
1420:National Security Agency
1332:"TWIRL and RSA Key Size"
1290:NIST Special Publication
1213:NIST Special Publication
1174:10.6028/NIST.SP.800-57p1
1162:NIST Special Publication
1129:National Security Agency
716:All parameters approved
449:public key cryptosystems
399:National Security Agency
341:Data Encryption Standard
74:symmetric-key algorithms
42:refers to the number of
18:Key space (cryptography)
1919:Public-key cryptography
1909:Symmetric-key algorithm
1712:Key derivation function
1672:Cryptographic primitive
1665:Authentication protocol
1655:Outline of cryptography
1650:History of cryptography
1595:TWIRL and RSA key sizes
1660:Cryptographic protocol
627:
619:
151:computational security
1813:End-to-end encryption
1759:Cryptojacking malware
1586:cryptographic toolkit
453:integer factorization
447:The effectiveness of
299:With a key of length
127:Kerckhoffs' principle
54:algorithm (such as a
1929:Quantum cryptography
1853:Trusted timestamping
251:improve this article
1692:Cryptographic nonce
694:SHA-384 or SHA-512
677:CRYSTALS-Dilithium
376:symmetric algorithm
315:capable of running
202:commerce should be
121:(in the 1880s) and
67:brute-force attacks
1798:Subliminal channel
1782:Pseudorandom noise
1729:Key (cryptography)
1391:BlackBerry Limited
1168:. Table 4, p. 66.
1080:Shimomura, Tsutomu
1068:Diffie, Whitefield
580:Grover's algorithm
529:Grover's algorithm
361:parallel computing
317:Grover's algorithm
287:Brute-force attack
223:Brute-force attack
139:information theory
119:Auguste Kerckhoffs
1979:
1978:
1975:
1974:
1858:Key-based routing
1848:Trapdoor function
1719:Digital signature
1524:media.defense.gov
1072:Rivest, Ronald L.
846:quantum computing
817:
816:
720:
719:
485:The Finite Field
461:quantum computers
417:security strength
395:quantum computers
393:'s quality until
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187:level of security
16:(Redirected from
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313:quantum computer
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871:
866:
865:
856:
852:
843:
839:
834:
822:
666:CRYSTALS-Kyber
521:
482:with 829 bits.
463:in the future.
457:asymmetric keys
445:
372:EFF DES cracker
333:
289:
279:
268:
262:
259:
248:
236:
225:
183:Feistel ciphers
159:
143:perfect secrecy
95:
28:
23:
22:
15:
12:
11:
5:
2005:
2003:
1995:
1994:
1992:Key management
1984:
1983:
1977:
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1970:
1969:
1958:
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1944:Random numbers
1941:
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1906:
1901:
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1868:Garlic routing
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1795:
1790:
1788:Secure channel
1785:
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1777:
1766:
1761:
1756:
1751:
1749:Key stretching
1746:
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1726:
1721:
1716:
1715:
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1709:
1699:
1697:Cryptovirology
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1682:Cryptocurrency
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1569:External links
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826:Key stretching
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603:Diffie-Hellman
540:Diffie-Hellman
520:
517:
487:Diffie-Hellman
444:
441:
357:Martin Hellman
337:Lucifer cipher
332:
329:
285:Main article:
281:
280:
239:
237:
230:
224:
221:
158:
155:
123:Claude Shannon
94:
91:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2004:
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1990:
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1949:Steganography
1947:
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1932:
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1920:
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1904:Stream cipher
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1863:Onion routing
1861:
1859:
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1844:
1843:Shared secret
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1739:Key generator
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1702:Hash function
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1677:Cryptanalysis
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1563:Citeseer link
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1459:
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1448:
1447:
1440:
1437:
1426:on 2022-02-18
1425:
1421:
1417:
1411:
1408:
1397:on 2016-09-27
1396:
1392:
1388:
1382:
1379:
1368:on 2020-02-28
1367:
1363:
1356:
1353:
1342:on 2017-04-17
1341:
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1326:
1323:
1315:
1311:
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1303:
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1263:on 2017-01-13
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1200:
1198:
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1149:
1146:
1135:on 2009-02-07
1134:
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1120:
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1108:
1103:
1100:
1089:
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1073:
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1065:
1059:
1056:
1045:on 2012-05-03
1044:
1040:
1036:
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1027:
1016:
1012:
1006:
1003:
995:
988:
987:
978:
975:
971:. 2015-05-20.
