Shafrira Goldwasser is a professor of electrical engineering and computer science at MIT, and a professor of mathematical sciences at the Weizmann Institute of Science, Israel.
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Silvio Micali
Silvio Micali (born October 13, 1954) is an Italian-born computer scientist at MIT Computer Science and Artificial Intelligence Laboratory and a professor of computer science in MIT's Department of Electrical Engineering and Computer Science since 1983. His research centers on the theory of cryptography and information security. He received his Ph.D. from the University of California, Berkeley in 1982; his thesis adviser was Manuel Blum. Micali won the Gödel Prize in 1993.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra.
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Discrete logarithm
In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga(b) is a solution of the equation a = b over the real or complex numbers. Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation g = h is called a discrete logarithm to the base g of h in the group G.
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List of finite simple groups
In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type (including the Tits group, which strictly speaking is not of Lie type), or one of 26 sporadic groups. The list below gives all finite simple groups, together with their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small representations, and lists of all duplicates.
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Finite group
In mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of solvable groups and nilpotent groups. A complete determination of the structure of all finite groups is too much to hope for; the number of possible structures soon becomes overwhelming.
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Co-NP
In computational complexity theory, co-NP is a complexity class. A problem is a member of co-NP if and only if its complement is in the complexity class NP. In simple terms, co-NP is the class of problems for which efficiently verifiable proofs of no instances, sometimes called counterexamples, exist.
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Polynomial hierarchy
In computational complexity theory, the polynomial hierarchy is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic.
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