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LOKI

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:''This page is about the Norse god Loki. For other uses of the word see Loki (disambiguation).'' Image:Manuscript_loki.jpg 18th century.html" title="Meaning of thumb thumb|right|350px|This picture, from an [[18th century Iceland Icelandic manuscript, shows Loki with his invention - the fishing net..html" title="Meaning of right|350px|This picture, from an [[18th century">thumb|right|350px|This picture, from an [[18th century Iceland Icelandic manuscript, shows Loki with his invention - the fishing net.">right|350px|This picture, from an [[18th century">thumb|right|350px|This picture, from an [[18th century Iceland Icelandic manuscript, shows Loki with his invention - the fishing net. '''Loki Laufeyjarson''' is the god of mischief in Norse mythology, a son of the Jotun giants Fárbauti and Laufey. He is described as the "contriver of all fraud". He mixed freely with the gods for a long time, even becoming Odin's blood brother. Despite much research, "the figure of Loki remains obscure; there is no trace of a cult, and the name does not appear in place-names"Encyclopædia Britannica, 2004. The composer Richard Wagner presented Loki under an invented German language Germanized name '''Loge''' in his operas Das Rheingold and Die Walküre.

Nature
The trickster god is a complex character, a master of guile and deception. Loki was not so much a figure of unmitigated badness as a kind of celestial con man. Loki is an adept Shapeshifting shape-shifter, with the ability to change both form (examples include transmogrification to a salmon, horse, bird, flea, etc.) and sex. According to some scholarly theories Loki is conceived of as a fire spiritual being spirit, with all the potential for good and ill associated with fire. However, this view is probably due to linguistic confusion with ''logi'' "fire", as there is little indication of it in myth where Loki's role is predominantly associated with Odin, either as Odin's wily counterpart or antagonist. StrömFolke Ström, ''Loki. Ein mythologisches Problem'', Göteborg (1956) identifies the two gods to the point of calling Loki "a hypostasis of Odin", and RübekeilLudwi Rübekeil, ''Wodan und andere forschungsgeschichtliche Leichen: exhumiert'', Beiträge zur Namenforschung 38 (2003), 25–42 suggests that the two gods were originally identical, deriving from Celtic Lugus (the name of which would be continued in ''Loki'').

Children
Image:IdunandlokibyJohnBauer.jpg Iðunn.html"_title="Meaning of thumb thumb|300px|right|[[Iðunn_and Loki, by John Bauer.html" title="Meaning of 300px|right|[[Iðunn">thumb|300px|right|[[Iðunn and Loki, by John Bauer">300px|right|[[Iðunn">thumb|300px|right|[[Iðunn and Loki, by John Bauer Loki was the father (and in one instance the mother) of many beasts, humans and monsters. Having liaisons with giantesses was nothing unusual for gods in Norse mythology—both Odin and Freyr are good examples; and since Loki was actually a giant himself, there is nothing unusual about this activity. Together with Angrboda, he had three children: *Jörmungandr, the sea serpent; *Fenrir the giant wolf preordained to slay Odin at the time of Ragnarök; *Hel (being) Hel, ruler of the realm of the dead. While he was in the form of a mare Loki also gave birth to Sleipnir, the eight-legged steed of Odin.

Scheming with fellow gods
Loki occasionally works with the other gods. For example, he tricked the unnamed jotun giant who built the walls around Asgard, out of being paid for his work by distracting his horse while disguised as a mare—thereby he became the ''mother'' of Odin's eight-legged horse Sleipnir. He also retrieved Gungnir Odin's spear, Skíðblaðnir Freyr's ship and Sif's wig from Dvalin, the Norse dwarves dwarf, as well as rescuing Iðunn. Finally, in ''Þrymskviða'', Loki manages, with Thor at his side, to get Mjolnir back when the giant Thrym secretly steals it, in order to ask for Freyja as a bride, in exchange. Image:Loki and Hod.jpg Höðr.html" title="Meaning of thumb thumb|left|230px|''Loki tricks [[Höðr into shooting Baldr''.html" title="Meaning of left|230px|''Loki tricks [[Höðr">thumb|left|230px|''Loki tricks [[Höðr into shooting Baldr''">left|230px|''Loki tricks [[Höðr">thumb|left|230px|''Loki tricks [[Höðr into shooting Baldr''

Slayer of Baldr
Loki may have overplayed his hand when, disguised as a giantess, he arranged the murder of Baldr. He used mistletoe, the only plant which had not sworn to never harm Baldr, and made a dart of it, which he tricked Baldr's blind brother Höðr into throwing at Baldr, thereby killing him. Another version of the myth, preserved in ''Gesta Danorum'', does not mention Loki.

