• Publications
  • Influence
Diversification improves interpolation
TLDR
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers, and provide the first provably stable algorithm (in the sense of relative error) for this problem. Expand
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Faster sparse multivariate polynomial interpolation of straight-line programs
TLDR
We present a new algorithm for interpolating a sparse multivariate polynomial F over Fq, the finite field of size q. Expand
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A Practical Oblivious Map Data Structure with Secure Deletion and History Independence
TLDR
We present a new oblivious RAM that supports variable-sized storage blocks (vORAM), which is the first ORAM to allow varying block sizes without trivial padding. Expand
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Faster Sparse Interpolation of Straight-Line Programs
TLDR
We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program, using probes of smaller degree than in previous methods. Expand
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Deterministic, Stash-Free Write-Only ORAM
TLDR
Write-Only Oblivious RAM (WoORAM) protocols provide privacy by encrypting the contents of data and also hiding the pattern of write operations over that data. Expand
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POPE: Partial Order Preserving Encoding
TLDR
We propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Expand
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Multivariate sparse interpolation using randomized Kronecker substitutions
  • Andrew Arnold, Daniel S. Roche
  • Mathematics, Computer Science
  • ISSAC
  • 26 January 2014
TLDR
We present new techniques for reducing a multivariate sparse polynomial to a univariate poyleomial. Expand
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Sparse interpolation over finite fields via low-order roots of unity
TLDR
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial f over an arbitrary finite field of size q. Expand
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Space- and time-efficient polynomial multiplication
TLDR
A new routine based on the Karatsuba/Ofman algorithm is presented with the same time complexity of <i>O</i>(<i>n</i><sup>1.59</sup>) but only <i>[log < i>N</i>) extra space for the computation. Expand
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Output-Sensitive Algorithms for Sumset and Sparse Polynomial Multiplication
  • Andrew Arnold, Daniel S. Roche
  • Mathematics, Computer Science
  • ISSAC '15
  • 20 January 2015
TLDR
We present randomized algorithms to compute the sumset (Minkowski sum) of two integer sets, and to multiply two univariate integer polynomials given by sparse representations. Expand
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