217.28.8.42: /* Particle properties */

2014-12-18T19:28:04Z

Particle properties

← Older revision		Revision as of 21:28, 18 December 2014
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	An '''MDS matrix (Maximum Distance Separable)''' is a [[matrix (mathematics)\|matrix]] representing a function with certain [[diffusion (cryptography)\|diffusion]] properties that have useful applications in [[cryptography]]. ~~Technically, an m×n matrix A over a [[finite field]] K is an MDS matrix if it~~ is ~~the [[transformation matrix]]~~		Friends contact him Royal. She is presently a cashier but soon she'll be on her own. Years ago we moved to Kansas. The factor I adore most bottle tops collecting and now I have time to take on new issues.<br><br>Here is my web site; [http://www.Thelamda.com/index.php?mod=users&action=view&id=3598 extended auto warranty]
	of a ~~[[linear transformation]] f(x)=Ax from K<sup>n</sup> to K<sup>m</sup> such that no two different (m+n)-tuples of the form (x,f(x)) coincide in n or more components~~.
	~~Equivalently, the set of all (m+n)-tuples (x,f(x)) is an [[Maximum distance separable code\|MDS code]], i.e. a [[linear code]] that reaches the [[Singleton bound]].~~

	~~Let <math>\tilde A = \left(\begin{array}{c}{\rm Id}_n\\ \hline{\rm A}\end{array}\right)</math> be the matrix obtained by joining the [[identity matrix]] Id<sub>n</sub>~~ to A.
	~~Then a necessary~~ and ~~sufficient condition for a matrix A~~ to ~~be MDS is that every possible n×n [[submatrix]] obtained by removing m rows from~~ <~~math~~>~~\tilde A~~<~~/math~~>
	is ~~[[non-singular matrix\|non-singular]].~~

	~~[[Reed-Solomon code]]s have the MDS property and are frequently used to obtain the MDS matrices used in cryptographic algorithms.~~

	[[Serge Vaudenay]] suggested using MDS matrices in [[cryptographic primitive]]s to produce what he called ''multipermutations'', not-necessarily linear functions with this same property. These functions have what he called ''perfect diffusion'': changing t of the inputs changes at least m-t+1 of the outputs. He showed how to exploit imperfect diffusion to [[cryptanalysis\|cryptanalyze]] functions that are not multipermutations.

	MDS matrices are used for diffusion in such [[block cipher]]s as [[Advanced Encryption Standard\|AES]], [[SHARK]], [[Square (cipher)\|Square]], [[Twofish]], [[Anubis (cipher)\|Anubis]], [[KHAZAD]], [[Manta (cipher)\|Manta]], [[Hierocrypt]], and [[Camellia (cipher)\|Camellia]], and in the [[stream cipher]] [[MUGI]] and the [[cryptographic hash function]] [[WHIRLPOOL]].

	~~== References ==~~

	* {{ cite conference

	~~\| author = Serge Vaudenay~~
	~~\| title = On the Need for Multipermutations: Cryptanalysis of MD4 and SAFER~~
	~~\| conference = 2nd International Workshop on [[Fast Software Encryption]] (FSE '94)~~
	~~\| pages = 286&ndash~~;~~297~~
	~~\| publisher =~~ [~~[Springer-Verlag]]~~
	~~\| date = November 16, 1994~~
	~~\| location = [[Leuven]]~~
	~~\| url =~~ http://~~citeseer~~.~~ist~~.~~psu.edu~~/~~vaudenay94need~~.~~html~~
	~~\| format~~ = ~~[[PDF]]/[[PostScript]]~~
	~~\| accessdate~~ = ~~2007-03-05 }}~~

	* {{ cite conference

	~~\| author = [[Vincent Rijmen]], [[Joan Daemen]], [[Bart Preneel]], Anton Bosselaers, Erik De Win~~
	~~\| title = The Cipher SHARK~~
	~~\| conference = 3rd International Workshop on Fast Software Encryption (FSE '96)~~
	~~\| pages = 99~~&~~ndash;111~~
	~~\| publisher = Springer-Verlag~~
	~~\| date = February 1996~~
	~~\| location = [[Cambridge]]~~
	~~\| url = http://citeseer.ist.psu.edu/rijmen96cipher.html~~
	~~\| format = PDF/PostScript~~
	~~\| accessdate = 2007-03-06 }}~~

	* {{ cite paper

	~~\| author~~ = ~~[[Bruce Schneier]], [[John Kelsey (cryptanalyst)\|John Kelsey]], Doug Whiting, [[David A. Wagner\|David Wagner]], Chris Hall, [[Niels Ferguson]]~~
	~~\| title = The Twofish Encryption Algorithm~~
	~~\| date = June 15, 1998~~
	~~\| url = http://www.schneier.com/paper-twofish-paper.html~~
	~~\| format = PDF/PostScript~~
	~~\| accessdate = 2007-03-04 }}~~

