Lilya Budaghyan | |
|---|---|
 | |
| Born | 29 January 1976 |
| Citizenship |
|
| Occupations |
|
Lilya Budaghyan (born January 29, 1976) is a Norwegian-Armenian cryptographer, computer scientist, and discrete mathematician known for her work on cryptographic Boolean functions. She is a professor at the Department of Informatics of the University of Bergen in Norway, [1] where she directs the Selmer Center in Secure Communication [2] and leads Boolean functions team. [3]
Budaghyan earned a diploma with honour in mathematics from Yerevan State University in 1998. After additional graduate research at Yerevan State University, she completed a PhD at Otto von Guericke University Magdeburg in Germany in 2005. [4] Her PhD dissertation is The equivalence of almost bent and almost perfect nonlinear functions and their generalizations. [5]
After postdoctoral research at the University of Trento, Italy, the University of Bergen, and the University of Paris 8 Vincennes-Saint-Denis, she became a professor at the University of Bergen in 2019. [4]
Budaghyan is the author of the book Construction and Analysis of Cryptographic Functions (Springer, 2014). [6]
Budaghyan won the Emil Artin Junior Prize in Mathematics for outstanding contributions in algebra, geometry and number theory in 2011 for a joint paper with Tor Helleseth titled “New commutative semifields defined by new PN multinomials”. [7] [8] In 2022 another paper co-authored by Budaghyan led to Emil Artin Junior Prize "Relation between o-equivalence and EA-equivalence for Niho bent functions".[ citation needed ]
She is a member of the Norwegian Academy of Technological Sciences, [9] elected in 2019. [10]
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Shannon's property of confusion. Mathematically, an S-box is a nonlinear vectorial Boolean function.
Emil Artin was an Austrian mathematician of Armenian descent.
John Torrence Tate Jr. was an American mathematician distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings, as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities and allowing "varieties" defined over any commutative ring.
Vincent Rijmen is a Belgian cryptographer and one of the two designers of the Rijndael, the Advanced Encryption Standard. Rijmen is also the co-designer of the WHIRLPOOL cryptographic hash function, and the block ciphers Anubis, KHAZAD, Square, NOEKEON and SHARK.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set. Alternative names are switching function, used especially in older computer science literature, and truth function, used in logic. Boolean functions are the subject of Boolean algebra and switching theory.
In cryptography, the avalanche effect is the desirable property of cryptographic algorithms, typically block ciphers and cryptographic hash functions, wherein if an input is changed slightly, the output changes significantly. In the case of high-quality block ciphers, such a small change in either the key or the plaintext should cause a drastic change in the ciphertext. The actual term was first used by Horst Feistel, although the concept dates back to at least Shannon's diffusion.
Michael Artin is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
Dorian Morris Goldfeld is an American mathematician working in analytic number theory and automorphic forms at Columbia University.
Richard Jay Lipton is an American computer scientist who is Associate Dean of Research, Professor, and the Frederick G. Storey Chair in Computing in the College of Computing at the Georgia Institute of Technology. He has worked in computer science theory, cryptography, and DNA computing.
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. The abstract perspective on algebra has become so fundamental to advanced mathematics that it is simply called "algebra", while the term "abstract algebra" is seldom used except in pedagogy.
In the mathematical field of combinatorics, a bent function is a Boolean function that is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change.
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.
Ernst Sejersted Selmer was a Norwegian mathematician, who worked in number theory, as well as a cryptologist. The Selmer group of an Abelian variety is named after him. His primary contributions to mathematics reside within the field of diophantine equations. He started working as a cryptologist during the Second World War; due to his work, Norway became a NATO superpower in the field of encryption.
Established in 2001, the Emil Artin Junior Prize in Mathematics is presented usually every year to a former student of an Armenian university, who is under the age of thirty-five, for outstanding contributions in algebra, geometry, topology, and number theory. The award is announced in the Notices of the American Mathematical Society. The prize is named after Emil Artin, who was of Armenian descent. Although eligibility for the prize is not fully international, as the recipient has to have studied in Armenia, awards are made only for specific outstanding publications in leading international journals.
Helene (Hel) Braun was a German mathematician who specialized in number theory and modular forms. Her autobiography, The Beginning of A Scientific Career, described her experience as a female scientist working in a male-dominated field at the time, in the Third Reich.
Sarah Livia Zerbes is a German algebraic number theorist at ETH Zurich. Her research interests include L-functions, modular forms, p-adic Hodge theory, and Iwasawa theory, and her work has led to new insights towards the Birch and Swinnerton-Dyer conjecture, which predicts the number of rational points on an elliptic curve by the behavior of an associated L-function.
Della Jeanne Dumbaugh is an American mathematician and historian of mathematics, focusing on the history of algebra and number theory. She is a professor of mathematics at the University of Richmond, and the editor-in-chief of The American Mathematical Monthly.
{{citation}}: CS1 maint: untitled periodical (link){{citation}}: CS1 maint: untitled periodical (link)