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Fully KeyHomomorphic Encryption, Arithmetic Circuit ABE, and Compact Garbled Circuits
, 2014
"... We construct the first (keypolicy) attributebased encryption (ABE) system with short secret keys: the size of keys in our system depends only on the depth of the policy circuit, not its size. Our constructions extend naturally to arithmetic circuits with arbitrary fanin gates thereby further redu ..."
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Cited by 19 (2 self)
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We construct the first (keypolicy) attributebased encryption (ABE) system with short secret keys: the size of keys in our system depends only on the depth of the policy circuit, not its size. Our constructions extend naturally to arithmetic circuits with arbitrary fanin gates thereby further
Compact Reusable Garbled Circuits
, 2014
"... Garbled circuits are integral to secure function evaluation. A garbled circuit C ̂ for a circuit C enables a user to compute C(x) and nothing more about C or x, when given an encoding x ̂ for the input x. Earlier, garbling schemes produced only singleuse garbled circuits which did not offer securit ..."
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could hope for. The main technical ingredient of our work is a “fully ” keyhomomorphic encryption scheme; an object that we define and construct based on learning with errors (LWE) assumption. A fully keyhomomorphic
How to Compress (Reusable) Garbled Circuits
, 2013
"... A fundamental question about (reusable) circuit garbling schemes is: how small can the garbled circuit be? Our main result is a reusable garbling scheme which produces garbled circuits that are the same size as the original circuit plus an additive poly(λ) bits, where λ is the security parameter. Sa ..."
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. Save the additive poly(λ) factor, this is the best one could hope for. In contrast, all previous constructions of even singleuse garbled circuits incurred a multiplicative poly(λ) blowup. Our techniques result in constructions of attributebased and (single key secure) functional encryption schemes
Partial Garbling Schemes and Their Applications
"... Abstract. Garbling schemes (aka randomized encodings of functions) represent a function F by a “simpler” randomized function F ̂ such that F ̂ (x) reveals F (x) and no additional information about x. Garbling schemes have found applications in many areas of cryptography. Motivated by the goal of imp ..."
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Cited by 3 (1 self)
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”. This notion considers garbling schemes in which part of the input is public, in the sense that it can be leaked by F ̂. – We present constructions of partial garbling schemes for (boolean and arithmetic) formulas and branching programs which take advantage of the public input to gain better efficiency. – We
Predicate encryption for circuits from LWE
, 2015
"... In predicate encryption, a ciphertext is associated with descriptive attribute values x in addition to a plaintext µ, and a secret key is associated with a predicate f. Decryption returns plaintext µ if and only if f(x) = 1. Moreover, security of predicate encryption guarantees that an adversary le ..."
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Cited by 3 (0 self)
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learns nothing about the attribute x or the plaintext µ from a ciphertext, given arbitrary many secret keys that are not authorized to decrypt the ciphertext individually. We construct a leveled predicate encryption scheme for all circuits, assuming the hardness of the subexponential learning with errors
Combinational Circuits
, 2000
"... Univ.ofTokushima,Japan 3. Design and Implementation of the Treelike Multiplier GiYong Song, JaeJin Lee, HoJun Lee, and HoJeong Song, Chungbuk Nat'l Univ., ..."
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Univ.ofTokushima,Japan 3. Design and Implementation of the Treelike Multiplier GiYong Song, JaeJin Lee, HoJun Lee, and HoJeong Song, Chungbuk Nat'l Univ.,
Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 221 (14 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, machine learning, control theory, and numerous other areas. The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic varieties is the central theme of computational algebraic geometry. Exciting recent developments in symbolic algebra and numerical software for geometric calculations have revolutionized the field, making formerly inaccessible problems tractable, and providing fertile ground for experimentation and conjecture. The first half of this book furnishes an introduction and represents a snapshot of the state of the art regarding systems of polynomial equations. Afficionados of the wellknown text books by Cox, Little, and O’Shea will find familiar themes in the first five chapters: polynomials in one variable, Gröbner
Algorithms for Sequential Decision Making
, 1996
"... Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of ..."
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Cited by 212 (8 self)
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Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one of a finite set of actions, "should" is maximize a longrun measure of reward, and "I" is an automated planning or learning system (agent). In particular,
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