2204:
670:
122:
454:
2184:
2014:
782:
Li, Chengqing; Liu, Yuansheng; Zhang, Leo Yu; Chen, Michael Z. Q. (2013-04-01). "Breaking a chaotic image encryption algorithm based on modulo addition and xor operation".
364:
292:
322:
537:
505:
594:
1852:
690:
614:
557:
476:
272:
248:
228:
208:
184:
164:
144:
1787:
868:
31:
that mix additions over two different groups (e.g. addition modulo 2 and addition over GF(2)) and where input and output differences are expressed as XORs.
1614:
970:
1604:
1098:
1505:
1767:
1741:
1609:
1582:
1845:
619:
1751:
861:
2237:
1630:
2232:
2063:
1994:
1808:
47:
1838:
898:
2179:
2134:
1937:
1694:
854:
374:
2058:
1711:
1621:
1599:
912:
28:
2174:
1716:
1572:
1525:
1000:
2164:
2154:
2009:
1782:
1664:
1539:
908:
762:
2159:
2149:
1942:
1902:
1895:
1880:
1875:
1721:
1510:
881:
1947:
1890:
1813:
1689:
1684:
1636:
1485:
2207:
2053:
1999:
1803:
1626:
1063:
761:
Helger Lipmaa, Johan Wallén, Philippe Dumas: On the
Additive Differential Probability of Exclusive-Or.
2169:
2093:
1706:
1589:
1515:
1198:
1178:
801:
1922:
1669:
1646:
965:
2038:
2022:
1964:
1654:
1562:
1274:
1203:
1173:
1118:
825:
791:
751:
729:
560:
700:
Solution to an arbitrary set of DEA (either in batch and or in adaptive query model) was due to
747:
2098:
2088:
1954:
1374:
1073:
1033:
1028:
995:
955:
903:
817:
570:
In 2013, some properties of a special form of DEA were reported by
Chengqing Li et al., where
746:, Near Optimal Algorithms for Solving Differential Equations of Addition With Batch Queries,
331:
277:
2242:
2033:
1885:
1746:
1641:
1520:
1379:
1259:
1228:
922:
809:
564:
300:
1593:
1577:
1566:
1500:
1459:
1424:
1354:
1334:
1208:
1088:
1083:
1038:
739:
721:
701:
513:
481:
573:
805:
2108:
2028:
1984:
1927:
1912:
1731:
1679:
1490:
1475:
1414:
1409:
1294:
1043:
675:
599:
542:
461:
257:
233:
213:
193:
169:
149:
129:
2226:
2189:
2144:
2103:
2083:
1974:
1932:
1907:
1726:
1674:
1553:
1535:
1324:
1299:
1289:
1113:
1103:
950:
829:
2139:
1979:
1969:
1959:
1917:
1861:
1659:
1480:
1444:
1309:
1188:
1143:
975:
927:
877:
743:
725:
705:
20:
559:. It has been proved that the satisfiability of an arbitrary set of DEA is in the
2118:
1269:
1264:
1148:
2078:
2048:
2043:
2004:
1701:
1419:
1359:
1243:
1238:
1183:
1053:
916:
813:
821:
2068:
1434:
1429:
1319:
1233:
1128:
1108:
2113:
2073:
1772:
1736:
1530:
1193:
1068:
1048:
960:
1439:
1389:
1349:
1339:
1284:
1279:
1123:
932:
728:, Solving Systems of Differential Equations of Addition, ACISP 2005.
