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Polybius square

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telegraphy, specifically fire-signalling. To send a message, the sender would initially hold up two torches and wait for the recipient to do the same to signal that they were ready to receive the message. The sender would then hold up the first set of torches on his left side to indicate to the recipient which tablet (or row of the square) was to be consulted. The sender would then raise a set of torches on his right side to indicate which letter on the tablet was intended for the message. Both parties would need the same tablets, a telescope (a tube to narrow view, no real magnification), and torches.
2767: 20: 1666: 86:, and further developed by Polybius himself. The device partitioned the alphabet into five tablets with five letters each (except for the last one with only four). There are no surviving tablets from antiquity. Letters are represented by two numbers from one to five, allowing the representation of 25 characters using only 5 numeric symbols. 457:
Each letter is then represented by its coordinates in the grid. For example, "BAT" becomes "12 11 44". The 26 letters of the Latin/English alphabet do not fit in a 5 × 5 square, two letters must be combined (usually I and J as above, though C and K is an alternative). Alternatively, a 6 × 6 grid may
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Polybius outlines the need for effective signalling in warfare, leading to the development of the square. Previously, fire-signalling was useful only for expected, predetermined messages, with no way to convey novel messages about unexpected events. According to Polybius, in the 4th century BCE,
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consisting of matching vessels with sectioned rods labelled with different messages such as "Heavy Infantry", "Ships", and "Corn". This system was slightly better than the basic fire-signalling, but still lacked the ability to convey any needed message. The Polybius square was used to aid in
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using a shift equal to the side of our square (5). To do it, locate the letter of the text and insert the one immediately below it in the same column for the ciphertext. If the letter is in the bottom row, take the one from the top of the same column.
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could be used to reorder the alphabet in the square, with the letters (without duplicates) of the key being placed at the beginning and the remaining letters following it in alphabetical order. For example, the key phrase
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This alphabet, and this latter form of the Polybius square, is used when implementing the square in other Western European languages such as English, Spanish, French, German, Italian, Portuguese, and Dutch.
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An advanced variation, which involves the following: the obtained primary ciphertext (result From Method2) is encrypted again. In this case, it is written out without being split into pairs.
66:. The device was originally used for fire signalling, allowing for the coded transmission of any message, not just a finite number of predetermined options as was the convention before. 2747: 2577: 2004: 1931: 1935: 2430: 1776:
The Polybius square is also used as a basic cipher called the Polybius cipher. This cipher is quite insecure by modern standards, as it is a
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The resulting sequence of digits is cyclically shifted to the left by one step (an odd number of steps (move 3 to the end)):
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The message is transformed into coordinates on the Polybius square, and the coordinates are recorded vertically:
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Modern Greek still uses that same alphabet, as do implementations of the Polybius square in that language.
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The Polybius square and the Polybius cipher can be combined with other cryptographic methods such as the
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There are several encryption methods using the Polybius square. Three of them are described below.
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in a string, stitches on a quilt, contiguous letters before a wider space or many other ways.
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characters so that they can be represented by a smaller set of symbols, which is useful for
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with characters being substituted for pairs of digits, which is easily broken through
1740:.) Indeed, it can be signalled in many simple ways (flashing lamps, blasts of sound, 2661: 2651: 2522: 2336: 2256: 2225: 2119: 2050: 1913: 1903: 1810: 1737: 1699: 462: 2596: 2013: 1732: 1713: 458:
be used to allow numerals or special characters to be included as well as letters.
