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pro vyhledávání: '"Narayanan, Anand Kumar"'
Quantum imaginary-time evolution (QITE) is a promising tool to prepare thermal or ground states of Hamiltonians, as convergence is guaranteed when the evolved state overlaps with the ground state. However, its implementation using a parameterized qua
Externí odkaz:
http://arxiv.org/abs/2407.03123
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 fault-tolerant quantum computers. The Shortest Vector Problem (SVP) is to
Externí odkaz:
http://arxiv.org/abs/2309.16256
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 bounded by positive constants is called asymptotically good. Rate being c
Externí odkaz:
http://arxiv.org/abs/1909.07413
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 are identied with functions in certain Riemann-Roch spaces associated
Externí odkaz:
http://arxiv.org/abs/1712.10052
We present a novel randomized algorithm to factor polynomials over a finite field $\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomi
Externí odkaz:
http://arxiv.org/abs/1712.00669
The fastest known algorithm for factoring univariate polynomials over finite fields is the Kedlaya-Umans (fast modular composition) implementation of the Kaltofen-Shoup algorithm. It is randomized and takes $\widetilde{O}(n^{3/2}\log q + n \log^2 q)$
Externí odkaz:
http://arxiv.org/abs/1606.04592
Autor:
Narayanan, Anand Kumar
We present novel algorithms to factor polynomials over a finite field $\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial $f(x) \in
Externí odkaz:
http://arxiv.org/abs/1606.00898
Autor:
Narayanan, Anand Kumar
We propose a randomized algorithm to compute isomorphisms between finite fields using elliptic curves. To compute an isomorphism between two fields of cardinality $q^n$, our algorithm takes $$n^{1+o(1)} \log^{1+o(1)}q + \max_{\ell} \left(\ell^{n_\ell
Externí odkaz:
http://arxiv.org/abs/1604.03072
Publikováno v:
In Journal of Symbolic Computation July-August 2021 105:199-213
Autor:
Narayanan, Anand Kumar
We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank $2$ Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from Euler-Poincare cha
Externí odkaz:
http://arxiv.org/abs/1504.07697