1989:
1777:
1399:
1394:
1329:
1314:
1304:
1249:
1223:
1218:
1213:
1093:
1078:
709:
708:. The solution techniques have been used to attack the stream cipher
616:
is assumed known. Essentially, the special DEA can be represented as
1495:
1454:
1404:
1384:
1369:
1158:
1138:
1058:
1023:
796:
1344:
1253:
1168:
1163:
1153:
1133:
1005:
990:
1834:
850:
1449:
1364:
985:
980:
755:
733:
665:{\displaystyle (x\dotplus \alpha )\oplus (x\dotplus \beta )=c}
672:. Based on the found properties, an algorithm for deriving
117:{\displaystyle (x+y)\oplus ((x\oplus a)+(y\oplus b))=c}
2015:
Cryptographically secure pseudorandom number generator
678:
622:
602:
576:
545:
516:
484:
464:
377:
334:
303:
280:
260:
236:
216:
196:
172:
152:
132:
50:
27:(DEA) are one of the most basic equations related to
838:
2127:
1868:
1796:
1760:
1549:
1468:
1014:
941:
889:
684:
664:
608:
588:
551:
531:
499:
470:
448:
358:
316:
286:
266:
242:
222:
202:
178:
158:
138:
116:
449:{\displaystyle S=\{(a_{i},b_{i},c_{i})|i<k\}}
328:respectively. The above equation is denoted by
784:International Journal of Bifurcation and Chaos
1846:
862:
8:
443:
384:
1853:
1839:
1831:
869:
855:
847:
843:
839:
795:
677:
621:
601:
575:
544:
515:
483:
463:
429:
420:
407:
394:
376:
333:
308:
302:
279:
259:
235:
215:
195:
171:
151:
131:
49:
774:
16:Equations in differential cryptanalysis
563:when a brute force search requires an
7:
40:Differential equations of addition
25:differential equations of addition
14:
42:(DEA) are of the following form:
2203:
2202:
2064:Information-theoretic security
653:
641:
635:
623:
526:
520:
494:
488:
430:
426:
387:
353:
335:
105:
102:
90:
84:
72:
69:
63:
51:
1:
2180:Message authentication code
2135:Cryptographic hash function
1938:Cryptographic hash function
692:was proposed and analyzed.
2259:
2059:Harvest now, decrypt later
29:differential cryptanalysis
2198:
2175:Post-quantum cryptography
1830:
1752:Time/memory/data tradeoff
846:
842:
814:10.1142/S0218127413500752
2165:Quantum key distribution
2155:Authenticated encryption
2010:Random number generation
1540:Whitening transformation
2160:Public-key cryptography
2150:Symmetric-key algorithm
1943:Key derivation function
1903:Cryptographic primitive
1896:Authentication protocol
1881:Outline of cryptography
1876:History of cryptography
1511:Confusion and diffusion
359:{\displaystyle (a,b,c)}
287:{\displaystyle \oplus }
254:variables. The symbols
2238:Theory of cryptography
1948:Secure Hash Algorithms
1891:Cryptographic protocol
686:
666:
610:
590:
553:
533:
501:
472:
450:
360:
318:
288:
268:
244:
224:
204:
180:
160:
140:
118:
2233:Cryptographic attacks
2054:End-to-end encryption
2000:Cryptojacking malware
1804:Initialization vector
687:
667:
611:
591:
554:
534:
502:
473:
451:
361:
319:
317:{\displaystyle 2^{n}}
289:
269:
245:
225:
205:
181:
161:
141:
119:
2170:Quantum cryptography
2094:Trusted timestamping
1583:3-subset MITM attack
1199:Intel Cascade Cipher
1179:Hasty Pudding cipher
676:
620:
600:
574:
543:
532:{\displaystyle k(n)}
514:
500:{\displaystyle k(n)}
482:
462:
375:
332:
326:bitwise exclusive-or
301:
278:
258:
234:
214:
194:
170:
150:
130:
48:
1923:Cryptographic nonce
1622:Differential-linear
806:2013IJBC...2350075L
589:{\displaystyle a=0}
539:is a polynomial in
478:denote a system of
2039:Subliminal channel
2023:Pseudorandom noise
1965:Key (cryptography)
1695:Differential-fault
913:internal mechanics
682:
662:
606:
586:
561:complexity class P
549:
529:
497:
468:
446:
356:
314:
284:
264:
240:
220:
200:
176:
156:
136:
114:
2220:
2219:
2216:
2215:
2099:Key-based routing
2089:Trapdoor function
1955:Digital signature
1826:
1825:
1822:
1821:
1809:Mode of operation
1486:Lai–Massey scheme
