213:. However, unexpected correlations have been found in several such ostensibly independent processes. From an information-theoretic point of view, the amount of randomness, the entropy that can be generated, is equal to the entropy provided by the system. But sometimes, in practical situations, numbers are needed with more randomness than the available entropy can provide. Also, the processes to extract randomness from a running system are slow in actual practice. In such instances, a CSPRNG can sometimes be used. A CSPRNG can "stretch" the available entropy over more bits.
3774:
76:
2201:
All these above-mentioned schemes, save for X9.17, also mix the state of a CSPRNG with an additional source of entropy. They are therefore not "pure" pseudorandom number generators, in the sense that the output is not completely determined by their initial state. This addition aims to prevent attacks
278:
Most PRNGs are not suitable for use as CSPRNGs and will fail on both counts. First, while most PRNGs' outputs appear random to assorted statistical tests, they do not resist determined reverse engineering. Specialized statistical tests may be found specially tuned to such a PRNG that shows the random
2244:
When the maximum number of bits output from this PRNG is equal to the 2, the resulting output delivers the mathematically expected security level that the key size would be expected to generate, but the output is shown to not be indistinguishable from a true random number generator. When the maximum
260:
Every CSPRNG should withstand "state compromise extension attacks". In the event that part or all of its state has been revealed (or guessed correctly), it should be impossible to reconstruct the stream of random numbers prior to the revelation. Additionally, if there is an entropy input while
1877:
the requested randomness is output by running additional cycles. This is wasteful from a performance perspective, but does not immediately cause issues with forward secrecy. However, realizing the performance implications, the NIST recommends an "extended AES-CTR-DRBG interface" for its
1882:
submissions. This interface allows multiple sets of randomness to be generated without intervening erasure, only erasing when the user explicitly signals the end of requests. As a result, the key could remain in memory for an extended time if the "extended interface" is misused. Newer
2968:
Is there any serious argument that adding new entropy all the time is a good thing? The Linux /dev/urandom manual page claims that without new entropy the user is "theoretically vulnerable to a cryptographic attack", but (as I've mentioned in various venues) this is a ludicrous
2403:
where hardware vendors use a hardcoded seed key for the ANSI X9.31 RNG algorithm, stating "an attacker can brute-force encrypted data to discover the rest of the encryption parameters and deduce the master encryption key used to encrypt web sessions or
2025:, the successor to Yarrow, which does not attempt to evaluate the entropic quality of its inputs; it uses SHA-256 and "any good block cipher". Fortuna is used in FreeBSD. Apple changed to Fortuna for most or all Apple OSs beginning around Dec. 2019.
621:
2359:. The NSA worked covertly to get its own version of the NIST draft security standard approved for worldwide use in 2006. The leaked document states that "eventually, NSA became the sole editor". In spite of the known potential for a
2351:. Both papers reported that, as independent security experts long suspected, the NSA had been introducing weaknesses into CSPRNG standard 800-90; this being confirmed for the first time by one of the top-secret documents leaked to
97:
929:
275:. However, this algorithm is not cryptographically secure; an attacker who determines which bit of pi is currently in use (i.e. the state of the algorithm) will be able to calculate all preceding bits as well.
279:
numbers not to be truly random. Second, for most PRNGs, when their state has been revealed, all past random numbers can be retrodicted, allowing an attacker to read all past messages, as well as future ones.
3125:
Rukhin, Andrew; Soto, Juan; Nechvatal, James; Smid, Miles; Barker, Elaine; Leigh, Stefan; Levenson, Mark; Vangel, Mark; Banks, David; Heckert, N.; Dray, James; Vo, San; Bassham, Lawrence (April 30, 2010).
3807:
774:
382:
1483:
1326:
1242:
1591:
2245:
number of bits output from this PRNG is less than it, the expected security level is delivered and the output appears to be indistinguishable from a true random number generator.
206:
guarantee of perfect secrecy only holds if the key material comes from a true random source with high entropy, and thus any kind of pseudorandom number generator is insufficient.
1726:
1659:
1940:
provides a conditional security proof for the Blum Blum Shub algorithm. However the algorithm is very inefficient and therefore impractical unless extreme security is needed.
1401:
2754:"2017.07.23: Fast-key-erasure random-number generators: An effort to clean up several messes simultaneously. #rng #forwardsecrecy #urandom #cascade #hmac #rekeying #proofs"
271:
in sequence, starting from some unknown point in the binary expansion, it may well satisfy the next-bit test and thus be statistically random, as pi is conjectured to be a
2813:
1154:
425:
673:
1057:
997:
1808:
can remove a considerable amount of the bias in any bit stream, which should be applied to each bit stream before using any variation of the Santha–Vazirani design.
1518:
2067:
1784:
1757:
1353:
1115:
1084:
1024:
956:
445:
2241:
of the underlying block cipher when the number of bits output from this PRNG is greater than two to the power of the underlying block cipher's block size in bits.
818:
647:
221:
The requirements of an ordinary PRNG are also satisfied by a cryptographically secure PRNG, but the reverse is not true. CSPRNG requirements fall into two groups:
1879:
3422:
1800:
Santha and
Vazirani proved that several bit streams with weak randomness can be combined to produce a higher-quality, quasi-random bit stream. Even earlier,
2735:
2799:
3300:
3080:
1964:
209:
Ideally, the generation of random numbers in CSPRNGs uses entropy obtained from a high-quality source, generally the operating system's randomness
2081:
823:
2943:
2903:
2590:
2565:
2532:
2073:
2367:
continued using Dual_EC_DRBG until the backdoor was confirmed in 2013. RSA Security received a $ 10 million payment from the NSA to do so.
3182:
2767:
2475:
432:
3812:
3802:
3415:
2718:
2691:
2653:
1988:
in the Dual_EC_DRBG standard (which were revealed in 2013 to be probably backdoored by NSA) are replaced with non-backdoored values.
123:
3208:
2015:, which attempts to evaluate the entropic quality of its seeding inputs, and uses SHA-1 and 3DES internally. Yarrow was used in
1848:
693:
680:
301:
252:
proved in 1982 that a generator passing the next-bit test will pass all other polynomial-time statistical tests for randomness.
3633:
3564:
2510:
Kelsey, John; Schneier, Bruce; Wagner, David; Hall, Chris (1998). "Cryptanalytic
Attacks on Pseudorandom Number Generators".
1867:
101:
3234:
257:
They hold up well under serious attack, even when part of their initial or running state becomes available to an attacker:
2223:
This withdrawn standard has four PRNGs. Two of them are uncontroversial and proven: CSPRNGs named Hash_DRBG and HMAC_DRBG.
1936:. Since the only known way to solve that problem is to factor the modulus, it is generally regarded that the difficulty of
1409:
2340:
1933:
389:
47:
3408:
2191:
1860:
1247:
1163:
261:
running, it should be infeasible to use knowledge of the input's state to predict future conditions of the CSPRNG state.
