Karan Khathuria

Research Scientist Theoretical Cryptography

Quantinuum

About me

I am currently a research scientist at Quantinuum/Cambridge Quantum Computing, United Kingdoms.

Between March 2021 and December 2022, I was 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.

Research interests

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

Research projects

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"

Publications

Journal articles

H. Hollmann, K. Khathuria, A.-E. Riet, V. Skachek. On some batch code properties of the simplex code. Designs, Codes and Cryptography (2022) [Extended arXiv version arXiv:2110.07421]
E. Byrne, A.-L. Horlemann, K. Khathuria and V. Weger. Density of Free Modules over Finite Chain Rings. Linear Algebra and its Applications (2022), 651, 1-25, 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

Conference proceedings

J. Bariffi, K. Khathuria, V. Weger. Information Set Decoding for Lee-Metric Codes using Restricted Balls. Code-Based Cryptography CBCrypto 2022. Lecture Notes in Computer Science, vol 13839. Springer, Cham.(2022) arXiv:2205.12903
I. E. Bocharova, H. D. L. Hollmann, K. Khathuria, B. D. Kudryashov and V. Skachek. Coding with Cyclic PAM and Vector Quantization for the RLWE/MLWE Channel. 2022 IEEE International Symposium on Information Theory (ISIT), 2022, pp. 666-671.
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)

Preprints

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

Thesis

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).

Teaching

Teaching assitant and tutor

Fall 2022	Design and Analysis of Algorithms	Institute of Computer Science, University of Tartu
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

Talks

On some batch code properties of the simplex code. Neuchatel-St. Gallen-Zurich Seminar in Coding Theory, University of St. Gallen (November 16, 2022)
On some batch code properties of the simplex code. Invited talks at the Technical University of Munich (October 4, 2022)
Recent Advances in Decoding General Lee Metric Codes. International Symposium on Mathematical Theory of Networks and Systems (MTNS) 2022, University of Bayreuth (September 12, 2022)
Coding with cyclic PAM and vector quantization for the RLWE/MLWE channel. 2022 IEEE International Symposium on Information Theory (ISIT), Aalto University (June 27, 2022) [slides]
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]

Activities

Memberships

Conference Organization

Coding Theory and Cryptography: a conference in honor of Joachim Rosenthal's 60^th birthday, July 11-15, 2022
Algebraic Coding Theory (ACT) Summer School 2022, July 4-8, 2022
Algebraic Coding Theory (ACT) eSummer School 2021, June 7-11, 2021

Some Useful Resources

Programs

	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.

Contact Me

Email: karan(dot)khathuria(at)quantinuum.com