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783:
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768:
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750:
747:256-bit keys
746:
743:
740:
739:
735:
732:
729:
728:
725:
724:
715:
712:
709:
708:
704:
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698:
697:
693:
690:
687:
686:
682:
679:
676:
675:
671:
668:
665:
664:
661:256-bit keys
660:
657:
654:
653:
649:
646:
643:
642:
639:
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634:
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626:
622:
618:
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266:
256:
252:
246:
245:
240:This section
238:
234:
229:
228:
222:
220:
217:
216:Logjam attack
212:
209:
208:Arjen Lenstra
205:
200:
194:
192:
188:
184:
180:
176:
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164:
156:
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103:
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68:
64:
59:
57:
53:
52:cryptographic
49:
45:
41:
37:
33:
19:
1899:Block cipher
1744:Key schedule
1734:Key exchange
1724:Kleptography
1687:Cryptosystem
1636:Cryptography
1591:Burt Kaliski
1551:
1532:. Retrieved
1523:
1511:
1500:. Retrieved
1498:. 2022-09-07
1486:
1475:. Retrieved
1458:
1444:
1439:
1428:. Retrieved
1424:the original
1410:
1399:. Retrieved
1395:the original
1381:
1370:. Retrieved
1366:the original
1355:
1344:. Retrieved
1340:the original
1325:
1289:
1276:
1265:. Retrieved
1261:the original
1247:
1236:. Retrieved
1212:
1185:. Retrieved
1161:
1148:
1137:. Retrieved
1133:the original
1102:
1091:. Retrieved
1058:
1047:. Retrieved
1043:the original
1038:
1029:
1018:. Retrieved
1014:
1005:
985:
977:
968:
959:
948:. Retrieved
945:Ars Technica
944:
934:
923:. Retrieved
921:. 2007-05-23
918:
909:
898:. Retrieved
894:
853:
840:
769:Curve P-384
758:Curve P-384
722:
721:
636:
635:
628:
624:
620:
596:
592:
587:
583:
565:
533:
522:
509:
495:
484:
476:RSA Security
472:
465:
446:
414:
407:
384:
368:Cracking DES
367:
365:
347:, which the
334:
309:out of reach
304:
300:
298:
290:
269:
260:
249:Please help
244:verification
241:
213:
195:
160:
147:one-time pad
131:
96:
93:Significance
71:
60:
39:
35:
32:cryptography
29:
1887:Mathematics
1878:Mix network
1064:Blaze, Matt
736:Parameters
650:Parameters
263:August 2012
177:used (e.g.
114:open source
1838:Ciphertext
1808:Decryption
1803:Encryption
1764:Ransomware
1597:(May 2003)
1534:2024-04-14
1502:2024-04-14
1477:2024-04-21
1430:2020-07-12
1401:2016-09-24
1372:2020-07-12
1346:2017-11-24
1267:2016-09-24
1238:2017-11-24
1187:2019-01-08
1139:2016-09-24
1093:2011-10-14
1049:2016-09-24
1020:2016-09-24
969:weakdh.org
950:2016-09-24
925:2016-09-24
900:2023-02-11
869:References
730:Algorithm
644:Algorithm
421:Triple DES
380:Triple DES
204:deprecated
110:algorithms
102:ciphertext
78:Triple DES
50:used by a
40:key length
1828:Plaintext
1310:243189598
733:Function
647:Function
214:The 2015
175:algorithm
135:Shannon's
106:plaintext
1986:Category
1967:Category
1873:Kademlia
1833:Codetext
1776:(CSPRNG)
1314:Archived
1229:Archived
1178:Archived
1039:Toad.com
1015:EE Times
994:Archived
919:PC World
861:article.
820:See also
780:SHA-384
723:CNSA 1.0
683:Level V
672:Level V
637:CNSA 2.0
548:Brassard
437:Fortezza
429:Skipjack
137:work on
63:security
36:key size
1643:General
1088:Fortify
572:Twofish
480:RSA-250
345:56 bits
112:or are
1754:Keygen
1308:
1296:: 53.
1219:: 12.
609:, and
423:, and
335:IBM's
56:cipher
1784:(PRN)
1584:NIST
1520:(PDF)
1467:(PDF)
1317:(PDF)
1306:S2CID
1286:(PDF)
1232:(PDF)
1209:(PDF)
1181:(PDF)
1158:(PDF)
997:(PDF)
990:(PDF)
891:(PDF)
832:Notes
611:ECDSA
293:space
104:) to
72:Most
46:in a
807:RSA
796:RSA
615:NIST
607:ECDH
542:and
527:and
510:The
410:NIST
385:The
355:and
181:and
169:and
98:Keys
44:bits
1298:doi
1221:doi
1170:doi
599:RSA
576:SHA
570:or
568:AES
563:".
556:SSH
552:SSL
536:RSA
512:NSA
505:AES
468:RSA
433:NSA
425:AES
391:AES
349:NSA
325:AES
321:DES
253:by
191:RSA
179:ECC
167:RSA
163:AES
58:).
48:key
38:or
30:In
1988::
1593::
1526:.
1522:.
1494:.
1469:.
1449:.
1418:.
1389:.
1334:.
1312:.
1304:.
1292:.
1288:.
1255:.
1227:.
1215:.
1211:.
1196:^
1176:.
1164:.
1160:.
1127:.
1114:^
1086:.
1078:;
1074:;
1070:;
1066:;
1037:.
1013:.
967:.
943:.
917:.
893:.
876:^
605:,
601:,
538:,
405:.
34:,
1628:e
1621:t
1614:v
1537:.
1505:.
1480:.
1433:.
1404:.
1375:.
1349:.
1300::
1270:.
1241:.
1223::
1190:.
1172::
1142:.
1096:.
1052:.
1023:.
953:.
928:.
903:.
588:n
584:n
559:"
305:n
301:n
276:)
270:(
265:)
261:(
247:.
20:)
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