176:
17:
3749:
3704:
3507:
1900:
3628:
3156:
2392:
2252:
for CTR_DRBG depends on limiting the total number of generate requests and the bits provided per generate request.
1948:
1944:
3744:
2417:
1523:
2237:. It has an uncontroversial design but has been proven to be weaker in terms of distinguishing attack, than the
3734:
3724:
3579:
2645:
2396:
2332:
86:
2198:
is leaked, the entire X9.17 stream can be predicted; this weakness is cited as a reason for creating Yarrow.
3729:
3719:
3512:
3472:
3465:
3450:
3445:
3249:
2405:
105:
90:
3351:
2467:
2272:
This is essentially NIST SP 800-90A with Dual_EC_DRBG removed, and is the withdrawn standard's replacement.
3517:
3460:
2827:
187:
3391:
3777:
3623:
3569:
2921:"Yarrow-160: Notes on the Design and Analysis of the Yarrow Cryptographic Pseudorandom Number Generator"
2421:
1937:
153:
3128:"A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications"
2920:
1664:
3356:
2511:
1596:
3739:
3663:
2895:
2336:
1805:
1795:
3267:
2889:
2376:
1358:
3492:
3342:
3127:
2959:
2490:
2441:
1914:
primitive can be used as a base of a CSPRNG, for example, as part of the construct that NIST calls
627:
295:
195:
183:
163:
158:
2607:
2461:
3608:
3592:
3534:
2710:
Embedded
Systems Security: Practical Methods for Safe and Secure Software and Systems Development
2327:
1825:
1120:
203:
191:
2782:"Linux 5.17 Random Number Generator Seeing Speed-Ups, Switching From SHA1 To BLAKE2s - Phoronix"
1997:"Practical" CSPRNG schemes not only include an CSPRNG algorithm, but also a way to initialize ("
182:
The "quality" of the randomness required for these applications varies. For example, creating a
3352:
Java standard class providing a cryptographically strong pseudo-random number generator (PRNG).
2363:
backdoor and other known significant deficiencies with Dual_EC_DRBG, several companies such as
395:
3668:
3658:
3524:
2939:
2899:
2857:
2714:
2687:
2649:
2586:
2561:
2538:
2528:
2471:
2249:
652:
616:{\displaystyle \left|\Pr _{x\gets \{0,1\}^{k}}-\Pr _{r\gets \{0,1\}^{p(k)}}\right|<\mu (k)}
1029:
969:
3603:
3455:
3382:, Reza Rezaeian Farashahi and Berry Schoenmakers and Andrey Sidorenko, IACR ePrint 2006/321.
3329:
3271:
3135:
3107:
3079:
2981:
2931:
2675:
2520:
2380:
2012:
2001:") it while keeping the seed secret. A number of such schemes have been defined, including:
1801:
1488:
226:
3370:, Daniel R. L. Brown and Kristian Gjosteen, IACR ePrint 2007/048. To appear in CRYPTO 2007.
2420:, Japan used a cipher machine for diplomatic communications; the United States was able to
1762:
1735:
1520:
by splitting its output into the next state and the actual output. This is done by setting
1331:
1093:
1090:, that withstands state compromise extensions in the following sense. If the initial state
1062:
1002:
934:
3346:
2344:
2217:
794:
632:
241:
1883:"fast-key-erasure" RNGs erase the key with randomness as soon as randomness is requested.
2865:
2494:
1980:(amount of bits provided per iteration) than in the Dual_EC_DRBG standard, and that the
3678:
3598:
3554:
3497:
3482:
3275:
3025:"The Notorious PRG: Formal verification of the HMAC-DRBG pseudorandom number generator"
2861:
2853:
2683:
2384:
2356:
2238:
2058:
2022:
1929:
1903:
might also be a base of a good CSPRNG, using, for example, a construct that NIST calls
1889:
148:
2634:
2347:, which allows the NSA to readily decrypt material that was encrypted with the aid of
3796:
3759:
3714:
3673:
3653:
3544:
3502:
3477:
2497:. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science, 1982.
2388:
2019:
and other Apple OS' up until about
December 2019, after which it switched to Fortuna.
283:
272:
233:
1870:
_DRBG is often used as a random number generator in systems that use AES encryption.
3709:
3549:
3539:
3529:
3487:
3431:
3024:
2364:
2360:
2348:
2321:
2315:
2260:
2256:
2234:
2230:
2156:
1959:
1844:
267:
For instance, if the PRNG under consideration produces output by computing bits of
199:
137:
51:
2070:, offered on Windows. Different versions of Windows use different implementations.
2708:
2259:. It has been shown to not be cryptographically secure and is believed to have a
3688:
3368:
A Security
Analysis of the NIST SP 800-90 Elliptic Curve Random Number Generator
3333:
3055:"Security Bounds for the NIST Codebook-based Deterministic Random Bit Generator"
2097:
1998:
1831:
75:
2781:
3648:
3618:
3613:
3574:
3340:
Java "entropy pool" for cryptographically secure unpredictable random numbers.
3140:
2089:
2085:
2038:
249:
3106:
Computer
Security Division, Information Technology Laboratory (24 May 2016).
2963:
2753:
2678:(1963-03-01). "Various techniques for use in connection with random digits".
2542:
2524:
1888:
A stream cipher can be converted into a CSPRNG. This has been done with RC4,
3638:
2935:
2282:
ANSI X9.62-1998 Annex A.4, obsoleted by ANSI X9.62-2005, Annex D (HMAC_DRBG)
2063:
1915:
1904:
392:(PRNG, or PRG in some references), if it stretches the length of its input (
3157:"Revealed: how US and UK spy agencies defeat internet privacy and security"
2440:
The use of entropy-mixing after CSPRNG initialization has been question by
924:{\displaystyle G_{k}\colon \{0,1\}^{k}\to \{0,1\}^{k}\times \{0,1\}^{t(k)}}
435:
from true randomness, i.e. for any probabilistic polynomial time algorithm
3081:"Government Announces Steps to Restore Confidence on Encryption Standards"
27:
Type of functions designed for being unsolvable by root-finding algorithms
3683:
3643:
3357:
Cryptographically Secure Random number on
Windows without using CryptoAPI
2642:
Proceedings of the 25th IEEE Symposium on
Foundations of Computer Science
2226:
2103:. Each time a random number is required, it executes the following steps:
2051:
1955:
1893:
1856:
2872:
2293:
There are also standards for statistical testing of new CSPRNG designs:
2999:
2029:
3385:
3301:"DUHK Crypto Attack Recovers Encryption Keys, Exposes VPN Connections"
3054:
2298:
A Statistical Test Suite for Random and
Pseudorandom Number Generators
248:+1)th bit with probability of success non-negligibly better than 50%.
