25:
82:
5127:
705:
1397:
972:
2813:
1190:
1633:
3280:
3123:
3431:
1929:
2961:
509:
1201:
776:
3489:. For example, an appropriately chosen matrix can guarantee that small differences before the matrix multiplication will result in large differences after the matrix multiplication. Indeed, some modern ciphers use a matrix multiplication step to provide diffusion. For example, the MixColumns step in
2326:
1421:
Thus, if we work modulo 26 as above, the determinant must be nonzero, and must not be divisible by 2 or 13. If the determinant is 0, or has common factors with the modular base, then the matrix cannot be used in the Hill cipher, and another matrix must be chosen (otherwise it will not be possible to
3477:
plaintext/ciphertext character pairs can set up a linear system which can (usually) be easily solved; if it happens that this system is indeterminate, it is only necessary to add a few more plaintext/ciphertext pairs. Calculating this solution by standard linear algebra algorithms then takes very
2190:
2062:
4228:
Unfortunately the gearing arrangements (and thus the key) were fixed for any given machine, so triple encryption was recommended for security: a secret nonlinear step, followed by the wide diffusive step from the machine, followed by a third secret nonlinear step. (The much later
2639:
2574:
1023:
1431:
3132:
2972:
4155:
442:
3291:
1789:
2821:
700:{\displaystyle {\begin{pmatrix}6&24&1\\13&16&10\\20&17&15\end{pmatrix}}{\begin{pmatrix}0\\2\\19\end{pmatrix}}={\begin{pmatrix}67\\222\\319\end{pmatrix}}\equiv {\begin{pmatrix}15\\14\\7\end{pmatrix}}{\pmod {26}}}
1392:{\displaystyle {\begin{pmatrix}8&5&10\\21&8&21\\21&12&8\end{pmatrix}}{\begin{pmatrix}15\\14\\7\end{pmatrix}}={\begin{pmatrix}260\\574\\539\end{pmatrix}}\equiv {\begin{pmatrix}0\\2\\19\end{pmatrix}}{\pmod {26}}}
967:{\displaystyle {\begin{pmatrix}6&24&1\\13&16&10\\20&17&15\end{pmatrix}}{\begin{pmatrix}2\\0\\19\end{pmatrix}}={\begin{pmatrix}31\\216\\325\end{pmatrix}}\equiv {\begin{pmatrix}5\\8\\13\end{pmatrix}}{\pmod {26}}}
2201:
2071:
1940:
3940:
2808:{\displaystyle K^{-1}\equiv 9^{-1}{\begin{pmatrix}5&23\\24&3\end{pmatrix}}\equiv 3{\begin{pmatrix}5&23\\24&3\end{pmatrix}}\equiv {\begin{pmatrix}15&17\\20&9\end{pmatrix}}{\pmod {26}}}
1778:
3804:
2440:
1185:{\displaystyle {\begin{pmatrix}6&24&1\\13&16&10\\20&17&15\end{pmatrix}}^{-1}{\pmod {26}}\equiv {\begin{pmatrix}8&5&10\\21&8&21\\21&12&8\end{pmatrix}}}
1628:{\displaystyle {\begin{vmatrix}6&24&1\\13&16&10\\20&17&15\end{vmatrix}}=6(16\cdot 15-10\cdot 17)-24(13\cdot 15-10\cdot 20)+1(13\cdot 17-16\cdot 20)=441\equiv 25{\pmod {26}}}
765:
498:
4212:, and in fact is weaker than either, and slightly more laborious to operate by pencil-and-paper. As the dimension increases, the cipher rapidly becomes infeasible for a human to operate by hand.
3275:{\displaystyle {\begin{pmatrix}15&17\\20&9\end{pmatrix}}{\begin{pmatrix}0\\19\end{pmatrix}}={\begin{pmatrix}323\\171\end{pmatrix}}\equiv {\begin{pmatrix}11\\15\end{pmatrix}}{\pmod {26}}}
3118:{\displaystyle {\begin{pmatrix}15&17\\20&9\end{pmatrix}}{\begin{pmatrix}7\\8\end{pmatrix}}={\begin{pmatrix}241\\212\end{pmatrix}}\equiv {\begin{pmatrix}7\\4\end{pmatrix}}{\pmod {26}},}
4160:
Additionally it seems to be prudent to avoid too many zeroes in the key matrix, since they reduce diffusion. The net effect is that the effective keyspace of a basic Hill cipher is about
5107:
4937:
3617:
2428:
350:
26). The cipher can, of course, be adapted to an alphabet with any number of letters; all arithmetic just needs to be done modulo the number of letters instead of modulo 26.
4194:
3951:
1701:
2629:
3556:
3426:{\displaystyle {\begin{pmatrix}7\\4\end{pmatrix}},{\begin{pmatrix}11\\15\end{pmatrix}}\to {\begin{pmatrix}H\\E\end{pmatrix}},{\begin{pmatrix}L\\P\end{pmatrix}}\to HELP}
1924:{\displaystyle HELP\to {\begin{pmatrix}H\\E\end{pmatrix}},{\begin{pmatrix}L\\P\end{pmatrix}}\to {\begin{pmatrix}7\\4\end{pmatrix}},{\begin{pmatrix}11\\15\end{pmatrix}}}
4364:
3647:
2956:{\displaystyle HIAT\to {\begin{pmatrix}H\\I\end{pmatrix}},{\begin{pmatrix}A\\T\end{pmatrix}}\to {\begin{pmatrix}7\\8\end{pmatrix}},{\begin{pmatrix}0\\19\end{pmatrix}}}
1669:
367:
4233:
also uses an unkeyed diffusive middle step). Such a combination was actually very powerful for 1929, and indicates that Hill apparently understood the concepts of a
2363:
3475:
3657:
matrices. This is only an upper bound because not every matrix is invertible and thus usable as a key. The number of invertible matrices can be computed via the
4790:
2321:{\displaystyle {\begin{pmatrix}7\\8\end{pmatrix}},{\begin{pmatrix}0\\19\end{pmatrix}}\to {\begin{pmatrix}H\\I\end{pmatrix}},{\begin{pmatrix}A\\T\end{pmatrix}}}
4276:
2185:{\displaystyle {\begin{pmatrix}3&3\\2&5\end{pmatrix}}{\begin{pmatrix}11\\15\end{pmatrix}}\equiv {\begin{pmatrix}0\\19\end{pmatrix}}{\pmod {26}}}
1710:. Consequently, a useful variant of the Hill cipher adds 3 extra symbols (such as a space, a period and a question mark) to increase the modulus to 29.
2057:{\displaystyle {\begin{pmatrix}3&3\\2&5\end{pmatrix}}{\begin{pmatrix}7\\4\end{pmatrix}}\equiv {\begin{pmatrix}7\\8\end{pmatrix}}{\pmod {26}},}
4357:
46:
3822:
1724:
109:
in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
4783:
3686:
68:
2569:{\displaystyle {\begin{pmatrix}a&b\\c&d\end{pmatrix}}^{-1}=(ad-bc)^{-1}{\begin{pmatrix}d&-b\\-c&a\end{pmatrix}}}
4350:
3661:. I.e., a matrix is invertible modulo 26 if and only if it is invertible both modulo 2 and modulo 13. The number of invertible
4986:
2579:
720:
453:
4776:
3490:
3481:
While matrix multiplication alone does not result in a secure cipher it is still a useful step when combined with other
5102:
5057:
4870:
4196:. For a 5 × 5 Hill cipher, that is about 114 bits. Of course, key search is not the most efficient known attack.
