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LOKI
*** Shopping-Tip: LOKI
:''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. Ström
[Folke Ström, ''Loki. Ein mythologisches Problem'', Göteborg (1956)] identifies the two gods to the point of calling Loki "a hypostasis of Odin", and Rübekeil
[Ludwi 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,
SkÃðblaðnir 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
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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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