3559:
3280:"Practical state recovery attacks against legacy RNG implementations"
2930:. Lecture Notes in Computer Science. Vol. 1758. pp. 13–33.
2399:, released details of the DUHK (Don't Use Hard-coded Keys) attack on
1821:
190:
needs only uniqueness. On the other hand, the generation of a master
171:
141:
2190:
Obviously, the technique is easily generalized to any block cipher;
3279:
3250:"Exclusive: Secret contract tied NSA and security industry pioneer"
2424:, mostly because the "key values" used were insufficiently random.
2028:
The Linux kernel CSPRNG, which uses ChaCha20 to generate data, and
3379:
3373:
3367:
3361:
2016:
167:
690:
There is an equivalent characterization: For any function family
298:, a family of deterministic polynomial time computable functions
3392:
NIST Statistical Test Suite documentation and software download.
3376:, Berry Schoenmakers and Andrey Sidorenko, IACR ePrint 2006/190.
2635:"Generating quasi-random sequences from slightly-random sources"
2400:
2287:
1911:
1852:
3404:
3374:
Cryptanalysis of the Dual
Elliptic Curve Pseudorandom Generator
2828:"FreeBSD 12.0-RELEASE Release Notes: Runtime Libraries and API"
2919:
Kelsey, John; Schneier, Bruce; Ferguson, Niels (August 1999).
2047:
1932:
algorithm has a security proof based on the difficulty of the
210:
69:
3380:
Efficient Pseudorandom Generators Based on the DDH Assumption
3209:"Did NSA Put a Secret Backdoor in New Encryption Standard?"
1485:
can be turned into a forward secure PRNG with block length
268:
769:{\displaystyle G_{k}\colon \{0,1\}^{k}\to \{0,1\}^{p(k)}}
377:{\displaystyle G_{k}\colon \{0,1\}^{k}\to \{0,1\}^{p(k)}}
3362:
Conjectured Security of the ANSI-NIST Elliptic Curve RNG
3339:
3183:"N.S.A. Able to Foil Basic Safeguards of Privacy on Web"
1786:
as the pseudorandom output block of the current period.
50:(PRNG) with properties that make it suitable for use in
3808:
Cryptographically secure pseudorandom number generators
2928:
Sixth Annual Workshop on Selected Areas in Cryptography
282:
CSPRNGs are designed explicitly to resist this type of
18:
Cryptographically secure pseudo-random number generator
3585:
Cryptographically secure pseudorandom number generator
32:
cryptographically secure pseudorandom number generator
2210:
Several CSPRNGs have been standardized. For example:
1830:
Designs based on mathematical problems thought to be
1765:
1738:
1667:
1599:
1526:
1491:
1478:{\displaystyle G\colon \{0,1\}^{k}\to \{0,1\}^{p(k)}}
1412:
1361:
1334:
1250:
1166:
1123:
1096:
1065:
1032:
1005:
972:
937:
826:
797:
696:
655:
635:
448:
398:
304:
3396:
3388:, Zvi Gutterman and Benny Pinkas and Tzachy Reinman.
2255:
The fourth and final PRNG in this standard is named
2006:
1947:
has a security proof based on the difficulty of the
784:
cannot be predicted by a polynomial time algorithm.
3697:
3438:
2310:
NSA kleptographic backdoor in the Dual_EC_DRBG PRNG
3155:James Borger; Glenn Greenwald (6 September 2013).
3000:"Analysis of Underlying Assumptions in NIST DRBGs"
2707:Kleidermacher, David; Kleidermacher, Mike (2012).
2519:. Berlin, Heidelberg: Springer Berlin Heidelberg.
2248:It is noted in the next revision that the claimed
1820:Designs based on cryptographic primitives such as
1778:
1751:
1720:
1653:
1585:
1512:
1477:
1395:
1347:
1321:{\displaystyle (r_{1},r_{2},\dots ,r_{i},s_{i+1})}
1320:
1237:{\displaystyle (y_{1},y_{2},\dots ,y_{i},s_{i+1})}
1236:
1148:
1109:
1078:
1051:
1018:
991:
950:
923:
812:
768:
667:
641:
615:
419:
376:
2734:Cox, George; Dike, Charles; Johnston, DJ (2011).
1851:using, for example, a special construct that the
2736:"Intel's Digital Random Number Generator (DRNG)"
2078:Financial Institution Key Management (wholesale)
2042:, a CSPRNG in Unix-like systems that seeds from
1847:can be converted into a CSPRNG by running it in
780:is a PRNG if and only if the next output bit of
526:
455:
2891:Malicious Cryptography: Exposing Cryptovirology
2633:Miklos Santha, Umesh V. Vazirani (1984-10-24).
2609:Lecture 5 Notes of Introduction to Cryptography
1244:must be computationally indistinguishable from
3235:"RSA warns developers not to use RSA products"
3416:
3386:Analysis of the Linux Random Number Generator
2495:Theory and applications of trapdoor functions
1816:CSPRNG designs are divided into two classes:
8:
2866:"Chapter 5: Pseudorandom Bits and Sequences"
1976:. The 2006 proof explicitly assumes a lower
1561:
1457:
1444:
1432:
1419:
1375:
1362:
1137:
1124:
903:
890:
878:
865:
853:
840:
748:
735:
723:
710:
549:
536:
478:
465:
356:
343:
331:
318:
3364:, Daniel R. L. Brown, IACR ePrint 2006/117.
3048:
3046:
3044:
1586:{\displaystyle G(s)=G_{0}(s)\Vert G_{1}(s)}
439:, which outputs 1 or 0 as a distinguisher,
104:. Unsourced material may be challenged and
40:cryptographic pseudorandom number generator
3423:
3409:
3401:
3397:
2583:Foundations of cryptography I: Basic Tools
2558:Foundations of cryptography I: Basic Tools
2202:even if the initial state is compromised.
3139:
3053:Campagna, Matthew J. (November 1, 2006).
2585:, Cambridge: Cambridge University Press,
2560:, Cambridge: Cambridge University Press,
1838:Designs based on cryptographic primitives
1770:
1764:
1743:
1737:
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1677:
1668:
1666:
1640:
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1624:
1609:
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1525:
1490:
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1435:
1411:
1378:
1360:
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1303:
1290:
1271:
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1249:
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1187:
1174:
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1140:
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1101:
1095:
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1064:
1037:
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1004:
977:
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906:
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856:
831:
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796:
751:
726:
701:
695:
654:
634:
552:
529:
481:
458:
447:
397:
359:
334:
309:
303:
124:Learn how and when to remove this message
2964:"cr.yp.to: 2014.02.05: Entropy Attacks!"
2505:
2503:
2460:Katz, Jonathan; Lindell, Yehuda (2008).
1873:The NIST CTR_DRBG scheme erases the key
194:requires a higher quality, such as more
166:in certain signature schemes, including
3078:Perlroth, Nicole (September 10, 2013).