4328:
39:
33:
4225:) for this device, which performed a 6 × 6 matrix multiplication modulo 26 using a system of gears and chains.
5155:
4981:
5097:
4234:
3658:
50:
5087:
5077:
4932:
3510:
98:
4300:
4230:
1422:
decrypt). Fortunately, matrices which satisfy the conditions to be used in the Hill cipher are fairly common.
5082:
5072:
4875:
4835:
4828:
4818:
4813:
3486:
982:
3569:
2368:
1706:
The risk of the determinant having common factors with the modulus can be eliminated by making the modulus
4823:
3443:
90:
5130:
4976:
4922:
4701:
4392:
1783:
be the key and suppose the plaintext message is 'HELP'. Then this plaintext is represented by two pairs
978:
4626:
331:
26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
4150:{\displaystyle 26^{n^{2}}(1-1/2)(1-1/2^{2})\cdots (1-1/2^{n})(1-1/13)(1-1/13^{2})\cdots (1-1/13^{n}).}
5092:
5016:
4732:
4636:
4590:
4580:
4575:
4570:
4562:
3670:
324:
113:
4855:
4751:
4746:
4660:
4494:
4296:
4163:
1674:
977:
which corresponds to a ciphertext of 'FIN'. Every letter has changed. The Hill cipher has achieved
3513:
is the set of all possible keys. The key space size is the number of possible keys. The effective
2586:
4961:
4945:
4892:
4727:
4646:
4552:
4484:
1014:
347:
335:
328:
125:
4415:
3527:
437:{\displaystyle {\begin{pmatrix}6&24&1\\13&16&10\\20&17&15\end{pmatrix}}}
5021:
5011:
4882:
4696:
4616:
4585:
4479:
4410:
3622:
2435:
1641:
1410:
314:
4215:
A Hill cipher of dimension 6 was implemented mechanically. Hill and a partner were awarded a
3945:
The number of invertible matrices modulo 26 is the product of those two numbers. Hence it is
128:
26. Though this is not an essential feature of the cipher, this simple scheme is often used:
4956:
4373:
3518:
3501:
is a combination of non-linear S-boxes with a carefully chosen matrix multiplication (MDS).
2338:
1002:
1001:
In order to decrypt, we turn the ciphertext back into a vector, then simply multiply by the
81:
3453:
4517:
4474:
4443:
4425:
4249:
4205:
4289:
Jeffrey
Overbey, William Traves, and Jerzy Wojdylo, On the Keyspace of the Hill Cipher,
5031:
4951:
4912:
4860:
4845:
4736:
4631:
4512:
4405:
4400:
4204:
When operating on 2 symbols at once, a Hill cipher offers no particular advantage over
106:
102:
5149:
5112:
5067:
5026:
5006:
4902:
4865:
4840:
4688:
4542:
4522:
4502:
4453:
4433:
4259:
1703:, 25 has no common factors with 26, and this matrix can be used for the Hill cipher.
4282:
Lester S. Hill, Concerning
Certain Linear Transformation Apparatus of Cryptography,
5062:
4907:
4897:
4887:
4850:
4799:
4621:
4532:
4438:
4254:
4209:
1707:
310:
4321:
4314:
5041:
4706:
4673:
4668:
4291:
1414:
5001:
4971:
4966:
4927:
4740:
4722:
4527:
4458:
4221:
3482:
711:
4237:
as well as confusion and diffusion. Unfortunately, his machine did not sell.
3809:
Equally, the number of invertible matrices modulo 13 (i.e. the order of GL(n,
4991:
4678:
5036:
4996:
4448:
3514:
3498:
4917:
4641:
4507:
4381:
4216:
3447:
447:
Since 'A' is 0, 'C' is 2 and 'T' is 19, the message is the vector:
4611:
4606:
4547:
3935:{\displaystyle 13^{n^{2}}(1-1/13)(1-1/13^{2})\cdots (1-1/13^{n}).}
80:
4245:
Other practical "pencil-and-paper" polygraphic ciphers include:
1773:{\displaystyle K={\begin{pmatrix}3&3\\2&5\end{pmatrix}}}
4772:
4346:
1017:
26, the inverse of the matrix used in the previous example is:
3799:{\displaystyle 2^{n^{2}}(1-1/2)(1-1/2^{2})\cdots (1-1/2^{n}).}
714:
of 'POH'. Now, suppose that our message is instead 'CAT', or:
338:, and it should be chosen randomly from the set of invertible
18:
4317:" implements the Hill cipher and shows the matrices involved
112:
The following discussion assumes an elementary knowledge of
3649:
is an upper bound on the key size of the Hill cipher using
1405:
One complications exist in picking the encrypting matrix:
1195:
Taking the previous example ciphertext of 'POH', we get:
2578:
This formula still holds after a modular reduction if a
4324:" illustrates the linear algebra behind the Hill Cipher
4271:
Lester S. Hill, Cryptography in an
Algebraic Alphabet,
4938:
Cryptographically secure pseudorandom number generator
3485:
operations, because matrix multiplication can provide
3387:
3358:
3329:
3300:
3235:
3206:
3177:
3141:
3075:
3046:
3017:
2981:
2932:
2903:
2874:
2845:
2758:
2719:
2677:
2529:
2450:
2297:
2268:
2239:
2210:
2145:
2116:
2080:
2014:
1985:
1949:
1900:
1871:
1842:
1813:
1739:
1440:
1345:
1309:
1273:
1210:
1124:
1033:
920:
884:
848:
785:
760:{\displaystyle {\begin{pmatrix}2\\0\\19\end{pmatrix}}}
729:
653:
617:
581:
518:
493:{\displaystyle {\begin{pmatrix}0\\2\\19\end{pmatrix}}}
462:
376:
4166:
3954:
3825:
3689:
3625:
3572:
3530:
3456:
3294:
3135:
2975:
2824:
2642:
2589:
2443:
2371:
2341:
2204:
2074:
1943:
1792:
1727:
1677:
1644:
1434:
1413:. The matrix will have an inverse if and only if its
1204:
1026:
779:
723:
512:
456:
370:
353:
Consider the message 'ACT', and the key below (or GYB
4334:
1417:
is inversible modulo n, where n is the modular base.
5050:
4806:
4715:
4687:
4659:
4599:
4561:
4493:
4467:
4424:
4391:
4380:
4188:
4149:
3934:
3798:
3641:
3611:
3550:
3469:
3425:
3274:
3117:
2955:
2807:
2623:
2568:
2422:
2357:
2320:
2184:
2056:
1923:
1772:
1695:
1663:
1627:
1391:
1184:
989:-dimensional Hill cipher can diffuse fully across
966:
759:
699:
492:
436:
85:Hill's cipher machine, from figure 4 of the patent
4275:Vol.36, June–July 1929, pp. 306–312. (
3669:matrices modulo 2 is equal to the order of the
4295:, Vol.29, No.1, January 2005, pp59–72. (
770:This time, the enciphered vector is given by:
4784:
4358:
334:The matrix used for encryption is the cipher
8:
1638:So, modulo 26, the determinant is 25. Since
16:Substitution cipher based on linear algebra
4791:
4777:
4769:
4388:
4365:
4351:
4343:
4339:
4335:
4331:" outlines the Hill Cipher with a Web page
1402:which gets us back to 'ACT', as expected.
