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...eprint.iacr.org/2004/072.pdf Christopher Wolf and Bart Preneel, Asymmetric Cryptography: Hidden Field Equations]</ref> ...utogenerated1">[http://eprint.iacr.org/2001/029.pdf Nicolas T. Courtois On Multivariate Signature-only public key cryptosystems]</ref> We start with the simplest k ...

| known_for = [[Cryptography]], [[security]] | contribution = Efficient algorithms for solving overdefined systems of multivariate polynomial equations ...

The field of [[cryptography]] utilizes the fact that certain number-theoretic functions are randomly se ...it is clear that ''PERM''(''M'') for any ''n''-by-''n'' matrix ''M'' is a multivariate polynomial of degree ''n'' over the entries in ''M''. Calculating the perma ...

In [[cryptography]], the '''''eXtended Sparse Linearization'' (XSL) attack''' is a method of ...ization'', is then applied to solve these equations and recover the [[key (cryptography)|key]]. ...

{{Short description|Term used in theoretical computer science and cryptography}} In [[theoretical computer science]] and [[cryptography]], a '''pseudorandom generator (PRG)''' for a class of [[statistical test]] ...

...], computes the [[Gröbner basis]] of an [[ideal (ring theory)|ideal]] of a multivariate [[polynomial ring]]. The algorithm uses the same mathematical principles a ...ved by F5,{{cn|date=November 2020}} as were a number of systems related to cryptography; for example [[Hidden Field Equations|HFE]] and C^*.{{cn|date=Nov ...

...t1=Paul L.|last2=Beer|first2=Randall D.|title=Nonnegative Decomposition of Multivariate Information|year=2010|class=cs.IT}}</ref><ref>{{Cite journal|arxiv = 2008.0 ...= Bruce | last = Schneier | author-link = Bruce Schneier | title = Applied Cryptography: Protocols, Algorithms, and Source Code in C | url = https://archive.org/de ...

...metric-key algorithm|symmetric key]] [[block cipher]] with a [[block size (cryptography)|block size]] of 128 [[bit]]s and [[key size]]s of 128, 192 and 256 bits. I ...The cipher also uses input and output [[key whitening]]. The [[Diffusion (cryptography)|diffusion]] layer uses a [[linear transformation]] based on a [[Matrix (ma ...

...|polynomial greatest common divisor]], [[Gröbner basis]] computation and [[cryptography]]. ...author-first3=Thomas |author-last3=Plantard |title=Efficient RNS bases for Cryptography |journal=IMACS'05: World Congress: Scientific Computation Applied Mathemati ...

Articles related to cryptography include: [[Advantage (cryptography)]] [[Talk:Advantage (cryptography)| ]] • ...

...The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography|year=2006}} Cambridge PhD thesis. *'''McG54''' W.J. McGill, "Multivariate Information Transmission", IRE Trans. Info. Theory '''4''' (1954) 93–111. ...

...testing]]. Identity testing is the problem of determining whether a given multivariate [[polynomial]] is the generators and in key generation for [[cryptography]]. Therefore, finding very large prime numbers ...

There are irreducible [[multivariate polynomial]]s of every degree over the complex numbers. For example, the po ...3 = Vanstone | author-link3 = Scott Vanstone | title = Handbook of applied cryptography | publisher = [[CRC Press]] | year = 1997 | isbn = 978-0-8493-8523-0 | url- ...

| for his contributions in a number of mathematical areas including complex multivariate analysis, partial differential equations and sub-elliptical problems. | for his fundamental contributions to Mathematical Cryptography.<ref>[https://wolffund.org.il/adi-shamir/ Wolf Prize 2024 - Mathematics]</r ...

Gröbner basis computation can be seen as a multivariate, non-linear generalization of both [[polynomial greatest common divisor#Euc ...liography/gbbib_files/publication_776.pdf}}</ref> An analogous concept for multivariate [[power series]] was developed independently by [[Heisuke Hironaka]] in 196 ...

* [[Multivariate analysis]]&nbsp;– analysis of data involving several variables, such as by ...ce]] applies [[cryptanalysis]] and [[frequency analysis]] to break [[code (cryptography)|codes]] and [[cipher]]s. [[Business intelligence]] applies theories of [[c ...

* [[Multivariate division algorithm]]: for [[polynomial]]s in several indeterminates * [[Multivariate interpolation]] ...

...ical problems]]. Classically, it studies [[zero of a function|zeros]] of [[multivariate polynomial]]s; the modern approach generalizes this in a few different aspe ...is strongly related to [[Francis Sowerby Macaulay|Macaulay]]'s [[Resultant|multivariate resultant]]. ...

...lisher=Springer Science|location=New York|isbn=978-0-387-95364-9}}</ref> [[cryptography]], [[neurobiology]],<ref name="Spikes">{{cite book|title=Spikes: Exploring ...tps://www.taylorfrancis.com/books/9780429881329 |title=Handbook of Applied Cryptography |last2=van Oorschot |first2=Paul C. |last3=Vanstone |first3=Scott A. |date= ...

{{defn|no=4|In [[cryptography]] often denotes an error in place of a regular value.}} ...for example, <math>f(x)</math>, <math>\sin(x+y)</math>. In the case of a [[multivariate function]], the parentheses contain several expressions separated by commas ...