Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Khathuria, Karan"'
The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternat
Externí odkaz:
http://arxiv.org/abs/2205.12903
The binary $k$-dimensional simplex code is known to be a $2^{k-1}$-batch code and is conjectured to be a $2^{k-1}$-functional batch code. Here, we offer a simple, constructive proof of a result that is "in between" these two properties. Our approach
Externí odkaz:
http://arxiv.org/abs/2110.07421
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely related with many other topics in discrete mathematics, such as graphs
Externí odkaz:
http://arxiv.org/abs/2107.14214
In this paper we focus on modules over a finite chain ring $\mathcal{R}$ of size $q^s$. We compute the density of free modules of $\mathcal{R}^n$, where we separately treat the asymptotics in $n,q$ and $s$. In particular, we focus on two cases: one w
Externí odkaz:
http://arxiv.org/abs/2106.09403
Autor:
Aragon, Nicolas, Baldi, Marco, Deneuville, Jean-Christophe, Khathuria, Karan, Persichetti, Edoardo, Santini, Paolo
We present an attack against a code-based signature scheme based on the Lyubashevsky protocol that was recently proposed by Song, Huang, Mu, Wu and Wang (SHMWW). The private key in the SHMWW scheme contains columns coming in part from an identity mat
Externí odkaz:
http://arxiv.org/abs/2011.08326
Autor:
Khathuria, Karan
Recently, Dor\"oz et al. (2017) proposed a new hard problem, called the finite field isomorphism problem, and constructed a fully homomorphic encryption scheme based on this problem. In this paper, we generalize the problem to the case of Galois ring
Externí odkaz:
http://arxiv.org/abs/2008.11927
In this paper, we present a new perspective of single server private information retrieval (PIR) schemes by using the notion of linear error-correcting codes. Many of the known single server schemes are based on taking linear combinations between dat
Externí odkaz:
http://arxiv.org/abs/2008.06417
Autor:
Weger, Violetta, Khathuria, Karan, Horlemann, Anna-Lena, Battaglioni, Massimo, Santini, Paolo, Persichetti, Edoardo
In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the $3$-dimensional matching problem. Th
Externí odkaz:
http://arxiv.org/abs/2002.12785
We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides
Externí odkaz:
http://arxiv.org/abs/1906.00745
In this paper we generalize the Ball-Collision Algorithm by Bernstein, Lange, Peters from the binary field to a general finite field. We also provide a complexity analysis and compare the asymptotic complexity to other generalized information set dec
Externí odkaz:
http://arxiv.org/abs/1812.10955