2680:The Collected Works of John von Neumann
2452:
2433:
2050:, but all main implementations now use
1962:, based on the assumed hardness of the
240:bits of a random sequence, there is no
3336:, Randomness Requirements for Security
2888:Young, Adam; Yung, Moti (2004-02-01).
2084:standard as well. It takes as input a
56:cryptographic random number generator
7:
3181:Nicole Perlroth (5 September 2013).
2096:and (the initial value of) a 64-bit
1965:Decisional Diffie–Hellman assumption
1355:are chosen uniformly at random from
102:adding citations to reliable sources
3233:Matthew Green (20 September 2013).
3207:Bruce Schneier (15 November 2007).
2463:Introduction to Modern Cryptography
2111:to the maximum resolution possible.
1117:is chosen uniformly at random from
3023:Ye, Katherine Qinru (April 2016).
2300:, NIST Special Publication 800-22.
2286:A good reference is maintained by
1059:and the pseudorandom output block
25:
2998:Kan, Wilson (September 4, 2007).
2225:The third PRNG in this standard,
1880:Post-Quantum Cryptography Project
1721:{\displaystyle |G_{1}(s)|=p(k)-k}
433:computationally indistinguishable
3773:
3772:
3248:Joseph Menn (20 December 2013).
2874:Handbook of Applied Cryptography
1958:wrote a 2006 security proof for
1654:{\displaystyle |G_{0}(s)|=|s|=k}
244:algorithm that can predict the (
232:Every CSPRNG should satisfy the
74:
2194:has been suggested. If the key
2080:), which has been adopted as a
962:is the current state at period
3634:Information-theoretic security
2422:crack it and read its messages
2412:Japanese PURPLE cipher machine
2279:ANSI X9.31-1998 Appendix A.2.4
1732:is a forward secure PRNG with
1709:
1703:
1693:
1689:
1683:
1669:
1641:
1633:
1625:
1621:
1615:
1601:
1580:
1574:
1558:
1552:
1536:
1530:
1501:
1495:
1470:
1464:
1441:
1396:{\displaystyle \{0,1\}^{t(k)}}
1388:
1382:
1315:
1251:
1231:
1167:
916:
910:
862:
807:
801:
761:
755:
732:
659:
610:
604:
590:
581:
575:
569:
562:
556:
533:
519:
510:
507:
501:
495:
489:
462:
408:
402:
369:
363:
340:
54:. It is also referred to as a
1:
2341:pseudorandom number generator
2107:Obtain the current date/time
1951:but is also very inefficient.
1934:quadratic residuosity problem
1026:) consists of the next state
390:pseudorandom number generator
48:pseudorandom number generator
2046:. It originally is based on
1861:Advanced Encryption Standard
3750:Message authentication code
3705:Cryptographic hash function
3508:Cryptographic hash function
2768:"Github commit of random.c"
1899:A cryptographically secure
1149:{\displaystyle \{0,1\}^{k}}
236:. That is, given the first
3829:
3629:Harvest now, decrypt later
3144:– via csrc.nist.gov.
2393:University of Pennsylvania
2331:reported in 2013 that the
2313:
2276:ANSI X9.17-1985 Appendix C
2155:, where ⊕ denotes bitwise
2114:Compute a temporary value
1949:discrete logarithm problem
1859:. CTR_DBRG typically uses
1793:
138:cryptographic applications
3768:
3745:Post-quantum cryptography
3400:
3141:10.6028/NIST.SP.800-22r1a
2816:. CVS. November 16, 2014.
2814:"CVS log of arc4random.c"
2800:"CVS log of arc4random.c"
2713:. Elsevier. p. 256.
2134:Compute the random value
931:, where the input string
420:{\displaystyle p(k)>k}
3813:Cryptographic primitives
3803:Cryptographic algorithms
3735:Quantum key distribution
3725:Authenticated encryption
3580:Random number generation
2646:University of California
2581:Goldreich, Oded (2001),
2556:Goldreich, Oded (2001),
2525:10.1007/3-540-69710-1_12
2513:Fast Software Encryption
2397:Johns Hopkins University
2333:National Security Agency
1923:Number-theoretic designs
668:{\displaystyle x\gets X}
431:), and if its output is
3730:Public-key cryptography
3720:Symmetric-key algorithm
3513:Key derivation function
3473:Cryptographic primitive
3466:Authentication protocol
3451:Outline of cryptography
3446:History of cryptography
2936:10.1007/3-540-46513-8_2
2802:. CVS. October 1, 2013.
2770:. Github. July 2, 2016.
2406:virtual private network
1974:truncated point problem
1052:{\displaystyle s_{i+1}}
992:{\displaystyle s_{i+1}}
791:PRNG with block length
683:at random from the set
3518:Secure Hash Algorithms
3461:Cryptographic protocol
2009:in Unix-like systems.
1780:
1759:as the next state and
1753:
1722:
1655:
1587:
1514:
1513:{\displaystyle p(k)-k}
1479:
1397:
1349:
1322:
1238:
1150:
1111:
1080:
1053:
1020:
993:
952:
925:
814:
770:
669:
643:
617:
421:
378:
225:They pass statistical
154:initialization vectors
144:numbers, for example:
3624:End-to-end encryption
3570:Cryptojacking malware
2896:John Wiley & Sons
2752:Bernstein, Daniel J.
2466:. CRC press. p.
2375:On October 23, 2017,
2268:NIST SP 800-90A Rev.1
1945:Blum–Micali algorithm
1938:integer factorization
1781:
1779:{\displaystyle G_{1}}
1754:
1752:{\displaystyle G_{0}}
1723:
1656:
1588:
1515:
1480:
1398:
1350:
1348:{\displaystyle r_{i}}
1323:
1239:
1151:
1112:
1110:{\displaystyle s_{1}}
1081:
1079:{\displaystyle y_{i}}
1054:
1021:
1019:{\displaystyle y_{i}}
994:
953:
951:{\displaystyle s_{i}}
926:
815:
771:
670:
644:
618:
422:
379:
204:information-theoretic
198:. And in the case of
3740:Quantum cryptography
3664:Trusted timestamping
2686:. pp. 768–770.
2648:. pp. 434–440.
2408:(VPN) connections."
1855:in SP 800-90A calls
1826:cryptographic hashes
1796:Randomness extractor
1763:
1736:
1665:
1597:
1524:
1489:
1410:
1359:
1332:
1248:
1164:
1121:
1094:
1063:
1030:
1003:
970:
935:
824:
813:{\displaystyle t(k)}
795:
694:
653:
642:{\displaystyle \mu }
633:
446:
396:
384:for some polynomial
302:
98:improve this section
3493:Cryptographic nonce
2960:Daniel J. Bernstein
2491:Andrew Chi-Chih Yao
2442:Daniel J. Bernstein
2005:Implementations of
1970:x-logarithm problem
628:negligible function
3609:Subliminal channel
3593:Pseudorandom noise
3535:Key (cryptography)
3345:2008-12-02 at the
3187:The New York Times
3086:The New York Times
2858:van Oorschot, Paul
2328:The New York Times
2032:to ingest entropy.