685:{\displaystyle x}
609:{\displaystyle y}
552:{\displaystyle n}
471:{\displaystyle i}
267:{\displaystyle +}
243:{\displaystyle c}
223:{\displaystyle b}
203:{\displaystyle a}
179:{\displaystyle n}
159:{\displaystyle y}
139:{\displaystyle x}
2250:
2206:
2205:
2034:Insecure channel
1886:Classical cipher
1855:
1848:
1841:
1832:
1680:Power-monitoring
1521:Avalanche effect
1229:Khufu and Khafre
882:security summary
871:
864:
857:
848:
844:
840:
834:
833:
799:
779:
691:
689:
688:
683:
671:
669:
668:
663:
615:
613:
612:
607:
595:
593:
592:
587:
565:exponential time
558:
556:
555:
550:
538:
536:
535:
530:
506:
504:
503:
498:
477:
475:
474:
469:
455:
453:
452:
447:
433:
425:
424:
412:
411:
399:
398:
365:
363:
362:
357:
323:
321:
320:
315:
313:
312:
293:
291:
290:
285:
273:
271:
270:
265:
249:
247:
246:
241:
229:
227:
226:
221:
209:
207:
206:
201:
185:
183:
182:
177:
165:
163:
162:
157:
145:
143:
142:
137:
123:
121:
120:
115:
2258:
2257:
2253:
2252:
2251:
2249:
2248:
2247:
2223:
2222:
2221:
2212:
2194:
2123:
1864:
1859:
1818:
1792:
1761:Standardization
1756:
1685:Electromagnetic
1637:Integral/Square
1594:Piling-up lemma
1578:Biclique attack
1567:EFF DES cracker
1551:
1545:
1476:Feistel network
1464:
1089:CIPHERUNICORN-E
1084:CIPHERUNICORN-A
1016:
1010:
943:
937:
891:
885:
875:
837:
781:
780:
776:
772:
740:Souradyuti Paul
722:Souradyuti Paul
718:
716:Further reading
702:Souradyuti Paul
698:
674:
673:
618:
617:
598:
597:
572:
571:
541:
540:
512:
511:
480:
479:
460:
459:
416:
403:
390:
373:
372:
330:
329:
304:
299:
298:
296:addition modulo
276:
275:
256:
255:
232:
231:
212:
211:
192:
191:
168:
167:
148:
147:
128:
127:
46:
45:
37:
17:
12:
11:
5:
2256:
2254:
2246:
2245:
2240:
2235:
2225:
2224:
2218:
2217:
2214:
2213:
2211:
2210:
2199:
2196:
2195:
2193:
2192:
2187:
2185:Random numbers
2182:
2177:
2172:
2167:
2162:
2157:
2152:
2147:
2142:
2137:
2131:
2129:
2125:
2124:
2122:
2121:
2116:
2111:
2109:Garlic routing
2106:
2101:
2096:
2091:
2086:
2081:
2076:
2071:
2066:
2061:
2056:
2051:
2046:
2041:
2036:
2031:
2029:Secure channel
2026:
2020:
2019:
2018:
2007:
2002:
1997:
1992:
1987:
1985:Key stretching
1982:
1977:
1972:
1967:
1962:
1957:
1952:
1951:
1950:
1945:
1940:
1930:
1928:Cryptovirology
1925:
1920:
1915:
1913:Cryptocurrency
1910:
1905:
1900:
1899:
1898:
1888:
1883:
1878:
1872:
1870:
1866:
1865:
1860:
1858:
1857:
1850:
1843:
1835:
1828:
1827:
1824:
1823:
1820:
1819:
1817:
1816:
1811:
1806:
1800:
1798:
1794:
1793:
1791:
1790:
1785:
1780:
1775:
1770:
1764:
1762:
1758:
1757:
1755:
1754:
1749:
1744:
1739:
1734:
1729:
1724:
1719:
1714:
1709:
1704:
1699:
1698:
1697:
1692:
1687:
1682:
1677:
1667:
1662:
1657:
1652:
1644:
1639:
1634:
1627:Distinguishing
1624:
1619:
1618:
1617:
1612:
1607:
1597:
1587:
1586:
1585:
1580:
1570:
1559:
1557:
1547:
1546:
1544:
1543:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1498:
1493:
1491:Product cipher
1488:
1483:
1478:
1472:
1470:
1466:
1465:
1463:
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1392:
1387:
1382:
1377:
1372:
1367:
1362:
1357:
1352:
1347:
1342:
1337:
1332:
1327:
1322:
1317:
1312:
1307:
1302:
1297:
1292:
1287:
1282:
1277:
1272:
1267:
1262:
1257:
1246:
1241:
1236:
1231:
1226:
1221:
1216:
1211:
1206:
1201:
1196:
1191:
1186:
1181:
1176:
1171:
1166:
1161:
1156:
1151:
1146:
1141:
1136:
1131:
1126:
1121:
1119:Cryptomeria/C2
1116:
1111:
1106:
1101:
1096:
1091:
1086:
1081:
1076:
1071:
1066:
1061:
1056:
1051:
1046:
1041:
1036:
1031:
1026:
1020:
1018:
1012:
1011:
1009:
1008:
1003:
998:
993:
988:
983:
978:
973:
968:
963:
958:
953:
947:
945:
939:
938:
936:
935:
930:
925:
920:
906:
901:
895:
893:
887:
886:
876:
874:
873:
866:
859:
851:
836:
835:
790:(4): 1350075.