4174:
4165:
4135:
4126:
4102:
4093:
4070:
4049:
4040:
4016:
4007:
3984:
3964:
3959:
3953:
3920:
3911:
3887:
3878:
3855:
3835:
3830:
3824:
3784:
3775:
3751:
3742:
3719:
3699:
3694:
3688:
3633:
3624:
3598:
3593:
3577:
3571:
3540:
3535:
3529:
3493:is a matrix multiplication. The function
3461:
3455:
3442:The basic Hill cipher is vulnerable to a
3382:
3353:
3324:
3295:
3293:
3256:
3230:
3201:
3172:
3136:
3134:
3096:
3070:
3041:
3012:
2976:
2974:
2927:
2898:
2869:
2840:
2823:
2789:
2753:
2714:
2672:
2663:
2647:
2641:
2612:
2588:
2524:
2515:
2481:
2445:
2442:
2414:
2395:
2379:
2370:
2346:
2340:
2292:
2263:
2234:
2205:
2203:
2166:
2140:
2111:
2075:
2073:
2035:
2009:
1980:
1944:
1942:
1895:
1866:
1837:
1808:
1791:
1734:
1726:
1676:
1655:
1643:
1609:
1435:
1433:
1373:
1340:
1304:
1268:
1205:
1203:
1119:
1100:
1091:
1028:
1025:
948:
915:
879:
843:
780:
778:
724:
722:
681:
648:
612:
576:
513:
511:
457:
455:
371:
369:
69:Learn how and when to remove this message
503:Thus the enciphered vector is given by:
130:
32:This article includes a list of general
124:Each letter is represented by a number
4286:Vol.38, 1931, pp. 135–154.
3612:{\displaystyle \log _{2}(26^{n^{2}})}
2423:{\displaystyle KK^{-1}=K^{-1}K=I_{2}}
7:
2195:and continue encryption as follows:
301:To encrypt a message, each block of
3264:
3104:
2797:
2174:
2043:
1617:
1381:
1108:
956:
689:
38:it lacks sufficient corresponding
14:
4284:The American Mathematical Monthly
4273:The American Mathematical Monthly
5126:
5125:
23:
3257:
3097:
2790:
2633:Hence in this case, we compute
2167:
2036:
1610:
1374:
1101:
1013:VMI in letters). We find that,
949:
682:
99:polygraphic substitution cipher
4987:Information-theoretic security
4141:
4114:
4108:
4081:
4078:
4058:
4055:
4028:
4022:
3995:
3992:
3972:
3926:
3899:
3893:
3866:
3863:
3843:
3790:
3763:
3757:
3730:
3727:
3707:
3606:
3586:
3408:
3350:
3268:
3258:
3108:
3098:
2895:
2837:
2801:
2791:
2609:
2590:
2580:modular multiplicative inverse
2512:
2493:
2260:
2178:
2168:
2047:
2037:
1863:
1805:
1621:
1611:
1594:
1570:
1561:
1537:
1528:
1504:
1385:
1375:
1112:
1102:
960:
950:
693:
683:
1:
4189:{\displaystyle 4.64n^{2}-1.7}
3450:. An opponent who intercepts
2434:can be computed by using the
1696:{\displaystyle 26=2\times 13}
3517:, in number of bits, is the
2624:{\displaystyle (ad-bc)^{-1}}
1425:For our example key matrix:
5103:Message authentication code
5058:Cryptographic hash function
4871:Cryptographic hash function
5172:
4982:Harvest now, decrypt later
3551:{\displaystyle 26^{n^{2}}}
305:letters (considered as an
5121:
5098:Post-quantum cryptography
4768:
4342:
4338:
4235:meet-in-the-middle attack
4200:Mechanical implementation
3659:Chinese Remainder Theorem
3446:because it is completely
1409:Not all matrices have an
5088:Quantum key distribution
5078:Authenticated encryption
4933:Random number generation
4329:Hill's Cipher Calculator
3642:{\displaystyle 4.7n^{2}}
1664:{\displaystyle 25=5^{2}}
5083:Public-key cryptography
5073:Symmetric-key algorithm
4876:Key derivation function
4836:Cryptographic primitive
4829:Authentication protocol
4819:Outline of cryptography
4814:History of cryptography
3521:of the key space size.
710:which corresponds to a
53:more precise citations.
4824:Cryptographic protocol
4374:Classical cryptography
4190:
4151:
3936:
3800:
3643:
3613:
3558:matrices of dimension
3552:
3471:
3444:known-plaintext attack
3427:
3276:
3119:
2957:
2809:
2625:
2570:
2424:
2359:
2358:{\displaystyle K^{-1}}
2322:
2186:
2058:
1925:
1774:
1697:
1665:
1629:
1393:
1186:
1005:of the key matrix (IFK
968:
761:
701:
494:
438:
313:) is multiplied by an
91:classical cryptography
86:
4977:End-to-end encryption
4923:Cryptojacking malware
4322:Hill Cipher Explained
4222:U.S. patent 1,845,947
4191:
4152:
3937:
3801:
3644:
3614:
3553:
3472:
3470:{\displaystyle n^{2}}
3428:
3277:
3120:
2958:
2810:
2626:
2571:
2425:
2360:
2335:is invertible, hence
2323:
2187:
2059:
1926:
1775:
1698:
1666:
1630:
1394:
1187:
969:
762:
702:
495:
439:
84:
5093:Quantum cryptography
5017:Trusted timestamping
4733:Index of coincidence
4637:Reservehandverfahren
4164:
3952:
3823:
3687:
3671:general linear group
3623:
3570:
3528:
3454:
3292:
3133:
2973:
2822:
2640:
2587:
2441:
2369:
2339:
2202:
2072:
1941:
1790:
1725:
1675:
1642:
1432:
1202:
1024:
777:
721:
510:
454:
368:
4856:Cryptographic nonce
4752:Kasiski examination
4747:Information leakage
4315:Hill Cipher Web App
4231:Even–Mansour cipher
2582:is used to compute
4962:Subliminal channel
4946:Pseudorandom noise
4893:Key (cryptography)
4728:Frequency analysis
4627:RasterschlĂĽssel 44
4186:
4147:
3932:
3796:
3639:
3609:
3548:
3467:
3423:
3402:
3373:
3344:
3315:
3272:
3250:
3221:
3192:
3166:
3115:
3090:
3061:
3032:
3006:
2953:
2947:
2918:
2889:
2860:
2805:
2783:
2744:
2702:
2621:
2566:
2560:
2475:
2420:
2355:
2318:
2312:
2283:
2254:
2225:
2182:
2160:
2131:
2105:
2054:
2029:
2000:
1974:
1921:
1915:
1886:
1857:
1828:
1770:
1764:
1693:
1661:
1625:
1492:
1389:
1367:
1331:
1295:
1262:
1182:
1176:
1085:
964:
942:
906:
870:
837:
757:
751:
697:
675:
639:
603:
570:
490:
484:
434:
428:
87:
5156:Classical ciphers
5143:
5142:
5139:
5138:
5022:Key-based routing
5012:Trapdoor function
4883:Digital signature
4764:
4763:
4760:
4759:
4655:
4654:
2430:. The inverse of
2365:exists such that
993:symbols at once.
