9 citations · 29 across the 15 of their papers we have counts for
17 papers
Computing zeta functions of large polynomial systems over finite fields
Qi Cheng, J. Maurice Rojas, Daqing Wan
In this paper, we improve the algorithms of Lauder-Wan \cite{LW} and Harvey \cite{Ha} to compute the zeta function of a system of polynomial equations in variables over the…
On the ideal shortest vector problem over random rational primes
Yanbin Pan, Jun Xu, Nick Wadleigh +1
Any ideal in a number field can be factored into a product of prime ideals. In this paper we study the prime ideal shortest vector problem (SVP) in the ring …
Counting Roots of Polynomials Over Prime Power Rings
Qi Cheng, Shuhong Gao, J. Maurice Rojas +1
Suppose is a prime, is a positive integer, and is a univariate polynomial of degree with coefficients of absolute value . We show that f…
An Efficient Version of the Bombieri-Vaaler Lemma
Jun Zhang, Qi Cheng
In their celebrated paper "On Siegel's Lemma", Bombieri and Vaaler found an upper bound on the height of integer solutions of systems of linear Diophantine equations. Calculating t…
LWE from Non-commutative Group Rings
Qi Cheng, Jun Zhang, Jincheng Zhuang
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptograph…
Sparse Univariate Polynomials with Many Roots Over Finite Fields
Qi Cheng, Shuhong Gao, J. Maurice Rojas +1
Suppose is a prime power and is a univariate polynomial with exactly monomial terms and degree . To establish a finite field analogue of Descart…