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by tapping the numbers on pipes or walls. It is said to have been used by
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Next, the coordinates are converted into letters using the same square:
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Data privacy and security : encryption and information hiding
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And is replaced with the final ciphertext according to the table:
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without a key (or, in other words, with a key of plain alphabet):
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The Polybius square has also been used in the form of the "
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describes the code being used by political prisoners of
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Cryptographically secure pseudorandom number generator
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(Koestler had been a prisoner-of-war during the 1669:Diagram of a fire signal using the Polybius cipher 39:Cleoxenus and Democleitus, and made famous by the 2787: 1760:The simple representation also lends itself to 2424: 1998: 1930:: CS1 maint: multiple names: authors list ( 1730:in the 1930s in his anti-totalitarian novel 2431: 2417: 2012: 2005: 1991: 1954:"Cryptography Worksheet — Polybius Square" 1934:) CS1 maint: numeric names: authors list ( 1204:Then the coordinates are read row by row: 485:would lead to the reordered square below. 461:A 6 × 6 grid is also usually used for the 821:Let's encrypt the word "SOMETEXT" with a 1664: 18: 631: 2788: 1694:" to signal messages between cells in 23:The Greek letters of a Polybius square 2412: 1986: 1947: 1945: 923:A more complicated method involves a 1893: 1891: 1889: 1887: 1885: 1860: 1858: 1856: 1854: 1852: 1850: 1848: 1898:Salomon, D. (David), 1938- (2011). 13: 1942: 14: 2822: 1882: 1845: 1207:34 25 45 34 43 31 41 54 2766: 2765: 2438: 1866:"Polybius • Histories — Book 10" 1755: 1627:Thus, after encryption, we get: 1306:Thus, after encryption, we get: 893:Thus, after encryption, we get: 1796:, Homophonic cipher and more. 1771: 1655: 2627:Information-theoretic security 1787: 35:, is a device invented by the 1: 2801:History of telecommunications 1838: 1660: 89:The original square used the 69: 273:, this is the typical form: 7: 2743:Message authentication code 2698:Cryptographic hash function 2511:Cryptographic hash function 1799: 1331: 918: 816: 78:the device was invented by 10: 2827: 2622:Harvest now, decrypt later 1684:hydraulic semaphore system 2761: 2738:Post-quantum cryptography 2690: 2446: 2408: 2355: 2327: 2299: 2239: 2201: 2133: 2107: 2064: 2031: 2020: 1982: 1978: 47:. The device is used for 2728:Quantum key distribution 2718:Authenticated encryption 2573:Random number generation 1952:Daniel Rodriguez-Clark. 