	~~{{crypto-stub}}~~

	~~[[Category:Cryptography]~~]

en>Amr94: Add IUPAC definition

2013-07-25T14:05:07Z

Add IUPAC definition

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← Older revision		Revision as of 21:28, 18 December 2014
Line 1:		Line 1:
	An '''MDS matrix (Maximum Distance Separable)''' is a [[matrix (mathematics)\|matrix]] representing a function with certain [[diffusion (cryptography)\|diffusion]] properties that have useful applications in [[cryptography]]. ~~Technically, an m×n matrix A over a [[finite field]] K is an MDS matrix if it~~ is ~~the [[transformation matrix]]~~		Friends contact him Royal. She is presently a cashier but soon she'll be on her own. Years ago we moved to Kansas. The factor I adore most bottle tops collecting and now I have time to take on new issues.<br><br>Here is my web site; [http://www.Thelamda.com/index.php?mod=users&action=view&id=3598 extended auto warranty]
	of a ~~[[linear transformation]] f(x)=Ax from K<sup>n</sup> to K<sup>m</sup> such that no two different (m+n)-tuples of the form (x,f(x)) coincide in n or more components~~.
	~~Equivalently, the set of all (m+n)-tuples (x,f(x)) is an [[Maximum distance separable code\|MDS code]], i.e. a [[linear code]] that reaches the [[Singleton bound]].~~

	~~Let <math>\tilde A = \left(\begin{array}{c}{\rm Id}_n\\ \hline{\rm A}\end{array}\right)</math> be the matrix obtained by joining the [[identity matrix]] Id<sub>n</sub>~~ to A.
	~~Then a necessary~~ and ~~sufficient condition for a matrix A~~ to ~~be MDS is that every possible n×n [[submatrix]] obtained by removing m rows from~~ <~~math~~>~~\tilde A~~<~~/math~~>
	is ~~[[non-singular matrix\|non-singular]].~~

	~~[[Reed-Solomon code]]s have the MDS property and are frequently used to obtain the MDS matrices used in cryptographic algorithms.~~

	[[Serge Vaudenay]] suggested using MDS matrices in [[cryptographic primitive]]s to produce what he called ''multipermutations'', not-necessarily linear functions with this same property. These functions have what he called ''perfect diffusion'': changing t of the inputs changes at least m-t+1 of the outputs. He showed how to exploit imperfect diffusion to [[cryptanalysis\|cryptanalyze]] functions that are not multipermutations.

	MDS matrices are used for diffusion in such [[block cipher]]s as [[Advanced Encryption Standard\|AES]], [[SHARK]], [[Square (cipher)\|Square]], [[Twofish]], [[Anubis (cipher)\|Anubis]], [[KHAZAD]], [[Manta (cipher)\|Manta]], [[Hierocrypt]], and [[Camellia (cipher)\|Camellia]], and in the [[stream cipher]] [[MUGI]] and the [[cryptographic hash function]] [[WHIRLPOOL]].

	~~== References ==~~

	* {{ cite conference

	~~\| author = Serge Vaudenay~~
	~~\| title = On the Need for Multipermutations: Cryptanalysis of MD4 and SAFER~~
	~~\| conference = 2nd International Workshop on [[Fast Software Encryption]] (FSE '94)~~
	~~\| pages = 286&ndash~~;~~297~~
	~~\| publisher =~~ [~~[Springer-Verlag]]~~
	~~\| date = November 16, 1994~~
	~~\| location = [[Leuven]]~~
	~~\| url =~~ http://~~citeseer~~.~~ist~~.~~psu.edu~~/~~vaudenay94need~~.~~html~~
	~~\| format~~ = ~~[[PDF]]/[[PostScript]]~~
	~~\| accessdate~~ = ~~2007-03-05 }}~~

	* {{ cite conference

	~~\| author = [[Vincent Rijmen]], [[Joan Daemen]], [[Bart Preneel]], Anton Bosselaers, Erik De Win~~
	~~\| title = The Cipher SHARK~~
	~~\| conference = 3rd International Workshop on Fast Software Encryption (FSE '96)~~
	~~\| pages = 99~~&~~ndash;111~~
	~~\| publisher = Springer-Verlag~~
	~~\| date = February 1996~~
	~~\| location = [[Cambridge]]~~
	~~\| url = http://citeseer.ist.psu.edu/rijmen96cipher.html~~
	~~\| format = PDF/PostScript~~
	~~\| accessdate = 2007-03-06 }}~~

	* {{ cite paper

	~~\| author~~ = ~~[[Bruce Schneier]], [[John Kelsey (cryptanalyst)\|John Kelsey]], Doug Whiting, [[David A. Wagner\|David Wagner]], Chris Hall, [[Niels Ferguson]]~~
	~~\| title = The Twofish Encryption Algorithm~~
	~~\| date = June 15, 1998~~
	~~\| url = http://www.schneier.com/paper-twofish-paper.html~~
	~~\| format = PDF/PostScript~~
	~~\| accessdate = 2007-03-04 }}~~

	~~{{crypto-stub}}~~

	~~[[Category:Cryptography]~~]

Suspension polymerization - Revision history

217.28.8.42: /* Particle properties */

en>Amr94: Add IUPAC definition

en>FrescoBot: Bot: fixing section wikilinks to section redirects with conflicting sections