Vikraman Arvind, K.V. Subrahmanyam, N. V. Vinodchandran

In this paper we study program checking (in the

sense of Blum and Kannan) using constant-depth circuits as

checkers. Our focus is on the number of queries made by the

checker to the program being checked and we term this as the

query complexity of the checker for the given ...
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Benny Applebaum, Yuval Ishai, Eyal Kushilevitz

Yao's garbled circuit construction transforms a boolean circuit $C:\{0,1\}^n\to\{0,1\}^m$

into a ``garbled circuit'' $\hat{C}$ along with $n$ pairs of $k$-bit keys, one for each

input bit, such that $\hat{C}$ together with the $n$ keys

corresponding to an input $x$ reveal $C(x)$ and no additional information about $x$.

The garbled circuit ...
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Pranjal Dutta, Nitin Saxena, Amit Sinhababu

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the ... more >>>

Ashish Dwivedi, Rajat Mittal, Nitin Saxena

Polynomial factoring has famous practical algorithms over fields-- finite, rational \& $p$-adic. However, modulo prime powers it gets hard as there is non-unique factorization and a combinatorial blowup ensues. For example, $x^2+p \bmod p^2$ is irreducible, but $x^2+px \bmod p^2$ has exponentially many factors! We present the first randomized poly($\deg ... more >>>