1528:42 54 53 44 33 14 15 43 2723:Public-key cryptography 2713:Symmetric-key algorithm 2516:Key derivation function 2476:Cryptographic primitive 2469:Authentication protocol 2459:Outline of cryptography 2454:History of cryptography 1823:Straddling checkerboard 1539:Horizontal coordinate: 1218:Horizontal coordinate: 1144:Horizontal coordinate: 74:According to Polybius' 2464:Cryptographic protocol 2014:Classical cryptography 1833:Topics in cryptography 1670: 24: 2617:End-to-end encryption 2563:Cryptojacking malware 1870:penelope.uchicago.edu 1806:Optical communication 1668: 1568:Vertical coordinate: 1247:Vertical coordinate: 1173:Vertical coordinate: 471:cryptography in Japan 93:laid out as follows: 33:Polybius checkerboard 22: 2733:Quantum cryptography 2657:Trusted timestamping 2373:Index of coincidence 2277:Reservehandverfahren 632:Encryption Principle 31:, also known as the 2496:Cryptographic nonce 2392:Kasiski examination 2387:Information leakage 1778:substitution cipher 1635:Before encryption: 1631: 1535: 1314:Before encryption: 1310: 1214: 1111: 901:Before encryption: 897: 863:Cipher text letter 834:Letter of the text 830: 2602:Subliminal channel 2586:Pseudorandom noise 2533:Key (cryptography) 2368:Frequency analysis 2267:Rasterschlüssel 44 1782:frequency analysis 1671: 1643:After encryption: 1630: 1534: 1322:After encryption: 1309: 1213: 1110: 909:After encryption: 896: 829: 25: 2796:Classical ciphers 2783: 2782: 2779: 2778: 2662:Key-based routing 2652:Trapdoor function 2523:Digital signature 2404: 2403: 2400: 2399: 2295: 2294: 1909:978-1-4419-1816-1 1811:Optical telegraph 1738:Spanish Civil War 1702:prisoners of the 1650: 1649: 1625: 1624: 1522:4254534433141543 1516:3425453443314154 1511: 1510: 1329: 1328: 1304: 1303: 1201: 1200: 1105: 1104: 916: 915: 891: 890: 814: 813: 629: 628: 463:Cyrillic alphabet 451: 450: 264: 263: 2818: 2769: 2768: 2597:Insecure channel 2433: 2426: 2419: 2410: 2409: 2029: 2028: 2007: 2000: 1993: 1984: 1983: 1980: 1979: 1976: 1975: 1966: 1964: 1958: 1949: 1940: 1939: 1929: 1921: 1895: 1880: 1879: 1877: 1876: 1862: 1733:Darkness at Noon 1714:prisoners of war 1632: 1629: 1536: 1533: 1336: 1335: 1311: 1308: 1215: 1212: 1112: 1109: 930: 929: 898: 895: 831: 828: 639: 638: 488: 487: 483:polybius cipher" 276: 275: 96: 95: 2826: 2825: 2821: 2820: 2819: 2817: 2816: 2815: 2811:Ancient Arcadia 2786: 2785: 2784: 2775: 2757: 2686: 2442: 2437: 2396: 2351: 2323: 2291: 2235: 2197: 2129: 2103: 2066:Polybius square 2060: 2024: 2016: 2011: 1972: 1970: 1969: 1963:. pp. 1–3. 1956: 1950: 1943: 1923: 1922: 1910: 1896: 1883: 1874: 1872: 1864: 1863: 1846: 1841: 1802: 1790: 1774: 1758: 1724:Arthur Koestler 1680:Aeneas Tacticus 1663: 1658: 1652: 1529: 1523: 1517: 1334: 1208: 1203: 921: 819: 634: 72: 29:Polybius square 17: 12: 11: 5: 2824: 2814: 2813: 2808: 2803: 2798: 2781: 2780: 2777: 2776: 2774: 2773: 2762: 2759: 2758: 2756: 2755: 2750: 2748:Random numbers 2745: 2740: 2735: 2730: 2725: 2720: 2715: 2710: 2705: 2700: 2694: 2692: 2688: 2687: 2685: 2684: 2679: 2674: 2672:Garlic routing 2669: 2664: 2659: 2654: 2649: 2644: 2639: 2634: 2629: 2624: 2619: 2614: 2609: 2604: 2599: 2594: 2592:Secure channel 2589: 2583: 2582: 2581: 2570: 2565: 2560: 2555: 