773:
771:
768:
767:
766:
765:2004: 317-331.
759:
737:
717:
714:
697:
694:
681:
661:
658:
655:
652:
649:
646:
643:
640:
637:
634:
631:
628:
625:
605:
585:
582:
579:
548:
528:
525:
522:
519:
496:
493:
490:
487:
467:
445:
442:
439:
436:
432:
428:
423:
419:
415:
410:
406:
402:
397:
393:
389:
386:
383:
380:
355:
352:
349:
346:
343:
340:
337:
311:
307:
283:
263:
239:
219:
199:
190:variables and
175:
155:
135:
113:
110:
107:
104:
101:
98:
95:
92:
89:
86:
83:
80:
77:
74:
71:
68:
65:
62:
59:
56:
53:
36:
33:
15:
13:
10:
9:
6:
4:
3:
2:
2255:
2244:
2241:
2239:
2236:
2234:
2231:
2230:
2228:
2209:
2201:
2200:
2197:
2191:
2190:Steganography
2188:
2186:
2183:
2181:
2178:
2176:
2173:
2171:
2168:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2145:Stream cipher
2143:
2141:
2138:
2136:
2133:
2132:
2130:
2126:
2120:
2117:
2115:
2112:
2110:
2107:
2105:
2104:Onion routing
2102:
2100:
2097:
2095:
2092:
2090:
2087:
2085:
2084:Shared secret
2082:
2080:
2077:
2075:
2072:
2070:
2067:
2065:
2062:
2060:
2057:
2055:
2052:
2050:
2047:
2045:
2042:
2040:
2037:
2035:
2032:
2030:
2027:
2024:
2021:
2016:
2013:
2012:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1975:Key generator
1973:
1971:
1968:
1966:
1963:
1961:
1958:
1956:
1953:
1949:
1946:
1944:
1941:
1939:
1936:
1935:
1934:
1933:Hash function
1931:
1929:
1926:
1924:
1921:
1919:
1916:
1914:
1911:
1909:
1908:Cryptanalysis
1906:
1904:
1901:
1897:
1894:
1893:
1892:
1889:
1887:
1884:
1882:
1879:
1877:
1874:
1873:
1871:
1867:
1863:
1856:
1851:
1849:
1844:
1842:
1837:
1836:
1833:
1829:
1815:
1812:
1810:
1807:
1805:
1802:
1801:
1799:
1795:
1789:
1786:
1784:
1781:
1779:
1776:
1774:
1771:
1769:
1766:
1765:
1763:
1759:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1720:
1718:
1715:
1713:
1710:
1708:
1707:Interpolation
1705:
1703:
1700:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1678:
1676:
1673:
1672:
1671:
1668:
1666:
1663:
1661:
1658:
1656:
1653:
1651:
1650:
1645:
1643:
1640:
1638:
1635:
1632:
1628:
1625:
1623:
1620:
1616:
1613:
1611:
1608:
1606:
1603:
1602:
1601:
1598:
1595:
1591:
1588:
1584:
1581:
1579:
1576:
1575:
1574:
1571:
1568:
1564:
1561:
1560:
1558:
1555:
1554:cryptanalysis
1548:
1541:
1537:
1536:Key whitening
1534:
1532:
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1482:
1479:
1477:
1474:
1473:
1471:
1467:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1411:
1408:
1406:
1403:
1401:
1398:
1396:
1393:
1391:
1388:
1386:
1383:
1381:
1378:
1376:
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1336:
1333:
1331:
1328:
1326:
1325:New Data Seal
1323:
1321:
1318:
1316:
1313:
1311:
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1064:BEAR and LION
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878:Block ciphers
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2140:Block cipher
1980:Key schedule
1970:Key exchange
1960:Kleptography
1918:Cryptosystem
1862:Cryptography
1712:Partitioning
1670:Side-channel
1648:
1615:Higher-order
1600:Differential
1481:Key schedule
787:
783:
777:
752:Full version
744:Bart Preneel
730:Full version
726:Bart Preneel
706:Bart Preneel
699:
696:Applications
569:
507:
458:for integer
457:
371:
368:
325:
295:
251:
187:
125:
44:
39:
38:
24:
21:cryptography
18:
2128:Mathematics
2119:Mix network
1797:Utilization
1783:NSA Suite B