361:URP in letters):
299:
298:
79:
78:
71:
5163:
5129:
5128:
4957:Insecure channel
4793:
4786:
4779:
4770:
4389:
4367:
4360:
4353:
4344:
4340:
4336:
4224:
4195:
4193:
4192:
4187:
4179:
4178:
4156:
4154:
4153:
4148:
4140:
4139:
4130:
4107:
4106:
4097:
4074:
4054:
4053:
4044:
4021:
4020:
4011:
3988:
3971:
3970:
3969:
3968:
3941:
3939:
3938:
3933:
3925:
3924:
3915:
3892:
3891:
3882:
3859:
3842:
3841:
3840:
3839:
3805:
3803:
3802:
3797:
3789:
3788:
3779:
3756:
3755:
3746:
3723:
3706:
3705:
3704:
3703:
3648:
3646:
3645:
3640:
3638:
3637:
3618:
3616:
3615:
3610:
3605:
3604:
3603:
3602:
3582:
3581:
3557:
3555:
3554:
3549:
3547:
3546:
3545:
3544:
3519:binary logarithm
3476:
3474:
3473:
3468:
3466:
3465:
3432:
3430:
3429:
3424:
3407:
3406:
3378:
3377:
3349:
3348:
3320:
3319:
3281:
3279:
3278:
3273:
3271:
3255:
3254:
3226:
3225:
3197:
3196:
3171:
3170:
3124:
3122:
3121:
3116:
3111:
3095:
3094:
3066:
3065:
3037:
3036:
3011:
3010:
2966:Then we compute
2962:
2960:
2959:
2954:
2952:
2951:
2923:
2922:
2894:
2893:
2865:
2864:
2814:
2812:
2811:
2806:
2804:
2788:
2787:
2749:
2748:
2707:
2706:
2671:
2670:
2655:
2654:
2632:
2630:
2628:
2627:
2622:
2620:
2619:
2575:
2573:
2572:
2567:
2565:
2564:
2523:
2522:
2489:
2488:
2480:
2479:
2429:
2427:
2426:
2421:
2419:
2418:
2403:
2402:
2387:
2386:
2364:
2362:
2361:
2356:
2354:
2353:
2327:
2325:
2324:
2319:
2317:
2316:
2288:
2287:
2259:
2258:
2230:
2229:
2191:
2189:
2188:
2183:
2181:
2165:
2164:
2136:
2135:
2110:
2109:
2063:
2061:
2060:
2055:
2050:
2034:
2033:
2005:
2004:
1979:
1978:
1934:Then we compute
1930:
1928:
1927:
1922:
1920:
1919:
1891:
1890:
1862:
1861:
1833:
1832:
1779:
1777:
1776:
1771:
1769:
1768:
1702:
1700:
1699:
1694:
1670:
1668:
1667:
1662:
1660:
1659:
1634:
1632:
1631:
1626:
1624:
1497:
1496:
1398:
1396:
1395:
1390:
1388:
1372:
1371:
1336:
1335:
1300:
1299:
1267:
1266:
1191:
1189:
1188:
1183:
1181:
1180:
1115:
1099:
1098:
1090:
1089:
1012:
1008:
973:
971:
970:
965:
963:
947:
946:
911:
910:
875:
874:
842:
841:
766:
764:
763:
758:
756:
755:
706:
704:
703:
698:
696:
680:
679:
644:
643:
608:
607:
575:
574:
499:
497:
496:
491:
489:
488:
443:
441:
440:
435:
433:
432:
360:
356:
131:
74:
67:
63:
60:
54:
49:this article by
40:inline citations
27:
26:
19:
5171:
5170:
5166:
5165:
5164:
5162:
5161:
5160:
5146:
5145:
5144:
5135:
5117:
5046:
4802:
4797:
4756:
4711:
4683:
4651:
4595:
4557:
4489:
4463:
4426:Polybius square
4420:
4384:
4376:
4371:
4310:
4268:
4250:Playfair cipher
4243:
4220:
4202:
4170:
4162:
4161:
4131:
4098:
4045:
4012:
3960:
3955:
3950:
3949:
3916:
3883:
3831:
3826:
3821:
3820:
3815:
3780:
3747:
3695:
3690:
3685:
3684:
3679:
3629:
3621:
3620:
3594:
3589:
3573:
3568:
3567:
3536:
3531:
3526:
3525:
3507:
3457:
3452:
3451:
3440:
3401:
3400:
3394:
3393:
3383:
3372:
3371:
3365:
3364:
3354:
3343:
3342:
3336:
3335:
3325:
3314:
3313:
3307:
3306:
3296:
3290:
3289:
3249:
3248:
3242:
3241:
3231:
3220:
3219:
3213:
3212:
3202:
3191:
3190:
3184:
3183:
3173:
3165:
3164:
3159:
3153:
3152:
3147:
3137:
3131:
3130:
3089:
3088:
3082:
3081:
3071:
3060:
3059:
3053:
3052:
3042:
3031:
3030:
3024:
3023:
3013:
3005:
3004:
2999:
2993:
2992:
2987:
2977:
2971:
2970:
2946:
2945:
2939:
2938:
2928:
2917:
2916:
2910:
2909:
2899:
2888:
2887:
2881:
2880:
2870:
2859:
2858:
2852:
2851:
2841:
2820:
2819:
2782:
2781:
2776:
2770:
2769:
2764:
2754:
2743:
2742:
2737:
2731:
2730:
2725:
2715:
2701:
2700:
2695:
2689:
2688:
2683:
2673:
2659:
2643:
2638:
2637:
2608:
2585:
2584:
2583:
2559:
2558:
2553:
2544:
2543:
2535:
2525:
2511:
2474:
2473:
2468:
2462:
2461:
2456:
2446:
2444:
2439:
2438:
2410:
2391:
2375:
2367:
2366:
2342:
2337:
2336:
2311:
2310:
2304:
2303:
2293:
2282:
2281:
2275:
2274:
2264:
2253:
2252:
2246:
2245:
2235:
2224:
2223:
2217:
2216:
2206:
2200:
2199:
2159:
2158:
2152:
2151:
2141:
2130:
2129:
2123:
2122:
2112:
2104:
2103:
2098:
2092:
2091:
2086:
2076:
2070:
2069:
2028:
2027:
2021:
2020:
2010:
1999:
1998:
1992:
1991:
1981:
1973:
1972:
1967:
1961:
1960:
1955:
1945:
1939:
1938:
1914:
1913:
1907:
1906:
1896:
1885:
1884:
1878:
1877:
1867:
1856:
1855:
1849:
1848:
1838:
1827:
1826:
1820:
1819:
1809:
1788:
1787:
1763:
1762:
1757:
1751:
1750:
1745:
1735:
1723:
1722:
1716:
1673:
1672:
1651:
1640:
1639:
1491:
1490:
1485:
1480:
1474:
1473:
1468:
1463:
1457:
1456:
1451:
1446:
1436:
1430:
1429:
1366:
1365:
1359:
1358:
1352:
1351:
1341:
1330:
1329:
1323:
1322:
1316:
1315:
1305:
1294:
1293:
1287:
1286:
1280:
1279:
1269:
1261:
1260:
1255:
1250:
1244:
1243:
1238:
1233:
1227:
1226:
1221:
1216:
1206:
1200:
1199:
1175:
1174:
1169:
1164:
1158:
1157:
1152:
1147:
1141:
1140:
1135:
1130:
1120:
1084:
1083:
1078:
1073:
1067:
1066:
1061:
1056:
1050:
1049:
1044:
1039:
1029:
1027:
1022:
1021:
1010:
1006:
999:
941:
940:
934:
933:
927:
926:
916:
905:
904:
898:
897:
891:
890:
880:
869:
868:
862:
861:
855:
854:
844:
836:
835:
830:
825:
819:
818:
813:
808:
802:
801:
796:
791:
781:
775:
774:
750:
749:
743:
742:
736:
735:
725:
719:
718:
674:
673:
667:
666:
660:
659:
649:
638:
637:
631:
630:
624:
623:
613:
602:
601:
595:
594:
588:
587:
577:
569:
568:
563:
558:
552:
551:
546:
541:
535:
534:
529:
524:
514:
508:
507:
483:
482:
476:
475:
469:
468:
458:
452:
451:
427:
426:
421:
416:
410:
409:
404:
399:
393:
392:
387:
382:
372:
366:
365:
358:
354:
122:
75:
64:
58:
55:
45:Please help to
44:
28:
24:
17:
12:
11:
5:
5169:
5167:
5159:
5158:
5148:
5147:
5141:
5140:
5137:
5136:
5134:
5133:
5122:
5119:
5118:
5116:
5115:
5110:
5108:Random numbers
5105:
5100:
5095:
5090:
5085:
5080:
5075:
5070:
5065:
5060:
5054:
5052:
5048:
5047:
5045:
5044:
5039:
5034:
5032:Garlic routing
5029:
5024:
5019:
5014:
5009:
5004:
4999:
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4959:
4954:
4952:Secure channel
4949:
4943:
4942:
4941:
4930:
4925:
4920:
4915:
4913:Key stretching
4910:
4905:
4900:
4895:
4890:
4885:
4880:
4879:
4878:
4873:
4863:
4861:Cryptovirology
4858:
4853:
4848:
4846:Cryptocurrency
4843:
4838:
4833:
4832:
4831:
4821:
4816:
4810:
4808:
4804:
4803:
4798:
4796:
4795:
4788:
4781:
4773:
4766:
4765:
4762:
4761:
4758:
4757:
4755:
4754:
4749:
4744:
4730:
4725:
4719:
4717:
4713:
4712:
4710:
4709:
4704:
4699:
4693:
4691:
4685:
4684:
4682:
4681:
4676:
4671:
4665:
4663:
4657:
4656:
4653:
4652:
4650:
4649:
4644:
4639:
4634:
4632:Reihenschieber
4629:
4624:
4619:
4614:
4609:
4603:
4601:
4597:
4596:
4594:
4593:
4588:
4583:
4578:
4573:
4567:
4565:
4559:
4558:
4556:
4555:
4550:
4545:
4540:
4535:
4530:
4525:
4520:
4515:
4510:
4505:
4499:
4497:
4491:
4490:
4488:
4487:
4482:
4477:
4471:
4469:
4465:
4464:
4462:
4461:
4456:
4451:
4446:
4441:
4436:
4430:
4428:
4422:
4421:
4419:
4418:
4413:
4408:
4403:
4397:
4395:
4393:Polyalphabetic
4386:
4378:
4377:
4372:
4370:
4369:
4362:
4355:
4347:
4333:
4332:
4325:
4318:
4309:
4308:External links
4306:
4305:
4304:
4287:
4280:
4267:
4264:
4263:
4262:
4257:
4252:
4242:
4239:
4201:
4198:
4185:
4182:
4177:
4173:
4169:
4158:
4157:
4146:
4143:
4138:
4134:
4129:
4125:
4122:
4119:
4116:
4113:
4110:
4105:
4101:
4096:
4092:
4089:
4086:
4083:
4080:
4077:
4073:
4069:
4066:
4063:
4060:
4057:
4052:
4048:
4043:
4039:
4036:
4033:
4030:
4027:
4024:
4019:
4015:
4010:
4006:
4003:
4000:
3997:
3994:
3991:
3987:
3983:
3980:
3977:
3974:
3967:
3963:
3958:
3943:
3942:
3931:
3928:
3923:
3919:
3914:
3910:
3907:
3904:
3901:
3898:
3895:
3890:
3886:
3881:
3877:
3874:
3871:
3868:
3865:
3862:
3858:
3854:
3851:
3848:
3845:
3838:
3834:
3829:
3813:
3807:
3806:
3795:
3792:
3787:
3783:
3778:
3774:
3771:
3768:
3765:
3762:
3759:
3754:
3750:
3745:
3741:
3738:
3735:
3732:
3729:
3726:
3722:
3718:
3715:
3712:
3709:
3702:
3698:
3693:
3677:
3636:
3632:
3628:
3608:
3601:
3597:
3592:
3588:
3585:
3580:
3576:
3543:
3539:
3534:
3506:
3505:Key space size
3503:
3464:
3460:
3439:
3436:
3435:
3434:
3422:
3419:
3416:
3413:
3410:
3405:
3399:
3396:
3395:
3392:
3389:
3388:
3386:
3381:
3376:
3370:
3367:
3366:
3363:
3360:
3359:
3357:
3352:
3347:
3341:
3338:
3337:
3334:
3331:
3330:
3328:
3323:
3318:
3312:
3309:
3308:
3305:
3302:
3301:
3299:
3283:
3282:
3270:
3267:
3263:
3260:
3253:
3247:
3244:
3243:
3240:
3237:
3236:
3234:
3229:
3224:
3218:
3215:
3214:
3211:
3208:
3207:
3205:
3200:
3195:
3189:
3186:
3185:
3182:
3179:
3178:
3176:
3169:
3163:
3160:
3158:
3155:
3154:
3151:
3148:
3146:
3143:
3142:
3140:
3127:
3126:
3114:
3110:
3107:
3103:
3100:
3093:
3087:
3084:
3083:
3080:
3077:
3076:
3074:
3069:
3064:
3058:
3055:
3054:
3051:
3048:
3047:
3045:
3040:
3035:
3029:
3026:
3025:
3022:
3019:
3018:
3016:
3009:
3003:
3000:
2998:
2995:
2994:
2991:
2988:
2986:
2983:
2982:
2980:
2964:
2963:
2950:
2944:
2941:
2940:
2937:
2934:
2933:
2931:
2926:
2921:
2915:
2912:
2911:
2908:
2905:
2904:
2902:
2897:
2892:
2886:
2883:
2882:
2879:
2876:
2875:
2873:
2868:
2863:
2857:
2854:
2853:
2850:
2847:
2846:
2844:
2839:
2836:
2833:
2830:
2827:
2816:
2815:
2803:
2800:
2796:
2793:
2786:
2780:
2777:
2775:
2772:
2771:
2768:
2765:
2763:
2760:
2759:
2757:
2752:
2747:
2741:
2738:
2736:
2733:
2732:
2729:
2726:
2724:
2721:
2720:
2718:
2713:
2710:
2705:
2699:
2696:
2694:
2691:
2690:
2687:
2684:
2682:
2679:
2678:
2676:
2669:
2666:
2662:
2658:
2653:
2650:
2646:
2618:
2615:
2611:
2607:
2604:
2601:
2598:
2595:
2592:
2563:
2557:
2554:
2552:
2549:
2546:
2545:
2542:
2539:
2536:
2534:
2531:
2530:
2528:
2521:
2518:
2514:
2510:
2507:
2504:
2501:
2498:
2495:
2492:
2487:
2484:
2478:
2472:
2469:
2467:
2464:
2463:
2460:
2457:
2455:
2452:
2451:
2449:
2417:
2413:
2409:
2406:
2401:
2398:
2394:
2390:
2385:
2382:
2378:
2374:
2352:
2349:
2345:
2329:
2328:
2315:
2309:
2306:
2305:
2302:
2299:
2298:
2296:
2291:
2286:
2280:
2277:
2276:
2273:
2270:
2269:
2267:
2262:
2257:
2251:
2248:
2247:
2244:
2241:
2240:
2238:
2233:
2228:
2222:
2219:
2218:
2215:
2212:
2211:
2209:
2193:
2192:
2180:
2177:
2173:
2170:
2163:
2157:
2154:
2153:
2150:
2147:
2146:
2144:
2139:
2134:
2128:
2125:
2124:
2121:
2118:
2117:
2115:
2108:
2102:
2099:
2097:
2094:
2093:
2090:
2087:
2085:
2082:
2081:
2079:
2066:
2065:
2053:
2049:
2046:
2042:
2039:
2032:
2026:
2023:
2022:
2019:
2016:
2015:
2013:
2008:
2003:
1997:
1994:
1993:
1990:
1987:
1986:
1984:
1977:
1971:
1968:
1966:
1963:
1962:
1959:
1956:
1954:
1951:
1950:
1948:
1932:
1931:
1918:
1912:
1909:
1908:
1905:
1902:
1901:
1899:
1894:
1889:
1883:
1880:
1879:
1876:
1873:
1872:
1870:
1865:
1860:
1854:
1851:
1850:
1847:
1844:
1843:
1841:
1836:
1831:
1825:
1822:
1821:
1818:
1815:
1814:
1812:
1807:
1804:
1801:
1798:
1795:
1781:
1780:
1767:
1761:
1758:
1756:
1753:
1752:
1749:
1746:
1744:
1741:
1740:
1738:
1733:
1730:
1715:
1712:
1692:
1689:
1686:
1683:
1680:
1658:
1654:
1650:
1647:
1636:
1635:
1623:
1620:
1616:
1613:
1608:
1605:
1602:
1599:
1596:
1593:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1545:
1542:
1539:
1536:
1533:
1530:
1527:
1524:
1521:
1518:
1515:
1512:
1509:
1506:
1503:
1500:
1495:
1489:
1486:
1484:
1481:
1479:
1476:
1475:
1472:
1469:
1467:
1464:
1462:
1459:
1458:
1455:
1452:
1450:
1447:
1445:
1442:
1441:
1439:
1419:
1418:
1400:
1399:
1387:
1384:
1380:
1377:
1370:
1364:
1361:
1360:
1357:
1354:
1353:
1350:
1347:
1346:
1344:
1339:
1334:
1328:
1325:
1324:
1321:
1318:
1317:
1314:
1311:
1310:
1308:
1303:
1298:
1292:
1289:
1288:
1285:
1282:
1281:
1278:
1275:
1274:
1272:
1265:
1259:
1256:
1254:
1251:
1249:
1246:
1245:
1242:
1239:
1237:
1234:
1232:
1229:
1228:
1225:
1222:
1220:
1217:
1215:
1212:
1211:
1209:
1193:
1192:
1179:
1173:
1170:
1168:
1165:
1163:
1160:
1159:
1156:
1153:
1151:
1148:
1146:
1143:
1142:
1139:
1136:
1134:
1131:
1129:
1126:
1125:
1123:
1118:
1114:
1111:
1107:
1104:
1097:
1094:
1088:
1082:
1079:
1077:
1074:
1072:
1069:
1068:
1065:
1062:
1060:
1057:
1055:
1052:
1051:
1048:
1045:
1043:
1040:
1038:
1035:
1034:
1032:
1003:inverse matrix
998:
995:
975:
974:
962:
959:
955:
952:
945:
939:
936:
935:
932:
929:
928:
925:
922:
921:
919:
914:
909:
903:
900:
899:
896:
893:
892:
889:
886:
885:
883:
878:
873:
867:
864:
863:
860:
857:
856:
853:
850:
849:
847:
840:
834:
831:
829:
826:
824:
821:
820:
817:
814:
812:
809:
807:
804:
803:
800:
797:
795:
792:
790:
787:
786:
784:
768:
767:
754:
748:
745:
744:
741:
738:
737:
734:
731:
730:
728:
708:
707:
695:
692:
688:
685:
678:
672:
669:
668:
665:
662:
661:
658:
655:
654:
652:
647:
642:
636:
633:
632:
629:
626:
625:
622:
619:
618:
616:
611:
606:
600:
597:
596:
593:
590:
589:
586:
583:
582:
580:
573:
567:
564:
562:
559:
557:
554:
553:
550:
547:
545:
542:
540:
537:
536:
533:
530:
528:
525:
523:
520:
519:
517:
501:
500:
487:
481:
478:
477:
474:
471:
470:
467:
464:
463:
461:
445:
444:
431:
425:
422:
420:
417:
415:
412:
411:
408:
405:
403:
400:
398:
395:
394:
391:
388:
386:
383:
381:
378:
377:
375:
297:
296:
293:
290:
287:
284:
281:
278:
275:
272:
269:
266:
263:
260:
257:
254:
251:
248:
245:
242:
239:
236:
233:
230:
227:
224:
221:
218:
214:
213:
210:
207:
204:
201:
198:
195:
192:
189:
186:
183:
180:
177:
174:
171:
168:
165:
162:
159:
156:
153:
150:
147:
144:
141:
138:
135:
121:
118:
107:Lester S. Hill
105:. Invented by
103:linear algebra
77:
76:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
5168:
5157:
5154:
5153:
5151:
5132:
5124:
5123:
5120:
5114:
5113:Steganography
5111:
5109:
5106:
5104:
5101:
5099:
5096:
5094:
5091:
5089:
5086:
5084:
5081:
5079:
5076:
5074:
5071:
5069:
5068:Stream cipher
5066:
5064:
5061:
5059:
5056:
5055:
5053:
5049:
5043:
5040:
5038:
5035:
5033:
5030:
5028:
5027:Onion routing
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5008:
5007:Shared secret
5005:
5003:
5000:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4947:
4944:
4939:
4936:
4935:
4934:
4931:
4929:
4926:
4924:
4921:
4919:
4916:
4914:
4911:
4909:
4906:
4904:
4903:Key generator
4901:
4899:
4896:
4894:
4891:
4889:
4886:
4884:
4881:
4877:
4874:
4872:
4869:
4868:
4867:
4866:Hash function
4864:
4862:
4859:
4857:
4854:
4852:
4849:
4847:
4844:
4842:
4841:Cryptanalysis
4839:
4837:
4834:
4830:
4827:
4826:
4825:
4822:
4820:
4817:
4815:
4812:
4811:
4809:
4805:
4801:
4794:
4789:
4787:
4782:
4780:
4775:
4774:
4771:
4767:
4753:
4750:
4748:
4745:
4742:
4738:
4734:
4731:
4729:
4726:
4724:
4721:
4720:
4718:
4716:Cryptanalysis
4714:
4708:
4705:
4703:
4700:
4698:
4695:
4694:
4692:
4690:
4689:Steganography
4686:
4680:
4677:
4675:
4672:
4670:
4667:
4666:
4664:
4662:
4658:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4623:
4620:
4618:
4615:
4613:
4610:
4608:
4605:
4604:
4602:
4598:
4592:
4589:
4587:
4584:
4582:
4579:
4577:
4574:
4572:
4569:
4568:
4566:
4564:
4563:Transposition
4560:
4554:
4551:
4549:
4546:
4544:
4541:
4539:
4536:
4534:
4531:
4529:
4526:
4524:
4521:
4519:
4516:
4514:
4511:
4509:
4506:
4504:
4501:
4500:
4498:
4496:
4492:
4486:
4483:
4481:
4478:
4476:
4473:
4472:
4470:
4466:
4460:
4457:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4437:
4435:
4432:
4431:
4429:
4427:
4423:
4417:
4414:
4412:
4409:
4407:
4404:
4402:
4399:
4398:
4396:
4394:
4390:
4387:
4383:
4379:
4375:
4368:
4363:
4361:
4356:
4354:
4349:
4348:
4345:
4341:
4337:
4330:
4326:
4323:
4319:
4316:
4312:
4311:
4307:
4302:
4298:
4294:
4293:
4288:
4285:
4281:
4278:
4274:
4270:
4269:
4265:
4261:
4260:Trifid cipher
4258:
4256:
4253:
4251:
4248:
4247:
4246:
4240:
4238:
4236:
4232:
4226:
4223:
4218:
4213:
4211:
4207:
4199:
4197:
4183:
4180:
4175:
4171:
4167:
4144:
4136:
4132:
4127:
4123:
4120:
4117:
4111:
4103:
4099:
4094:
4090:
4087:
4084:
4075:
4071:
4067:
4064:
4061:
4050:
4046:
4041:
4037:
4034:
4031:
4025:
4017:
4013:
4008:
4004:
4001:
3998:
3989:
3985:
3981:
3978:
3975:
3965:
3961:
3956:
3948:
3947:
3946:
3929:
3921:
3917:
3912:
3908:
3905:
3902:
3896:
3888:
3884:
3879:
3875:
3872:
3869:
3860:
3856:
3852:
3849:
3846:
3836:
3832:
3827:
3819:
3818:
3817:
3812:
3793:
3785:
3781:
3776:
3772:
3769:
3766:
3760:
3752:
3748:
3743:
3739:
3736:
3733:
3724:
3720:
3716:
3713:
3710:
3700:
3696:
3691:
3683:
3682:
3681:
3676:
3672:
3668:
3664:
3660:
3656:
3652:
3634:
3630:
3626:
3599:
3595:
3590:
3583:
3578:
3574:
3565:
3561:
3541:
3537:
3532:
3522:
3520:
3516:
3512:
3504:
3502:
3500:
3496:
3492:
3488:
3484:
3479:
3478:little time.
3462:
3458:
3449:
3445:
3437:
3420:
3417:
3414:
3411:
3403:
3397:
3390:
3384:
3379:
3374:
3368:
3361:
3355:
3345:
3339:
3332:
3326:
3321:
3316:
3310:
3303:
3297:
3288:
3287:
3286:
3265:
3261:
3251:
3245:
3238:
3232:
3227:
3222:
3216:
3209:
3203:
3198:
3193:
3187:
3180:
3174:
3167:
3161:
3156:
3149:
3144:
3138:
3129:
3128:
3112:
3105:
3101:
3091:
3085:
3078:
3072:
3067:
3062:
3056:
3049:
3043:
3038:
3033:
3027:
3020:
3014:
3007:
3001:
2996:
2989:
2984:
2978:
2969:
2968:
2967:
2948:
2942:
2935:
2929:
2924:
2919:
2913:
2906:
2900:
2890:
2884:
2877:
2871:
2866:
2861:
2855:
2848:
2842:
2834:
2831:
2828:
2825:
2818:
2817:
2798:
2794:
2784:
2778:
2773:
2766:
2761:
2755:
2750:
2745:
2739:
2734:
2727:
2722:
2716:
2711:
2708:
2703:
2697:
2692:
2685:
2680:
2674:
2667:
2664:
2660:
2656:
2651:
2648:
2644:
2636:
2635:
2634:
2616:
2613:
2605:
2602:
2599:
2596:
2593:
2581:
2576:
2561:
2555:
2550:
2547:
2540:
2537:
2532:
2526:
2519:
2516:
2508:
2505:
2502:
2499:
2496:
2490:
2485:
2482:
2476:
2470:
2465:
2458:
2453:
2447:
2437:
2433:
2415:
2411:
2407:
2404:
2399:
2396:
2392:
2388:
2383:
2380:
2376:
2372:
2350:
2347:
2343:
2334:
2313:
2307:
2300:
2294:
2289:
2284:
2278:
2271:
2265:
2255:
2249:
2242:
2236:
2231:
2226:
2220:
2213:
2207:
2198:
2197:
2196:
2175:
2171:
2161:
2155:
2148:
2142:
2137:
2132:
2126:
2119:
2113:
2106:
2100:
2095:
2088:
2083:
2077:
2068:
2067:
2051:
2044:
2040:
2030:
2024:
2017:
2011:
2006:
2001:
1995:
1988:
1982:
1975:
1969:
1964:
1957:
1952:
1946:
1937:
1936:
1935:
1916:
1910:
1903:
1897:
1892:
1887:
1881:
1874:
1868:
1858:
1852:
1845:
1839:
1834:
1829:
1823:
1816:
1810:
1802:
1799:
1796:
1793:
1786:
1785:
1784:
1765:
1759:
1754:
1747:
1742:
1736:
1731:
1728:
1721:
1720:
1719:
1713:
1711:
1709:
1704:
1690:
1687:
1684:
1681:
1678:
1656:
1652:
1648:
1645:
1618:
1614:
1606:
1603:
1600:
1597:
1591:
1588:
1585:
1582:
1579:
1576:
1573:
1567:
1564:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1534:
1531:
1525:
1522:
1519:
1516:
1513:
1510:
1507:
1501:
1498:
1493:
1487:
1482:
1477:
1470:
1465:
1460:
1453:
1448:
1443:
1437:
1428:
1427:
1426:
1423:
1416:
1412:
1408:
1407:
1406:
1403:
1382:
1378:
1368:
1362:
1355:
1348:
1342:
1337:
1332:
1326:
1319:
1312:
1306:
1301:
1296:
1290:
1283:
1276:
1270:
1263:
1257:
1252:
1247:
1240:
1235:
1230:
1223:
1218:
1213:
1207:
1198:
1197:
1196:
1177:
1171:
1166:
1161:
1154:
1149:
1144:
1137:
1132:
1127:
1121:
1116:
1109:
1105:
1095:
1092:
1086:
1080:
1075:
1070:
1063:
1058:
1053:
1046:
1041:
1036:
1030:
1020:
1019:
1018:
1016:
1004:
996:
994:
992:
988:
984:
980:
957:
953:
943:
937:
930:
923:
917:
912:
907:
901:
894:
887:
881:
876:
871:
865:
858:
851:
845:
838:
832:
827:
822:
815:
810:
805:
798:
793:
788:
782:
773:
772:
771:
752:
746:
739:
732:
726:
717:
716:
715:
713:
690:
686:
676:
670:
663:
656:
650:
645:
640:
634:
627:
620:
614:
609:
604:
598:
591:
584:
578:
571:
565:
560:
555:
548:
543:
538:
531:
526:
521:
515:
506:
505:
504:
485:
479:
472:
465:
459:
450:
449:
448:
429:
423:
418:
413:
406:
401:
396:
389:
384:
379:
373:
364:
363:
362:
351:
349:
345:
341:
337:
332:
330:
326:
323:
319:
316:
312:
308:
304:
294:
291:
288:
285:
282:
279:
276:
273:
270:
267:
264:
261:
258:
255:
252:
249:
246:
243:
240:
237:
234:
231:
228:
225:
222:
219:
216:
215:
211:
208:
205:
202:
199:
196:
193:
190:
187:
184:
181:
178:
175:
172:
169:
166:
163:
160:
157:
154:
151:
148:
145:
142:
139:
136:
133:
132:
129:
127:
119:
117:
115:
110:
108:
104:
100:
96:
92:
83:
73:
70:
62:
59:February 2012
52:
48:
42:
41:
35:
30:
21:
20:
5063:Block cipher
4908:Key schedule
4898:Key exchange
4888:Kleptography
4851:Cryptosystem
4800:Cryptography
4622:One-time pad
4537:
4495:Substitution
4290:
4283:
4272:
4255:Bifid cipher
4244:
4227:
4214:
4210:bifid cipher
4203:
4159:
3944:
3810:
3808:
3674:
3666:
3662:
3654:
3650:
3563:
3559:
3523:
3508:
3494:
3480:
3441:
3284:
2965:
2577:
2431:
2332:
2330:
2194:
1933:
1782:
1717:
1705:
1637:
1424:
1420:
1404:
1401:
1194:
1000:
990:
986:
976:
769:
709:
502:
446:
352:
343:
339:
333:
321:
317:
306:
302:
300:
123:
111:
94:
88:
65:
56:
37:
5051:Mathematics
5042:Mix network
4674:Code talker
4553:Running key
4485:Four-square
4292:Cryptologia
3285:Therefore,
2331:The matrix
1415:determinant
309:-component
95:Hill cipher
51:introducing
5002:Ciphertext
4972:Decryption
4967:Encryption
4928:Ransomware
4723:Cryptogram
4617:Kama Sutra
4586:Rail fence
4581:Myszkowski
4528:Chaocipher
4480:Two-square
4459:VIC cipher
4411:Trithemius
4266:References
3680:). It is
3524:There are
3483:non-linear
997:Decryption
712:ciphertext
346:matrices (
327:, against
315:invertible
120:Encryption
34:references
4992:Plaintext
4647:Solitaire
4385:by family
4297:CiteSeerX
4181:−
4121:−
4112:⋯
4088:−
4065:−
4035:−
4026:⋯
4002:−
3979:−
3906:−
3897:⋯
3873:−
3850:−
3770:−
3761:⋯
3737:−
3714:−
3619:or about
3584:
3511:key space
3487:diffusion
3409:→
3351:→
3228:≡
3068:≡
2896:→
2838:→
2751:≡
2709:≡
2665:−
2657:≡
2649:−
2614:−
2600:−
2548:−
2538:−
2517:−
2503:−
2483:−
2397:−
2381:−
2348:−
2261:→
2138:≡
2007:≡
1864:→
1806:→
1688:×
1604:≡
1589:⋅
1583:−
1577:⋅
1556:⋅
1550:−
1544:⋅
1532:−
1523:⋅
1517:−
1511:⋅
1338:≡
1117:≡
1093:−
985:, and an
983:diffusion
913:≡
646:≡
101:based on
5150:Category
5131:Category
5037:Kademlia
4997:Codetext
4940:(CSPRNG)
4735:(Units:
4571:Columnar
4518:Beaufort
4475:Playfair
4449:Tap code
4444:Nihilist
4416:Vigenère
4241:See also
4206:Playfair
3515:key size
3438:Security
114:matrices
4807:General
4513:Autokey
4401:Alberti
4382:Ciphers
4208:or the
3566:. Thus
3499:Twofish
2436:formula
1714:Example
1411:inverse
979:Shannon
342:×
329:modulus
320:×
217:Number
134:Letter
47:improve
4918:Keygen
4702:Grille
4642:Slidex
4576:Double
4543:Pigpen
4523:Caesar
4508:Atbash
4503:Affine
4468:Square
4454:Trifid
4434:ADFGVX
4406:Enigma
4217:patent
3816:)) is
3448:linear
1015:modulo
348:modulo
325:matrix
311:vector
126:modulo
93:, the
36:, but
4948:(PRN)
4697:Bacon
4661:Codes
4612:DRYAD
4607:BATCO
4600:Other
4591:Route
4548:ROT13
4533:Great
4439:Bifid
3673:GL(n,
1708:prime
97:is a
4739:and
4707:Null
4679:Poem
4669:Book
4538:Hill
4168:4.64
3509:The
1718:Let
1671:and
4741:Nat
4737:Ban
4301:PDF
4299:) (
4277:PDF
4184:1.7
3627:4.7
3575:log
3497:in
3491:AES
3262:mod
3217:171
3210:323
3125:and
3102:mod
3057:212
3050:241
2795:mod
2172:mod
2064:and
2041:mod
1615:mod
1601:441
1379:mod
1327:539
1320:574
1313:260
1106:mod
1009:VIV
981:'s
954:mod
902:325
895:216
687:mod
635:319
628:222
357:NQK
336:key
295:25
89:In
5152::
4133:13
4100:13
4076:13
3957:26
3918:13
3885:13
3861:13
3828:13
3814:13
3665:Ă—
3653:Ă—
3591:26
3562:Ă—
3533:26
3340:15
3333:11
3266:26
3246:15
3239:11
3188:19
3157:20
3150:17
3145:15
3106:26
2997:20
2990:17
2985:15
2943:19
2799:26
2774:20
2767:17
2762:15
2735:24
2728:23
2693:24
2686:23
2250:19
2176:26
2156:19
2127:15
2120:11
2045:26
1911:15
1904:11
1691:13
1679:26
1646:25
1619:26
1607:25
1592:20
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1580:17
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1547:15
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1526:17
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1471:10
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1461:13
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1231:21
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1167:12
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1076:17
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958:26
938:13
888:31
866:19
833:15
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823:20
816:10
811:16
806:13
794:24
747:19
691:26
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657:15
621:67
599:19
566:15
561:17
556:20
549:10
544:16
539:13
527:24
480:19
424:15
419:17
414:20
407:10
402:16
397:13
385:24
292:24
289:23
286:22
283:21
280:20
277:19
274:18
271:17
268:16
265:15
262:14
259:13
256:12
253:11
250:10
212:Z
116:.
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149:E
146:D
143:C
140:B
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66:(
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