2553:Key stretching 2550: 2545: 2540: 2535: 2530: 2525: 2520: 2519: 2518: 2513: 2503: 2501:Cryptovirology 2498: 2493: 2488: 2486:Cryptocurrency 2483: 2478: 2473: 2472: 2471: 2461: 2456: 2450: 2448: 2444: 2443: 2436: 2435: 2428: 2421: 2413: 2406: 2405: 2402: 2401: 2398: 2397: 2395: 2394: 2389: 2384: 2370: 2365: 2359: 2357: 2353: 2352: 2350: 2349: 2344: 2339: 2333: 2331: 2325: 2324: 2322: 2321: 2316: 2311: 2305: 2303: 2297: 2296: 2293: 2292: 2290: 2289: 2284: 2279: 2274: 2272:Reihenschieber 2269: 2264: 2259: 2254: 2249: 2243: 2241: 2237: 2236: 2234: 2233: 2228: 2223: 2218: 2213: 2207: 2205: 2199: 2198: 2196: 2195: 2190: 2185: 2180: 2175: 2170: 2165: 2160: 2155: 2150: 2145: 2139: 2137: 2131: 2130: 2128: 2127: 2122: 2117: 2111: 2109: 2105: 2104: 2102: 2101: 2096: 2091: 2086: 2081: 2076: 2070: 2068: 2062: 2061: 2059: 2058: 2053: 2048: 2043: 2037: 2035: 2033:Polyalphabetic 2026: 2018: 2017: 2010: 2009: 2002: 1995: 1987: 1968: 1967: 1941: 1908: 1881: 1843: 1842: 1840: 1837: 1836: 1835: 1830: 1825: 1820: 1815: 1814: 1813: 1801: 1798: 1789: 1786: 1773: 1770: 1757: 1754: 1662: 1659: 1657: 1654: 1648: 1647: 1644: 1640: 1639: 1636: 1623: 1622: 1619: 1616: 1613: 1610: 1607: 1604: 1601: 1598: 1594: 1593: 1590: 1587: 1584: 1581: 1578: 1575: 1572: 1569: 1565: 1564: 1561: 1558: 1555: 1552: 1549: 1546: 1543: 1540: 1527: 1521: 1515: 1509: 1508: 1503: 1498: 1493: 1488: 1483: 1479: 1478: 1473: 1468: 1463: 1458: 1453: 1449: 1448: 1443: 1438: 1433: 1428: 1423: 1419: 1418: 1413: 1404: 1399: 1394: 1389: 1385: 1384: 1379: 1374: 1369: 1364: 1359: 1355: 1354: 1351: 1348: 1345: 1342: 1339: 1333: 1330: 1327: 1326: 1323: 1319: 1318: 1315: 1302: 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2678: 2675: 2673: 2670: 2668: 2667:Onion routing 2665: 2663: 2660: 2658: 2655: 2653: 2650: 2648: 2647:Shared secret 2645: 2643: 2640: 2638: 2635: 2633: 2630: 2628: 2625: 2623: 2620: 2618: 2615: 2613: 2610: 2608: 2605: 2603: 2600: 2598: 2595: 2593: 2590: 2587: 2584: 2579: 2576: 2575: 2574: 2571: 2569: 2566: 2564: 2561: 2559: 2556: 2554: 2551: 2549: 2546: 2544: 2543:Key generator 2541: 2539: 2536: 2534: 2531: 2529: 2526: 2524: 2521: 2517: 2514: 2512: 2509: 2508: 2507: 2506:Hash function 2504: 2502: 2499: 2497: 2494: 2492: 2489: 2487: 2484: 2482: 2481:Cryptanalysis 2479: 2477: 2474: 2470: 2467: 2466: 2465: 2462: 2460: 2457: 2455: 2452: 2451: 2449: 2445: 2441: 2434: 2429: 2427: 2422: 2420: 2415: 2414: 2411: 2407: 2393: 2390: 2388: 2385: 2382: 2378: 2374: 2371: 2369: 2366: 2364: 2361: 2360: 2358: 2356:Cryptanalysis 2354: 2348: 2345: 2343: 2340: 2338: 2335: 2334: 2332: 2330: 2329:Steganography 2326: 2320: 2317: 2315: 2312: 2310: 2307: 2306: 2304: 2302: 2298: 2288: 2285: 2283: 2280: 2278: 2275: 2273: 2270: 2268: 2265: 2263: 2260: 2258: 2255: 2253: 2250: 2248: 2245: 2244: 2242: 2238: 2232: 2229: 2227: 2224: 2222: 2219: 2217: 2214: 2212: 2209: 2208: 2206: 2204: 2203:Transposition 2200: 2194: 2191: 2189: 2186: 2184: 2181: 2179: 2176: 2174: 2171: 2169: 2166: 2164: 2161: 2159: 2156: 2154: 2151: 2149: 2146: 2144: 2141: 2140: 2138: 2136: 2132: 