1768:AES process
1717:Rubber-hose
1655:Related-key
1563:Brute-force
942:Less common
369:Let a set
2227:Categories
2079:Ciphertext
2049:Decryption
2044:Encryption
2005:Ransomware
1747:Chi-square
1665:Rotational
1605:Impossible
1526:Block size
1420:Spectr-H64
1244:Ladder-DES
1239:Kuznyechik
1184:Hierocrypt
1054:BassOmatic
1017:algorithms
944:algorithms
917:Triple DES
892:algorithms
770:References
2069:Plaintext
1722:Black-bag
1642:Boomerang
1631:Known-key
1610:Truncated
1435:Threefish
1430:SXAL/MBAL
1320:MultiSwap
1275:MacGuffin
1234:KN-Cipher
1174:Grand Cru
1129:CS-Cipher
1109:COCONUT98
822:0218-1274
797:1207.6536
748:Indocrypt
651:β
648:∔
639:⊕
633:α
630:∔
282:⊕
97:⊕
79:⊕
67:⊕
2208:Category
2114:Kademlia
2074:Codetext
2017:(CSPRNG)
1995:Machines
1773:CRYPTREC
1737:Weak key
1690:Acoustic
1531:Key size
1375:Red Pike
1194:IDEA NXT
1074:Chiasmus
1069:CAST-256
1049:BaseKing
1034:Akelarre
1029:Adiantum
996:Skipjack
961:CAST-128
956:Camellia
904:Blowfish
830:15990771
35:Examples
2243:Ciphers
1869:General
1814:Padding
1732:Rebound
1440:Treyfer
1390:SAVILLE
1350:PRESENT
1340:NOEKEON
1285:MAGENTA
1280:Madryga
1260:Lucifer
1124:CRYPTON
933:Twofish
923:Serpent
802:Bibcode
750:2005.
294:denote
188:unknown
1990:Keygen
1778:NESSIE
1727:Davies
1675:Timing
1590:Linear
1550:Attack
1469:Design
1460:Zodiac
1425:Square
1400:SHACAL
1395:SC2000
1355:Prince
1335:Nimbus
1330:NewDES
1315:MULTI2
1305:MISTY1
1248:LOKI (
1224:KHAZAD
1219:KeeLoq
1214:KASUMI
1209:Kalyna
1094:CLEFIA
1079:CIKS-1
1039:Anubis
890:Common
828:
820:
510:where
126:where
2025:(PRN)
1660:Slide
1516:Round
1501:P-box
1496:S-box
1455:XXTEA
1415:Speck
1410:Simon
1405:SHARK
1385:SAFER
1370:REDOC
1295:Mercy
1254:89/91
1204:Iraqi
1169:G-DES
1159:FEA-M
1139:DES-X
1104:Cobra
1059:BATON
1044:Ascon
1024:3-Way
1015:Other
826:S2CID
792:arXiv
710:Helix
252:known
186:-bit
1788:CNSA
1647:Mod
1573:MITM
1345:NUSH
1300:MESH
1290:MARS
1164:FROG
1154:FEAL
1134:DEAL
1114:Crab
1099:CMEA
1006:XTEA
991:SEED
971:IDEA
966:GOST
951:ARIA
818:ISSN
742:and
724:and
704:and
596:and
438:<
324:and
274:and
250:are
230:and
166:are
146:and
1742:Tau
1702:XSL
1506:SPN
1450:xmx
1445:UES
1380:S-1
1365:RC2
1310:MMB
1189:ICE
1144:DFC
1001:TEA
986:RC6
981:RC5
976:LEA
928:SM4
909:DES
899:AES
810:doi
763:FSE
756:PDF
734:PDF
567:.
508:DEA
19:In
2229::
1270:M8
1265:M6
1252:,
1250:97
1149:E2
915:,
824:.
816:.
808:.
800:.
788:23
786:.
712:.
366:.
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1565:(
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1552:(
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1538:(
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911:(
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880:(
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812::
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754:(
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645:x
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524:n
521:(
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492:n
489:(
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441:k
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351:c
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100:b
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82:a
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