1790:Entropy extraction
1776:
1749:
1718:
1651:
1583:
1510:
1475:
1393:
1345:
1318:
1234:
1146:
1107:
1076:
1049:
1016:
989:
966:, and the output (
948:
921:
810:
766:
665:
639:
613:
568:
488:
417:
374:
296:asymptotic setting
3790:
3789:
3786:
3785:
3669:Key-based routing
3659:Trapdoor function
3525:Digital signature
3307:. 25 October 2017
2945:978-3-540-67185-5
2905:978-0-7645-4975-5
2606:Dodis, Yevgeniy,
2592:978-0-511-54689-1
2567:978-0-511-54689-1
2534:978-3-540-64265-7
2335:(NSA) inserted a
2250:security strength
1993:Practical schemes
525:
454:
134:
133:
126:
16:(Redirected from
3820:
3776:
3775:
3604:Insecure channel
3456:Classical cipher
3425:
3418:
3411:
3402:
3398:
3317:
3316:
3314:
3312:
3297:
3291:
3290:
3284:
3272:Matthew D. Green
3264:
3258:
3257:
3245:
3239:
3238:
3230:
3224:
3223:
3221:
3219:
3204:
3198:
3197:
3195:
3193:
3178:
3172:
3171:
3169:
3167:
3152:
3146:
3145:
3143:
3122:
3116:
3115:
3103:
3097:
3096:
3094:
3092:
3083:
3075:
3069:
3068:
3066:
3064:
3059:
3050:
3039:
3038:
3036:
3034:
3029:
3020:
3014:
3013:
3011:
3009:
3004:
2995:
2989:
2988:
2986:
2978:
2972:
2971:
2956:
2950:
2949:
2925:
2916:
2910:
2909:
2885:
2879:
2878:
2870:
2850:
2844:
2843:
2841:
2839:
2824:
2818:
2817:
2810:
2804:
2803:
2796:
2790:
2789:
2786:www.phoronix.com
2778:
2772:
2771:
2764:
2758:
2757:
2749:
2743:
2742:
2740:
2731:
2725:
2724:
2704:
2698:
2697:
2676:John von Neumann
2672:
2666:
2665:
2663:
2662:
2639:
2630:
2624:
2622:
2621:
2619:
2614:
2603:
2597:
2596:, Theorem 3.3.7.
2595:
2578:
2572:
2570:
2553:
2547:
2546:
2518:
2507:
2498:
2488:
2482:
2481:
2457:
2445:
2438:
2229:, is based on a
2182:
2162:Update the seed
2154:
2130:
2076:X9.17 standard (
2045:
1954:Daniel Brown of
1896:, to name a few.
1806:simple algorithm
1802:John von Neumann
1785:
1783:
1782:
1777:
1775:
1774:
1758:
1756:
1755:
1750:
1748:
1747:
1731:
1727:
1725:
1724:
1719:
1696:
1682:
1681:
1672:
1660:
1658:
1657:
1652:
1644:
1636:
1628:
1614:
1613:
1604:
1592:
1590:
1589:
1584:
1573:
1572:
1551:
1550:
1519:
1517:
1516:
1511:
1484:
1482:
1481:
1476:
1474:
1473:
1440:
1439:
1402:
1400:
1399:
1394:
1392:
1391:
1354:
1352:
1351:
1346:
1344:
1343:
1327:
1325:
1324:
1319:
1314:
1313:
1295:
1294:
1276:
1275:
1263:
1262:
1243:
1241:
1240:
1235:
1230:
1229:
1211:
1210:
1192:
1191:
1179:
1178:
1159:
1155:
1153:
1152:
1147:
1145:
1144:
1116:
1114:
1113:
1108:
1106:
1105:
1089:
1085:
1083:
1082:
1077:
1075:
1074:
1058:
1056:
1055:
1050:
1048:
1047:
1025:
1023:
1022:
1017:
1015:
1014:
998:
996:
995:
990:
988:
987:
965:
961:
957:
955:
954:
949:
947:
946:
930:
928:
927:
922:
920:
919:
886:
885:
861:
860:
836:
835:
819:
817:
816:
811:
783:
779:
775:
773:
772:
767:
765:
764:
731:
730:
706:
705:
686:
678:
674:
672:
671:
666:
649:. (The notation
648:
646:
645:
640:
622:
620:
619:
614:
597:
593:
567:
566:
565:
487:
486:
485:
438:
430:
426:
424:
423:
418:
387:
383:
381:
380:
375:
373:
372:
339:
338:
314:
313:
227:randomness tests
177:token generation
129:
122:
118:
115:
109:
78:
70:
21:
3828:
3827:
3823:
3822:
3821:
3819:
3818:
3817:
3793:
3792:
3791:
3782:
3764:
3693:
3434:
3429:
3347:Wayback Machine
3326:
3321:
3320:
3310:
3308:
3299:
3298:
3294:
3282:
3266:
3265:
3261:
3247:
3246:
3242:
3232:
3231:
3227:
3217:
3215:
3206:
3205:
3201:
3191:
3189:
3180:
3179:
3175:
3165:
3163:
3154:
3153:
3149:
3124:
3123:
3119:
3108:"Random Number"
3105:
3104:
3100:
3090:
3088:
3077:
3076:
3072:
3062:
3060:
3057:
3052:
3051:
3042:
3032:
3030:
3027:
3022:
3021:
3017:
3007:
3005:
3002:
2997:
2996:
2992:
2984:
2980:
2979:
2975:
2958:
2957:
2953:
2946:
2923:
2918:
2917:
2913:
2906:
2887:
2886:
2882:
2868:
2862:Vanstone, Scott
2854:Menezes, Alfred
2852:
2851:
2847:
2837:
2835:
2826:
2825:
2821:
2812:
2811:
2807:
2798:
2797:
2793:
2780:
2779:
2775:
2766:
2765:
2761:
2751:
2750:
2746:
2738:
2733:
2732:
2728:
2721:
2706:
2705:
2701:
2694:
2674:
2673:
2669:
2660:
2658:
2656:
2637:
2632:
2631:
2627:
2617:
2615:
2612:
2605:
2604:
2600:
2593:
2580:
2579:
2575:
2568:
2555:
2554:
2550:
2535:
2516:
2509:
2508:
2501:
2489:
2485:
2478:
2459:
2458:
2454:
2449:
2448:
2439:
2435:
2430:
2414:
2373:
2345:NIST SP 800-90A
2318:
2312:
2307:
2273:
2265:
2218:NIST SP 800-90A
2208:
2186:
2172:
2163:
2144:
2135:
2124:
2115:
2090:keying option 2
2043:
1995:
1925:
1840:
1814:
1798:
1792:
1766:
1761:
1760:
1739:
1734:
1733:
1729:
1673:
1663:
1662:
1605:
1595:
1594:
1564:
1542:
1522:
1521:
1487:
1486:
1456:
1431:
1408:
1407:
1374:
1357:
1356:
1335:
1330:
1329:
1328:, in which the
1299:
1286:
1267:
1254:
1246:
1245:
1215:
1202:
1183:
1170:
1162:
1161:
1160:, the sequence
1157:
1156:, then for any
1136:
1119:
1118:
1097:
1092:
1091:
1087:
1066:
1061:
1060:
1033:
1028:
1027:
1006:
1001:
1000:
973:
968:
967:
963:
959:
938:
933:
932:
902:
877:
852:
827:
822:
821:
793:
792:
781:
777:
747:
722:
697:
692:
691:
684:
676:
651:
650:
631:
630:
548:
477:
453:
449:
444:
443:
436:
428:
394:
393:
385:
355:
330:
305:
300:
299:
292:
247:
242:polynomial-time
239:
219:
130:
119:
113:
110:
95:
79:
68:
28:
23:
22:
15:
12:
11:
5:
3826:
3824:
3816:
3815:
3810:
3805:
3795:
3794:
3788:
3787:
3784:
3783:
3781:
3780:
3769:
3766:
3765:
3763:
3762:
3757:
3755:Random numbers
3752:
3747:
3742:
3737:
3732:
3727:
3722:
3717:
3712:
3707:
3701:
3699:
3695:
3694:
3692:
3691:
3686:
3681:
3679:Garlic routing
3676:
3671:
3666:
3661:
3656:
3651:
3646:
3641:
3636:
3631:
3626:
3621:
3616:
3611:
3606:
3601:
3599:Secure channel
3596:
3590:
3589:
3588:
3577:
3572:
3567:
3562:
3557:
3555:Key stretching
3552:
3547:
3542:
3537:
3532:
3527:
3522:
3521:
3520:
3515:
3510:
3500:
3498:Cryptovirology
3495:
3490:
3485:
3483:Cryptocurrency
3480:
3475:
3470:
3469:
3468:
3458:
3453:
3448:
3442:
3440:
3436:
3435:
3430:
3428:
3427:
3420:
3413:
3405:
3395:
3394:
3389:
3383:
3377:
3371:
3365:
3359:
3354:
3349:
3337:
3325:
3324:External links
3322:
3319:
3318:
3292:
3287:duhkattack.com
3276:Nadia Heninger
3268:Shaanan Cohney
3259:
3240:
3225:
3199:
3173:
3147:
3117:
3098:
3070:
3040:
3015:
2990:
2973:
2962:(2014-02-05).
2951:
2944:
2911:
2904:
2898:. sect 3.5.1.
2880:
2845:
2834:. 5 March 2019
2819:
2805:
2791:
2773:
2759:
2744:
2726:
2719:
2699:
2692:
2684:Pergamon Press
2667:
2654:
2625:
2598:
2591:
2573:
2566:
2548:
2533:
2499:
2483:
2477:978-1584885511
2476:
2451:
2450:
2447:
2446:
2432:
2431:
2429:
2426:
2413:
2410:
2389:cryptographers
2385:Nadia Heninger
2377:Shaanan Cohney
2372:
2369:
2357:Edward Snowden
2314:Main article:
2311:
2308:
2306:
2305:Security flaws
2303:
2302:
2301:
2284:
2283:
2280:
2277:
2271:
2270:
2269:
2263:NSA backdoor.
2239:security level
2222:
2221:
2220:
2215:
2207:
2204:
2188:
2187:
2185:
2184:
2168:
2160:
2140:
2132:
2120:
2112:
2104:
2071:
2059:CryptGenRandom
2055:
2035:
2034:
2033:
2026:
2020:
1994:
1991:
1990:
1989:
1952:
1941:
1930:Blum Blum Shub
1924:
1921:
1920:
1919:
1908:
1897:
1886:
1885:
1884:
1871:
1839:
1836:
1835:
1834:
1828:
1813:
1810:
1804:proved that a
1794:Main article:
1791:
1788:
1773:
1769:
1746:
1742:
1717:
1714:
1711:
1708:
1705:
1702:
1699:
1695:
1691:
1688:
1685:
1680:
1676:
1671:
1650:
1647:
1643:
1639:
1635:
1631:
1627:
1623:
1620:
1617:
1612:
1608:
1603:
1582:
1579:
1576:
1571:
1567:
1563:
1560:
1557:
1554:
1549:
1545:
1541:
1538:
1535:
1532:
1529:
1509:
1506:
1503:
1500:
1497:
1494:
1472:
1469:
1466:
1463:
1459:
1455:
1452:
1449:
1446:
1443:
1438:
1434:
1430:
1427:
1424:
1421:
1418:
1415:
1390:
1387:
1384:
1381:
1377:
1373:
1370:
1367:
1364:
1342:
1338:
1317:
1312:
1309:
1306:
1302:
1298:
1293:
1289:
1285:
1282:
1279:
1274:
1270:
1266:
1261:
1257:
1253:
1233:
1228:
1225:
1222:
1218:
1214:
1209:
1205:
1201:
1198:
1195:
1190:
1186:
1182:
1177:
1173:
1169:
1143:
1139:
1135:
1132:
1129:
1126:
1104:
1100:
1073:
1069:
1046:
1043:
1040:
1036:
1013:
1009:
986:
983:
980:
976:
945:
941:
918:
915:
912:
909:
905:
901:
898:
895:
892:
889:
884:
880:
876:
873:
870:
867:
864:
859:
855:
851:
848:
845:
842:
839:
834:
830:
809:
806:
803:
800:
789:forward-secure
763:
760:
757:
754:
750:
746:
743:
740:
737:
734:
729:
725:
721:
718:
715:
712:
709:
704:
700:
664:
661:
658:
638:
624:
623:
612:
609:
606:
603:
600:
596:
592:
589:
586:
583:
580:
577:
574:
571:
564:
561:
558:
555:
551:
547:
544:
541:
538:
535:
532:
528:
524:
521:
518:
515:
512:
509:
506:
503:
500:
497:
494:
491:
484:
480:
476:
473:
470:
467:
464:
461:
457:
452:
416:
413:
410:
407:
404:
401:
371:
368:
365:
362:
358:
354:
351:
348:
345:
342:
337:
333:
329:
326:
323:
320:
317:
312:
308:
291:
288:
265:
264:
263:
262:
255:
254:
253:
245:
237:
218:
215:
180:
179:
174:
161:
156:
151:
149:key generation
132:
131:
82:
80:
73:
67:
64:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3825:
3814:
3811:
3809:
3806:
3804:
3801:
3800:
3798:
3779:
3771:
3770:
3767:
3761:
3760:Steganography
3758:
3756:
3753:
3751:
3748:
3746:
3743:
3741:
3738:
3736:
3733:
3731:
3728:
3726:
3723:
3721:
3718:
3716:
3715:Stream cipher
3713:
3711:
3708:
3706:
3703:
3702:
3700:
3696:
3690:
3687:
3685:
3682:
3680:
3677:
3675:
3674:Onion routing
3672:
3670:
3667:
3665:
3662:
3660:
3657:
3655:
3654:Shared secret
3652:
3650:
3647:
3645:
3642:
3640:
3637:
3635:
3632:
3630:
3627:
3625:
3622:
3620:
3617:
3615:
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3594:
3591:
3586:
3583:
3582:
3581:
3578:
3576:
3573:
3571:
3568:
3566:
3563:
3561:
3558:
3556:
3553:
3551:
3548:
3546:
3545:Key generator
3543:
3541:
3538:
3536:
3533:
3531:
3528:
3526:
3523:
3519:
3516:
3514:
3511:
3509:
3506:
3505:
3504:
3503:Hash function
3501:
3499:
3496:
3494:
3491:
3489:
3486:
3484:
3481:
3479:
3478:Cryptanalysis
3476:
3474:
3471:
3467:
3464:
3463:
3462:
3459:
3457:
3454:
3452:
3449:
3447:
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3341:
3338:
3335:
3331:
3328:
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3323:
3306:
3302:
3296:
3293:
3288:
3281:
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3273:
3269:
3263:
3260:
3255:
3251:
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3229:
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3214:
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3203:
3200:
3188:
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3102:
3099:
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3074:
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3056:
3049:
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3045:
3041:
3026:
3019:
3016:
3001:
2994:
2991:
2983:
2977:
2974:
2970:
2965:
2961:
2955:
2952:
2947:
2941:
2937:
2933:
2929:
2922:
2915:
2912:
2907:
2901:
2897:
2893:
2892:
2884:
2881:
2876:
2875:
2867:
2863:
2859:
2855:
2849:
2846:
2833:
2829:
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2820:
2815:
2809:
2806:
2801:
2795:
2792:
2787:
2783:
2777:
2774:
2769:
2763:
2760:
2755:
2748:
2745:
2737:
2730:
2727:
2722:
2720:9780123868862
2716:
2712:
2711:
2703:
2700:
2695:
2693:0-08-009566-6
2689:
2685:
2681:
2677:
2671:
2668:
2657:
2655:0-8186-0591-X
2651:
2647:
2643:
2636:
2629:
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2611:
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2602:
2599:
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2500:
2496:
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2425:
2423:
2419:
2411:
2409:
2407:
2402:
2398:
2394:
2390:
2386:
2382:
2381:Matthew Green
2378:
2370:
2368:
2366:
2362:
2361:kleptographic
2358:
2354:
2350:
2346:
2342:
2338:
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2296:
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2294:
2291:
2289:
2281:
2278:
2275:
2274:
2267:
2266:
2264:
2262:
2261:kleptographic
2258:
2253:
2251:
2246:
2242:
2240:
2236:
2232:
2228:
2219:
2216:
2213:
2212:
2211:
2205:
2203:
2199:
2197:
2193:
2180:
2176:
2171:
2166:
2161:
2158:
2152:
2148:
2143:
2138:
2133:
2128:
2123:
2118:
2113:
2110:
2106:
2105:
2102:
2099:
2095:
2092:) key bundle
2091:
2087:
2083:
2079:
2075:
2072:
2069:
2065:
2061:
2060:
2056:
2053:
2049:
2041:
2040:
2036:
2031:
2027:
2024:
2021:
2018:
2014:
2011:
2010:
2008:
2004:
2003:
2002:
2000:
1992:
1987:
1983:
1979:
1975:
1971:
1967:
1966:
1961:
1957:
1953:
1950:
1946:
1942:
1939:
1935:
1931:
1927:
1926:
1922:
1917:
1913:
1909:
1906:
1902:
1898:
1895:
1891:
1887:
1881:
1876:
1872:
1869:
1865:
1864:
1862:
1858:
1854:
1850:
1846:
1842:
1841:
1837:
1833:
1829:
1827:
1823:
1819:
1818:
1817:
1811:
1809:
1807:
1803:
1797:
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1787:
1771:
1767:
1744:
1740:
1715:
1712:
1706:
1700:
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1686:
1678:
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1637:
1629:
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1610:
1606:
1577:
1569:
1565:
1555:
1547:
1543:
1539:
1533:
1527:
1507:
1504:
1498:
1492:
1467:
1461:
1453:
1450:
1447:
1436:
1428:
1425:
1422:
1416:
1413:
1404:
1385:
1379:
1371:
1368:
1365:
1340:
1336:
1310:
1307:
1304:
1300:
1296:
1291:
1287:
1283:
1280:
1277:
1272:
1268:
1264:
1259:
1255:
1226:
1223:
1220:
1216:
1212:
1207:
1203:
1199:
1196:
1193:
1188:
1184:
1180:
1175:
1171:
1141:
1133:
1130:
1127:
1102:
1098:
1071:
1067:
1044:
1041:
1038:
1034:
1011:
1007:
984:
981:
978:
974:
943:
939:
913:
907:
899:
896:
893:
887:
882:
874:
871:
868:
857:
849:
846:
843:
837:
832:
828:
804:
798:
790:
785:
758:
752:
744:
741:
738:
727:
719:
716:
713:
707:
702:
698:
688:
682:
662:
656:
636:
629:
607:
601:
598:
594:
587:
584:
578:
572:
559:
553:
545:
542:
539:
530:
522:
516:
513:
504:
498:
492:
482:
474:
471:
468:
459:
450:
442:
441:
440:
434:
414:
411:
405:
399:
391:
366:
360:
352:
349:
346:
335:
327:
324:
321:
315:
310:
306:
297:
289:
287:
285:
284:cryptanalysis
280:
276:
274:
273:normal number
270:
259:
258:
256:
251:
243:
235:
234:next-bit test
231:
230:
228:
224:
223:
222:
216:
214:
212:
207:
205:
201:
200:one-time pads
197:
193:
189:
185:
178:
175:
173:
169:
165:
162:
160:
157:
155:
152:
150:
147:
146:
145:
143:
139:
128:
125:
117:
107:
103:
99:
93:
92:
88:
83:This section
81:
77:
72:
71:
65:
63:
61:
57:
53:
49:
45:
41:
37:
33:
19:
3754:
3710:Block cipher
3584:
3550:Key schedule
3540:Key exchange
3530:Kleptography
3488:Cryptosystem
3432:Cryptography
3309:. Retrieved
3305:slashdot.org
3304:
3295:
3286:
3262:
3253:
3243:
3228:
3216:. Retrieved
3212:
3202:
3190:. Retrieved
3186:
3176:
3164:. Retrieved
3161:The Guardian
3160:
3150:
3131:
3120:
3111:
3101:
3091:November 19,
3089:. Retrieved
3085:
3073:
3063:November 19,
3061:. Retrieved
3033:November 19,
3031:. Retrieved
3018:
3008:November 19,
3006:. Retrieved
2993:
2982:"FIPS 186-4"
2976:
2967:
2954:
2927:
2914:
2890:
2883:
2877:. CRC Press.