2126: 2123: 2121: 2118: 2116: 2113: 2112: 2110: 2106: 2100: 2097: 2095: 2092: 2090: 2087: 2085: 2082: 2080: 2077: 2075: 2072: 2071: 2069: 2067: 2063: 2057: 2054: 2052: 2049: 2047: 2044: 2042: 2039: 2038: 2036: 2034: 2030: 2027: 2023: 2019: 2015: 2008: 2003: 2001: 1996: 1994: 1989: 1988: 1985: 1981: 1977: 1973: 1962: 1961:Crypto Corner 1955: 1948: 1946: 1937: 1933: 1927: 1919: 1915: 1911: 1905: 1901: 1894: 1892: 1890: 1888: 1886: 1871: 1867: 1861: 1859: 1857: 1855: 1853: 1851: 1849: 1844: 1834: 1831: 1829: 1826: 1824: 1821: 1819: 1816: 1812: 1809: 1808: 1807: 1804: 1803: 1797: 1795: 1794:ADFGVX cipher 1785: 1783: 1779: 1769: 1767: 1763: 1762:steganography 1756:Steganography 1753: 1751: 1747: 1746:smoke signals 1743: 1739: 1735: 1734: 1729: 1725: 1721: 1719: 1715: 1712: 1708: 1705: 1701: 1697: 1693: 1688: 1685: 1681: 1676: 1667: 1653: 1645: 1642: 1641: 1637: 1634: 1633: 1628: 1620: 1617: 1614: 1611: 1608: 1605: 1602: 1599: 1596: 1595: 1591: 1588: 1585: 1582: 1579: 1576: 1573: 1570: 1567: 1566: 1562: 1559: 1556: 1553: 1550: 1547: 1544: 1541: 1538: 1537: 1532: 1526: 1520: 1514: 1507: 1504: 1502: 1499: 1497: 1494: 1492: 1489: 1487: 1484: 1481: 1480: 1477: 1474: 1472: 1469: 1467: 1464: 1462: 1459: 1457: 1454: 1451: 1450: 1447: 1444: 1442: 1439: 1437: 1434: 1432: 1429: 1427: 1424: 1421: 1420: 1417: 1414: 1412: 1408: 1405: 1403: 1400: 1398: 1395: 1393: 1390: 1387: 1386: 1383: 1380: 1378: 1375: 1373: 1370: 1368: 1365: 1363: 1360: 1357: 1356: 1352: 1349: 1346: 1343: 1340: 1338: 1337: 1324: 1321: 1320: 1316: 1313: 1312: 1307: 1299: 1296: 1293: 1290: 1287: 1284: 1281: 1278: 1275: 1274: 1270: 1267: 1264: 1261: 1258: 1255: 1252: 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Springer. 1899: 1873:. Retrieved 1869: 1791: 1775: 1772:Cryptography 1759: 1731: 1722: 1709:and also by 1689: 1674: 1672: 1656:Applications 1651: 1626: 1530: 1524: 1518: 1512: 1305: 1209: 1202: 1106: 925:Bifid cipher 922: 892: 820: 635: 608: 586: 564: 542: 520: 513: 508: 503: 498: 493: 482: 475: 460: 456: 452: 268: 265: 88: 75: 73: 64:cryptography 43:and scholar 32: 28: 26: 16:Type of code 2691:Mathematics 2682:Mix network 2314:Code talker 2193:Running key 2125:Four-square 1788:Adaptations 1718:Vietnam War 1716:during the 84:Democleitus 2790:Categories 2642:Ciphertext 2612:Decryption 2607:Encryption 2568:Ransomware 2363:Cryptogram 2257:Kama Sutra 2226:Rail fence 2221:Myszkowski 2168:Chaocipher 2120:Two-square 2099:VIC cipher 2051:Trithemius 1875:2020-04-13 1839:References 1818:Phryctoria 1750:Morse code 1692:knock code 1682:devised a 1675:Histories, 1661:Telegraphy 76:Histories, 70:Basic form 56:telegraphy 2632:Plaintext 2287:Solitaire 2025:by family 1926:cite book 1918:752480143 1646:iuptnqvo 1638:sometext 1325:swysocdu 1317:sometext 912:xtrkykcy 904:sometext 269:With the 80:Cleoxenus 52:plaintext 41:historian 2771:Category 2677:Kademlia 2637:Codetext 2580:(CSPRNG) 2375:(Units: 2211:Columnar 2158:Beaufort 2115:Playfair 2089:Tap code 2084:Nihilist 2056:Vigenère 1828:Tap code 1800:See also 1700:nihilist 1332:Method 3 919:Method 