I
am Anand Kumar Narayanan, a post doctoral researcher at the Computing and Mathematical Sciences Department, California Institute of Technology

working under the
advisement of Prof Chris Umans. I obtained my Ph.D in computer science at the University of Southern California under Prof. Ming-Deh Huang

My research interests
include Algebraic Function Fields, Algorithmic Number Theory,
Arithmetic Algebraic Geometry and their applications in Cryptography,
Coding Theory and Theoretical Computer Science.

Teaching :

In Fall 2016, I will be teaching

CS 101 : Number theoretic methods in cryptography

The objective of the course is to study computational number theoretic methods with an emphasis on applications in cryptography. Topics will include classical algorithms for factoring integers, like the number field sieve and Lenstra's elliptic curve factorization; and exciting recent developments including pseudo polynomial time algorithms for discrete logarithms in small characteristic finite fields, Diem's algorithm for the elliptic curve discrete logarithm problem and regularity assumptions in Grobner basis methods for finding zeroes of elliptic curve summation polynomials. Further applications in lattice based cryptography, coding theory and quantum computation will also be covered.
Schedule, grading policies and assignments can be found at the course website

Papers

Anand Kumar Narayanan, Factoring Polynomials over Finite Fields using Drinfeld Modules with Complex Multiplication, Presented at Milestones in Computer Algebra MICA 2016, To appear in the Journal of Symbolic Computation, Available at http://arxiv.org/abs/1606.00898

Anand Kumar Narayanan, Fast Computation of Isomorphisms between Finite Fields using Elliptic Curves, In submission, Available at http://arxiv.org/abs/1604.03072

Zeyu Guo, Anand Kumar Narayanan and Chris Umans, Algebraic Problems equivalent to beating the 3/2 exponent in Polynomial Factorization over Finite Fields, MFCS Mathematical Foundations of Computer Science 2016, Available at http://arxiv.org/abs/1606.04592

Anand Kumar Narayanan, Polynomial Factorization over Finite Fields by Computing Euler-Poincare Characteristics of Drinfeld Modules, Available at http://arxiv.org/abs/1504.07697

Ming-Deh Huang and Anand Kumar Narayanan, Computing Discrete Logarithms in Subfields of Residue Class Rings, Available at http://arxiv.org/abs/1402.6658

Ming-Deh Huang and Anand Kumar Narayanan, On the relation generation method of Joux for computing discrete logarithms, Available at http://arxiv.org/abs/1312.1674

Ming-Deh Huang and Anand Kumar Narayanan, Computing class groups of function fields using Stark units, Proc. 11th Int'l Conf. on Finite Fields and their Applications (Fq11), AMS Contemporary Mathematics Series. Available at http://arxiv.org/abs/1311.0560

Ming-Deh Huang and Anand Kumar Narayanan, Finding Primitive Elements in Finite Fields of Small Characteristic, Proc. 11th Int'l Conf. on Finite Fields and their Applications (Fq11), AMS Contemporary Mathematics Series. Available at http://arxiv.org/abs/1304.1206

Ming-Deh Huang and Anand Kumar Narayanan, Folded Algebraic Geometric Codes From Galois Extensions, Proc. 9th Int'l Conf. on Finite Fields and their Applications (Fq9), AMS Contemporary Mathematics Series, ed. by G. Mullen. 2010. Available at http://arxiv.org/abs/0901.1162

Giuseppe Caire, Tareq Al Naffouri and Anand Kumar Narayanan, Impulse noise cancellation in OFDM: an application of compressed sensing. IEEE International Symposium on Information Theory 2008. Available at http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4595196

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