40 citations · 81 across the 13 of their papers we have counts for
16 papers
Algorithms to Uniformly Generate Random Factored Smooth Integers
Eric Bach, Jonathan Sorenson
Let be integers. A positive integer is -smooth if all its prime divisors are at most . Let count the number of -smooth integers up to . We present s…
2-Designs and Redundant Syndrome Extraction for Quantum Error Correction
Vickram N. Premakumar, Hele Sha, Daniel Crow +2
Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this wo…
On Euclidean Methods for Cubic and Quartic Jacobi Symbols
Eric Bach, Bryce Sandlund
We study the bit complexity of two methods, related to the Euclidean algorithm, for computing cubic and quartic analogs of the Jacobi symbol. The main bottleneck in such procedures…
Submodular Goal Value of Boolean Functions
Eric Bach, Jeremie Dusart, Lisa Hellerstein +1
Recently, Deshpande et al. introduced a new measure of the complexity of a Boolean function. We call this measure the "goal value" of the function. The goal value of is defined…
Baby-Step Giant-Step Algorithms for the Symmetric Group
Eric Bach, Bryce Sandlund
We study discrete logarithms in the setting of group actions. Suppose that is a group that acts on a set . When , a solution to can be thought…
Infinitely Many Carmichael Numbers for a Modified Miller-Rabin Prime Test
Eric Bach, Rex Fernando
We define a variant of the Miller-Rabin primality test, which is in between Miller-Rabin and Fermat in terms of strength. We show that this test has infinitely many "Carmichael" nu…