2 817:Method 1 467:hiragana 45:Polybius 2447:General 2153:Autokey 2041:Alberti 2022:Ciphers 1704:Russian 1696:prisons 1673:In his 1597:Letter 1276:Letter 1115:Letter 2558:Keygen 2342:Grille 2282:Slidex 2216:Double 2183:Pigpen 2163:Caesar 2148:Atbash 2143:Affine 2108:Square 2094:Trifid 2074:ADFGVX 2046:Enigma 1965:  1916:  1906:  1728:Stalin 62:, and 2588:(PRN) 2337:Bacon 2301:Codes 2252:DRYAD 2247:BATCO 2240:Other 2231:Route 2188:ROT13 2173:Great 2079:Bifid 1957:(PDF) 1766:knots 1742:drums 1707:Czars 469:(see 2379:and 2347:Null 2319:Poem 2309:Book 2178:Hill 1936:link 1932:link 1914:OCLC 1904:ISBN 547:I/J 82:and 27:The 2381:Nat 2377:Ban 478:key 473:). 2792:: 1959:. 1944:^ 1928:}} 1924:{{ 1912:. 1884:^ 1868:. 1847:^ 1784:. 1744:, 1720:. 1711:US 1621:o 1618:v 1615:q 1612:n 1609:t 1606:p 1603:u 1600:i 1592:3 1589:5 1586:4 1583:3 1580:4 1577:3 1574:4 1571:2 1563:4 1560:1 1557:1 1554:3 1551:4 1548:5 1545:5 1542:4 1482:5 1452:4 1422:3 1388:2 1358:1 1353:5 1300:u 1297:d 1294:c 1291:o 1288:s 1285:y 1282:w 1279:s 1271:4 1268:1 1265:1 1262:3 1259:4 1256:5 1253:5 1250:4 1242:5 1239:4 1236:3 1233:4 1230:3 1227:4 1224:2 1221:3 1197:4 1194:5 1191:1 1188:4 1185:1 1182:3 1179:3 1176:4 1168:4 1165:3 1162:5 1159:4 1156:5 1153:2 1150:4 1147:3 1139:t 1136:x 1133:e 1130:t 1127:e 1124:m 1121:o 1118:s 1076:5 1046:4 1016:3 982:2 952:1 947:5 887:y 884:c 881:k 878:y 875:k 872:r 869:t 866:x 858:t 855:x 852:e 849:t 846:e 843:m 840:o 837:s 785:5 755:4 725:3 691:2 661:1 656:5 625:Z 622:X 619:W 616:V 613:T 603:Q 600:N 597:M 594:K 591:G 581:F 578:D 575:A 572:R 569:E 559:H 556:C 553:S 550:U 537:B 534:Y 531:L 528:O 525:P 476:A 422:5 392:4 362:3 328:2 298:1 293:5 238:5 208:4 178:3 148:2 118:1 113:5 58:, 2432:e 2425:t 2418:v 2383:) 2006:e 1999:t 1992:v 1938:) 1920:. 1878:. 1506:Z 1501:Y 1496:X 1491:W 1486:V 1476:U 1471:T 1466:S 1461:R 1456:Q 1446:P 1441:O 1436:N 1431:M 1426:L 1416:K 1411:J 1409:/ 1407:I 1402:H 1397:G 1392:F 1382:E 1377:D 1372:C 1367:B 1362:A 1350:4 1347:3 1344:2 1341:1 1100:Z 1095:Y 1090:X 1085:W 1080:V 1070:U 1065:T 1060:S 1055:R 1050:Q 1040:P 1035:O 1030:N 1025:M 1020:L 1010:K 1005:J 1003:/ 1001:I 996:H 991:G 986:F 976:E 971:D 966:C 961:B 956:A 944:4 941:3 938:2 935:1 809:Z 804:Y 799:X 794:W 789:V 779:U 774:T 769:S 764:R 759:Q 749:P 744:O 739:N 734:M 729:L 719:K 714:J 712:/ 710:I 705:H 700:G 695:F 685:E 680:D 675:C 670:B 665:A 653:4 650:3 647:2 644:1 609:5 587:4 565:3 543:2 521:1 514:5 509:4 504:3 499:2 494:1 481:" 446:Z 441:Y 436:X 431:W 426:V 416:U 411:T 406:S 401:R 396:Q 386:P 381:O 376:N 371:M 366:L 356:K 351:J 349:/ 347:I 342:H 337:G 332:F 322:E 317:D 312:C 307:B 302:A 290:4 287:3 284:2 281:1 257:Ω 252:Ψ 247:Χ 242:Φ 232:Υ 227:Τ 222:Σ 217:Ρ 212:Π 202:Ο 197:Ξ 192:Ν 187:Μ 182:Λ 172:Κ 167:Ι 162:Θ 157:Η 152:Ζ 142:Ε 137:Δ 132:Γ 127:Β 122:Α 110:4 107:3 104:2 101:1

Index


ancient Greeks
historian
Polybius
fractionating
plaintext
telegraphy
steganography
cryptography
Cleoxenus
Democleitus
Greek alphabet
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ

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