Karan Khathuria

Postdoctoral researcher

Institute of Computer Science
University of Tartu

About me

I am currently a Postdoc researcher at the University of Tartu in the Coding and Information Transmission Group lead by Prof. Vitaly Skachek.

In the Fall 2020, I completed my Ph.D. in Mathematics under the supervision of Prof. Joachim Rosenthal at the University of Zurich.

Algebraic Cryptography, Coding Theory, Computational Algebra and Algorithms, Commutative Algebra.

March, 2021 - December, 2022: Research member of Estonian Research Council project PRG49 "Cryptogrpahic protocols and coding theory"
November, 2019 - October, 2020: Fellow of UZH Forschung Kredit PhD grant K-71110-02 "Algebraic Techniques in Cryptography"

E. Byrne, A.-L. Horlemann, K. Khathuria and V. Weger. Density of Free Modules over Finite Chain Rings. To appear in Linear Algebra and its Applications (2021) arXiv:2106.09403
V. Weger, K. Khathuria, A.-L. Horlemann, M. Battaglioni, P. Santini and E. Persichetti. On the Hardness of the Lee Syndrome Decoding Problem. Advances of Mathematics of Communications (2022) arXiv:2002.12785
N. Aragon, M. Baldi, J.-C. Deneuville, K. Khathuria, E. Persichetti, P. Santini Cryptanalysis of a code-based full-time signature. Designs, Codes and Cryptography (2021): 1-16. arXiv:2011.08326
G. N. Alfarano, K. Khathuria and V. Weger. A survey on single server private information retrieval in a coding theory perspective. Applicable Algebra in Engineering, Communication and Computing (2021): 1-24.
C. Interlando, K. Khathuria, N. Rohrer, J. Rosenthal, and V. Weger. Generalization of the Ball-Collision Algorithm. Journal of Algebra Combinatorics Discrete Structures and Applications (2020); 7(2): 195-207. arXiv:1812.10955
K. Khathuria, G. Micheli, and V. Weger. On the Algebraic Structure of E_p^(m) and Applications to Cryptography. Applicable Algebra in Engineering, Communication and Computing (2019): 1-11. arXiv:1810.02964
K. Khathuria, J. Rosenthal, and V. Weger. Encryption Scheme Based on Expanded Reed-Solomon Codes. Advances in Mathematics of Communications (2019) arXiv:1906.00745

K. Khathuria, J. Rosenthal, and V. Weger. Weight Two Masking of the Reed-Solomon Structure in Conjugation with List Decoding. Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems – MTNS, 2018.
J. Beana, D. Cabarcas, D. Escudero, K. Khathuria, and J. Verbel. Rank Analysis of Cubic Multivariate Cryptosystems. In: Post-Quantum Cryptography. PQCrypto 2018. Lecture Notes in Computer Science, vol 10786. Springer, Cham. (ePrint)

J. Bariffi, K. Khathuria, V. Weger. Information Set Decoding for Lee-Metric Codes using Restricted Balls. (2022) arXiv:2205.12903
H. Hollmann, K. Khathuria, A.-E. Riet, V. Skachek. On some batch code properties of the simplex code. (2021) arXiv:2110.07421
G. N. Alfarano, K. Khathuria and S. Tinani. On Cyclic Matroids and their Applications (2021) arXiv:2107.14214
K. Khathuria. Galois ring isomorphism problem. (2020) arXiv:2008.11927
M. Baldi, K. Khathuria, E. Persichetti and P. Santini. Cryptanalysis of a Code-Based Signature Scheme Based on the Lyubashevsky Framework. (2020) eprint:2020/905

K. Khathuria. Algebraic Study of Some Recent Asymmetric Cryptosystems. Ph.D. thesis at the University of Zurich under the supervision of Prof. Dr. J. Rosenthal.
K. Khathuria. Hilbert-Samuel Polynomial and Cowsik's Conjecture. Masters thesis at the Centre for Excellence in Basic Sciences under the supervision of Prof. Dr. J. K. Verma (IIT Bombay).

Spring 2022	Theoretical Computer Science	Institute of Computer Science, University of Tartu
Fall 2021	Design and Analysis of Algorithms	Institute of Computer Science, University of Tartu
Fall 2020	Programming	Faculty of Mathematics and Natural Sciences, University of Zurich
Spring 2020	Stochastics	Faculty of Mathematics and Natural Sciences, University of Zurich
Fall 2019	Cryptography	Institute of Mathematics, University of Zurich
Spring 2019	Coding theory	Institute of Mathematics, University of Zurich
Fall 2018	Algebra I	Institute of Mathematics, University of Zurich
Spring 2018	Elliptic Curves	Institute of Mathematics, University of Zurich
Fall 2017	Cryptography	Institute of Mathematics, University of Zurich
Spring 2017	Numerical Analysis I	Institute of Mathematics, University of Zurich

Cryptography, coding theory and the future. Graduate and Undergraduate Student Seminar (GAUSS), University of Iowa (April 22, 2021)
An overview of single-server private information retrieval in a coding theory perspective. eSeminar Discrete Mathematics, Codes and Cryptography, University of Paris 8 (February 11, 2021) [slides]
WHAT IS ... Private Information Retrieval? Zurich Graduate Colloquium, Zurich, Switzerland (December 8, 2020) [slides]
Rank analysis of Cubic Multivariate Cryptosystems. SIAM Conference on Applied Algebraic Geometry, Bern, Switzerland (July 9, 2019) [slides]
New McEliece cryptosystem using Reed-Solomon codes over an extension field. 7th Code-Based Cryptography Workshop, Darmstadt, Germany (May 18, 2019). [slides]
The two-dimensional and three-dimensional MinRank problem. CIMPA Research School and Workshop: Quasi-Cyclic and Related Algebraic Codes, METU, Ankara, Turkey (September 4, 2018) [slides]
Rank analysis of Cubic Multivariate Cryptosystems. Coding Theory and Cryptography Seminar, University of Neuchatel, Switzerland (May 9, 2018) [slides]
McEliece cryptosystem based on weight two masking of Reed-Solomon codes. 3rd International Conference on Applied Mathematics and Informatics, San Andrés, Colombia (December 1, 2017).[slides]

	Programs to compute the complexity of ISD algorithms in the Lee metric. For the descrption of the algorithms, refer to the paper On the Hardness of the Lee Syndrome Decoding Problem.
	MAGMA code for an attack on DHDP protocol over the ring E_p^m, used in the paper On the Algebraic Structure of E_p^(m) and Applications to Cryptography.

Institute for Computer Science, University of Tartu, 51009 Tartu, Estonia.

Email: karan(dot)khathuria(at)ut(dot)ee