3 citations · 5 across the 9 of their papers we have counts for
14 papers
Arithmetic circuit lower bounds from sumset expansion
Anand Kumar Narayanan
Raz proposed a program to prove arithmetic circuit lower bounds through the explicit construction of elusive functions. These are polynomial maps from a low dimensional space to a…
Finding dense sub-lattices as low-energy states of a Hamiltonian
Júlia Barberà-Rodríguez, Nicolas Gama, Anand Kumar Narayanan +1
Lattice-based cryptography has emerged as one of the most prominent candidates for post-quantum cryptography, projected to be secure against the imminent threat of large-scale faul…
On Decoding Cohen-Haeupler-Schulman Tree Codes
Anand Kumar Narayanan, Matthew Weidner
Tree codes, introduced by Schulman, are combinatorial structures essential to coding for interactive communication. An infinite family of tree codes with both rate and distance bou…
Subquadratic time encodable codes beating the Gilbert-Varshamov bound
Anand Kumar Narayanan, Matthew Weidner
We construct explicit algebraic geometry codes built from the Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for alphabet sizes at least 192. Messages…
Drinfeld Modules with Complex Multiplication, Hasse Invariants and Factoring Polynomials over Finite Fields
Javad Doliskani, Anand Kumar Narayanan, Éric Schost
We present a novel randomized algorithm to factor polynomials over a finite field $\F_q$ of odd characteristic using rank Drinfeld modules with complex multiplication. The main…
Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields
Zeyu Guo, Anand Kumar Narayanan, Chris Umans
The fastest known algorithm for factoring univariate polynomials over finite fields is the Kedlaya-Umans (fast modular composition) implementation of the Kaltofen-Shoup algorithm.…