2873:
2848:
2836:. Retrieved
2831:
2822:
2808:
2794:
2785:
2776:
2762:
2747:
2729:
2709:
2702:
2679:
2670:
2659:. Retrieved
2641:
2628:
2616:, retrieved
2608:
2601:
2582:
2576:
2571:, def 3.3.1.
2557:
2551:
2512:
2486:
2462:
2455:
2436:
2418:World War II
2415:
2374:
2365:RSA Security
2353:The Guardian
2352:
2349:Dual EC DRBG
2326:
2322:The Guardian
2320:
2319:
2316:Dual_EC_DRBG
2297:
2292:
2285:
2257:Dual EC DRBG
2254:
2247:
2243:
2235:counter mode
2231:block cipher
2224:
2209:
2200:
2195:
2189:
2178:
2174:
2169:
2164:
2157:exclusive or
2150:
2146:
2141:
2136:
2126:
2121:
2116:
2108:
2100:
2093:
2077:
2057:
2037:
1996:
1985:
1981:
1977:
1973:
1969:
1963:
1960:Dual EC DRBG
1874:
1849:counter mode
1845:block cipher
1815:
1799:
1405:
958:with length
788:
786:
689:
625:
293:
281:
277:
266:
220:
217:Requirements
208:
181:
135:
120:
111:
96:Please help
84:
59:
55:
52:cryptography
43:
39:
35:
31:
29:
3698:Mathematics
3689:Mix network
3218:7 September
3192:7 September
3166:7 September
3112:CSRC | NIST
2832:FreeBSD.org
2371:DUHK attack
2233:running in
2098:random seed
2044:/dev/random
2007:/dev/random
1593:, in which
675:means that
290:Definitions
3797:Categories
3649:Ciphertext
3619:Decryption
3614:Encryption
3575:Ransomware
3311:25 October
2661:2006-11-29
2428:References
2343:(PRNG) of
2214:FIPS 186-4
2062:, part of
2039:arc4random
1972:, and the
1086:of period
820:is a PRNG
679:is chosen
250:Andrew Yao
172:RSASSA-PSS
66:Background
3639:Plaintext
2838:24 August
2618:3 January
2543:0302-9743
2206:Standards
2068:CryptoAPI
2064:Microsoft
1916:HMAC_DRBG
1905:Hash_DRBG
1843:A secure
1713:−
1562:‖
1505:−
1442:→
1417::
1406:Any PRNG
1281:…
1197:…
888:×
863:→
838::
733:→
708::
681:uniformly
660:←
637:μ
626:for some
602:μ
534:←
523:−
463:←
341:→
316::
188:protocols
114:June 2024
85:does not
3778:Category
3684:Kademlia
3644:Codetext
3587:(CSPRNG)
3565:Machines
3343:Archived
2969:argument
2864:(1996).
2623:, def 4.
2337:backdoor
2227:CTR_DRBG
2052:ChaCha20
1956:Certicom
1894:ChaCha20
1857:CTR_DRBG
427:for any
186:in some
140:require
3439:General
3254:Reuters
2416:During
2391:at the
2339:into a
2030:BLAKE2s
2023:Fortuna
1863:(AES).
1822:ciphers
1812:Designs
1728:; then
388:, is a
294:In the
196:entropy
106:removed
91:sources
46:) is a
3560:Keygen
3332:
2942:
2902:
2717:
2690:
2652:
2589:
2564:
2541:
2531:
2474:
2383:, and
2167:= TDEA
2139:= TDEA
2119:= TDEA
2013:Yarrow
1978:outlen
1968:, the
1892:, and
202:, the
159:nonces
142:random
36:CSPRNG
3595:(PRN)
3283:(PDF)
3213:Wired
3058:(PDF)
3028:(PDF)
3003:(PDF)
2985:(PDF)
2924:(PDF)
2869:(PDF)
2739:(PDF)
2638:(PDF)
2613:(PDF)
2517:(PDF)
2017:macOS
1890:ISAAC
1875:after
184:nonce
168:ECDSA
164:salts
136:Most
44:CPRNG
38:) or
3334:4086
3313:2017
3220:2013
3194:2013
3168:2013
3132:NIST
3093:2016
3065:2016
3035:2016
3010:2016
2940:ISBN
2900:ISBN
2840:2019
2715:ISBN
2688:ISBN
2650:ISBN
2620:2016
2587:ISBN
2562:ISBN
2539:ISSN
2529:ISBN
2472:ISBN
2401:WPA2
2395:and
2325:and
2288:NIST
2086:TDEA
2082:FIPS
2074:ANSI
1999:seed
1984:and
1943:The
1928:The
1912:HMAC
1901:hash
1866:AES-
1853:NIST
1832:hard
1824:and
1661:and
599:<
412:>
170:and
89:any
87:cite
60:CRNG
3330:RFC
3136:doi
2932:doi
2521:doi
2355:by
2192:AES
2066:'s
2048:RC4
1910:An
1868:CTR
687:.)
211:API
192:key
100:by
62:).
3799::
3303:.
3285:.
3278:.
3274:;
3270:;
3252:.
3211:.
3185:.
3159:.
3134:.
3130:.
3110:.
3084:.
3043:^
2966:.
2938:.
2926:.
2894:.
2871:.
2860:;
2856:;
2830:.
2784:.
2682:.
2644:.
2640:.
2537:.
2527:.
2502:^
2493:.
2470:.
2468:70
2387:,
2379:,
2290:.
2177:⊕
2149:⊕
2054:.
1403:.
999:,
787:A
776:,
527:Pr
456:Pr
286:.
269:pi
229::
30:A
3424:e
3417:t
3410:v
3315:.
3289:.
3256:.
3237:.
3222:.
3196:.
3170:.
3138::
3114:.
3095:.
3067:.
3037:.
3012:.
2987:.
2948:.
2934::
2908:.
2842:.
2788:.
2756:.
2741:.
2723:.
2696:.
2664:.
2545:.
2523::
2480:.
2444:.
2196:k
2183:.
2181:)
2179:t
2175:x
2173:(
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2159:.
2153:)
2151:t
2147:s
2145:(
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2131:.
2129:)
2127:D
2125:(
2122:k
2117:t
2109:D
2101:s
2094:k
2088:(
1986:Q
1982:P
1918:.
1907:.
1772:1
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1745:0
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1730:G
1716:k
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1707:k
1704:(
1701:p
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1694:|
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1630:=
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1619:s
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1471:)
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
