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Shielding circuits with groups
, 2012
"... We show how to efficiently compile any given circuit C into a leakageresistant circuit Ĉ such that any function on the wires of Ĉ that leaks information during a computation Ĉ(x) yields advantage in computing the product of ĈΩ(1) elements of the alternating group Au. In combination with new compr ..."
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We show how to efficiently compile any given circuit C into a leakageresistant circuit Ĉ such that any function on the wires of Ĉ that leaks information during a computation Ĉ(x) yields advantage in computing the product of ĈΩ(1) elements of the alternating group Au. In combination with new compression bounds for Au products, also obtained here, Ĉ withstands leakage from virtually any class of functions against which averagecase lower bounds are known. This includes communication protocols, and AC 0 circuits augmented with few arbitrary symmetric gates. If NC 1 = TC 0 then the construction resists TC 0 leakage as well. We also conjecture that our construction resists NC 1 leakage. In addition, we extend the construction to the multiquery setting by relying on a simple secure hardware component. We build on Barrington’s theorem [JCSS ’89] and on the previous leakageresistant constructions by Ishai et al. [Crypto ’03] and Faust et al. [Eurocrypt ’10]. Our construction exploits properties of Au beyond what is sufficient for Barrington’s theorem.
New Surprises from SelfReducibility
"... Abstract. Selfreducibility continues to give us new angles on attacking some of the fundamental questions about computation and complexity. 1 ..."
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Abstract. Selfreducibility continues to give us new angles on attacking some of the fundamental questions about computation and complexity. 1
On Circuit Complexity Classes and Iterated Matrix Multiplication
, 2012
"... In this thesis, we study small, yet important, circuit complexity classes within NC¹, such as ACC⁰ and TC⁰00 0. We also investigate the power of a closely related problem called Iterated Matrix Multiplication and its implications in low levels of algebraic complexity theory. More concretely, • We sh ..."
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In this thesis, we study small, yet important, circuit complexity classes within NC¹, such as ACC⁰ and TC⁰00 0. We also investigate the power of a closely related problem called Iterated Matrix Multiplication and its implications in low levels of algebraic complexity theory. More concretely, • We show that extremely modestsounding lower bounds for certain problems can lead to nontrivial derandomization results. – If the word problem over S5 requires constantdepth threshold circuits of size n1+ɛ for some ɛ> 0, then any language accepted by uniform polynomialsize probabilistic threshold circuits can be solved in subexponential time (and more strongly, can be accepted by a uniform family of deterministic constantdepth threshold circuits of subexponential size.) – If there are no constantdepth arithmetic circuits of size n1+ɛ for the problem of multiplying a sequence of n 3by3 matrices, then for every constant d, blackbox identity testing for depthd arithmetic circuits with bounded individual degree can be performed in subexponential time (and even by a uniform family of deterministic constantdepth AC circuits of subexponential size).