Friend to man
Not all Folklore lore depicts Loki as a malevolent being. An 18th century ballad (that may have drawn from a much earlier source) from the Faroe Islands, entitled ''Loka Táttur'', depicts Loki as a friend to man: when a ''thurs'' (troll or giant) comes to take a farmer's son away, the farmer and his wife pray to Odin to protect him. Odin hides the son in a field of wheat, but the thurs finds him. Odin rescues the son and takes him back to the farmer and his wife, saying that he is done hiding the son. The couple then prays to Hœnir, who hides the son in the neck-feathers of a swan, but again the thurs finds him. On the third day, they pray to Loki, who hides the son amidst the eggs of a flounder. The thurs finds the flounder, but Loki instructs the boy to run into a boathouse. The giant gets his head caught and Loki kills him by chopping off his leg and inserting a stick and a stone in the leg stump to prevent the thurs from regenerating. He takes the boy home, and the farmer and his wife embrace both of them.

Homologues
Some anthropologists have compared him to Coyote (mythology) Coyote, a trickster figure of Native American mythology. Others compare him to Hermes, who tricked Apollo and also often broke boundaries, or to the Slavic pantheon Slavic god Veles (god) Veles. Loki can at times be reminiscent of the Chinese mythology Chinese Monkey King whose persona in myth underwent changes over the centuries.

Loki in popular culture
{{main|Loki in popular culture}} Loki's appearances in popular culture can vary wildly in their interpretations of his character - some portray him as a trickster, some simply as evil.

Other spellings
* Common Danish, Swedish and Norwegian form: Loke * Nynorsk - Norwegian form: Lokkje * German form: Lohho

References


External links

- Loki - A Paean in Progress
- The Baldr Myth
- An essay on Loki
- The Lokasenna - "Loki's Wrangling": an insult competition between Loki and the other gods {{NorseMythology}} Category:Fire gods Category:Norse giants Category:Norse gods Category:Shapeshifting Category:Trickster gods bg:Локи ca:Loki cs:Loki da:Loke de:Loki el:Λόκι es:Loki eo:Loki fr:Loki gl:Loki he:לוקי ka:ლ�კე lt:Lokis lv:Loki nl:Loki ja:ロキ no:Loke nn:Loke pl:Loki pt:Loki ro:Loki ru:Локи sl:Loki fi:Loki sv:Loke uk:Локі zh:洛基 In cryptography, '''LOKI89''' and '''LOKI91''' are block ciphers designed as possible replacements for the Data Encryption Standard (DES). The ciphers were developed based on a body of work analysing DES, and are very similar to DES in structure. The '''LOKI''' algorithms were named for Loki, the god of mischief in Norse mythology.

LOKI89
LOKI89 was first published in 1990, then named just "LOKI", by Austrialian cryptographers Lawrie Brown, Josef Pieprzyk and Jennifer Seberry. LOKI89 was submitted to the European RIPE project for evaluation, but was not selected. The cipher uses a 64-bit block size (cryptography) block and a 64-bit key length key. Like Data Encryption Standard DES, it is a 16-round Feistel cipher and has a similar general structure, but differs in the choice of the particular S-boxes, the "P-permutation", and the "Expansion permutation". The S-Boxes use the non-linearity criteria developed by Josef Pieprzyk, making them as "complex" and "unpredicatable" as possible. Their effectiveness was compared against the known design criteria for the DES S-boxes. The permutations were designed to "mix" the outputs of the S-boxes as quickly as possible, promoting the avalanche and completeness properties, essential for a good Feistel cipher. However unlike their equivalents in the DES, they are intended to be as clean and simple as possible (in retrospect perhaps a little too simple), aiding the analysis of the design. Following the publication of LOKI89, information on the new differential cryptanalysis became available, as well as some early analysis results by (Knudsen 1993a). This resulted in the design being changed to become LOKI91.

LOKI91
LOKI 91 was designed in response to the attacks on LOKI89 (Brown et. al., 1991). The changes included removing the initial and final key whitening, a new S-box, and small alterations to the key schedule. More specifically, the S-boxes functions were changed to minimise the probability of seeing different inputs resulting in the same output (a hook which Differential cryptanalysis uses), thus improving LOKI91's immunity to this attack, as detailed by the attacks authors (Biham and Shamir 1991). The changes to the key schedule were designed to reduce the number of "equivalent" or "related" keys, which resulted in the exhaustive search space for the cipher being reduced. Whilst the resulting cipher is clearly stronger and more secure than LOKI89, there are a number of potential attacks, as detailed in the papers by Knudsen and Biham, listed in the References below. Consequently these ciphers should be viewed as academic efforts to advance the field of block cipher design, rather than algorithms. The number of citations and published critiques suggests this aim has been achieved.

See also
* LOKI97

References
* Eli Biham, "New Types of Cryptanalytic Attacks Using Related Keys", Journal of Cryptology, vol 7 no 4, pp 229-246, Springer-Verlag, 1994. * Eli Biham, Adi Shamir, "Differential Cryptanalysis of Snefru, Khafre, REDOC-II, LOKI and Lucifer", in Advances in Cryptology - CRYPTO'91, LNCS 576, pp 156-171, J Feigenbaum (ed), Springer-Verlag, 1991. * L. Brown, Josef Pieprzyk and Jennifer Seberry, " LOKI - A Cryptographic Primitive for Authentication and Secrecy Applications", in Advances in Cryptology - Auscrypt'90, LNCS 453, pp229-236, J Seberry, J Pieprzyk (eds), Springer-Verlag, 1990. * L. Brown, M Kwan, J Pieprzyk, J Seberry, " Improving Resistance to Differential Cryptanalysis and the Redesign of LOKI", in Advances in Cryptology - Asiacrypt'91", LNCs 739, pp 36-50, H Imai et al (eds), Springer-Verlag, 1993. * Lars R. Knudsen, "Cryptanalysis of LOKI", in Advances in Cryptology - ASIACRYPT'91, LNCS 739, pp 22-35, H Imai et al (eds), Springer-Verlag, 1993. * Lars R. Knudsen, "Cryptanalysis of LOKI91", in Advances in Cryptology - ASIACRYPT'92, LNCS 718, pp 196-208, J Seberry, Y Zheng (eds), Springer-Verlag, 1993. * Lars R. Knudsen, "New Potentially 'Weak' Keys for DES and LOKI", in Advances in Cryptology - EUROCRYPT'94, LNCS 950, pp 419-424, Springer-Verlag, 1994.* Lars R. Knudsen, M.J.B. Robshaw, "Non-linear Approximations in Linear Cryptanalysis", in Advances in Cryptology - Eurocrypt'96, LNCS 1070, pp 224-236, Springer-Verlag, 1996. * Kouichi Sakurai, Souichi Furuya, "Improving Linear Cryptanalysis of LOKI91 by Probabilistic Counting Method", in Fast Software Encryption, pp 114-133, Springer-Verlag, 1997. * Toshio Tokita, Tohru Sorimachi, Mitsuru Matsui, "Linear Cryptanalysis of LOKI and s2DES", in Advances in Cryptology - ASIACRYPT'94, LNCS 917, pp 293-303, Springer-Verlag, 1994.

External links

- LOKI91 home page
- Notes on LOKI89 and LOKI91 {{Block_ciphers}} Category:Block ciphers fr:LOKI89/91

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[The article LOKI is based on the the dictionary Wikipedia, the free encyklopedia. There you will find a list of all editors and the possibility to edit the original text of the article LOKI.
The texts from Wikipedia and this site follow the GNU Free Documentation License.]

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