arXiv subjects

Srinivasan Krishnaswamy

Publications and source records attributed to Srinivasan Krishnaswamy.

13 recordsLinked to original sources

arXiv2025

A symmetric LWE-based Multi-Recipient Cryptosystem

This article describes a post-quantum multirecipient symmetric cryptosystem whose security is based on the hardness of the LWE problem. In this scheme a single sender encrypts multiple messages for multiple recipients generating a single ciphertext which is broadcast to the recipients. Each recipient decrypts the ciphertext with her secret key to recover the message intended for her. In this process, the recipient cannot efficiently extract any information about the other messages. This scheme is intended for messages like images and sound that can tolerate a small amount of noise. This article introduces the scheme and establishes its security based on the LWE problem. Further, an example is given to demonstrate the application of this scheme for encrypting multiple images.

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arXiv2024

An iterative scheme for finite horizon model reduction of continuous-time linear time-varying systems

In this paper, we obtain the functional derivatives of a finite horizon error norm between a full-order and a reduced-order continuous-time linear time-varying (LTV) system. Based on the functional derivatives, first-order necessary conditions for optimality of the error norm are derived, and a projection-based iterative scheme for model reduction is proposed. The iterative scheme upon convergence produces reduced-order models satisfying the optimality conditions. Finally, through a numerical example, we demonstrate the better performance of the proposed model reduction scheme in comparison to the finite horizon balanced truncation algorithm for continuous-time LTV systems.

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arXiv2024

Information Security and Privacy in the Digital World: Some Selected Topics

In the era of generative artificial intelligence and the Internet of Things, while there is explosive growth in the volume of data and the associated need for processing, analysis, and storage, several new challenges are faced in identifying spurious and fake information and protecting the privacy of sensitive data. This has led to an increasing demand for more robust and resilient schemes for authentication, integrity protection, encryption, non-repudiation, and privacy-preservation of data. The chapters in this book present some of the state-of-the-art research works in the field of cryptography and security in computing and communications.

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arXiv2023

A Scheme to resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher

In LFSR-based stream ciphers, the knowledge of the feedback equation of the LFSR plays a critical role in most attacks. In word-based stream ciphers such as those in the SNOW series, even if the feedback configuration is hidden, knowing the characteristic polynomial of the state transition matrix of the LFSR enables the attacker to create a feedback equation over $GF(2)$. This, in turn, can be used to launch fast correlation attacks. In this work, we propose a method for hiding both the feedback equation of a word-based LFSR and the characteristic polynomial of the state transition matrix. Here, we employ a $z$-primitive $σ$-LFSR whose characteristic polynomial is randomly sampled from the distribution of primitive polynomials over $GF(2)$ of the appropriate degree. We propose an algorithm for locating $z$-primitive $σ$-LFSR configurations of a given degree. Further, an invertible matrix is generated from the key. This is then employed to generate a public parameter which is used to retrieve the feedback configuration using the key. If the key size is $n$- bits, the process of retrieving the feedback equation from the public parameter has a average time complexity $\mathbb{O}(2^{n-1})$. The proposed method has been tested on SNOW 2.0 and SNOW 3G for resistance to fast correlation attacks. We have demonstrated that the security of SNOW 2.0 and SNOW 3G increases from 128 bits to 256 bits.

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arXiv2022

H$_2$ Optimal Model Order Reduction over a Finite Time Interval

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method involves obtaining a reduced model which minimizes the time-limited H$_2$ norm, formulated as a nonlinear optimization problem. The optimization problem is solved using standard optimization software.

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arXiv2021

Near Optimal Interpolation based Time-Limited Model Order Reduction

This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time intervals of the form, $\begin{bmatrix}0 & τ\end{bmatrix}$ with $τ< \infty$ for linear time invariant (LTI) systems. Using the time limited $H_2$ norm, we derive interpolation based $H_{2,τ}$ optimality conditions. The LT-IRKA yields a near optimal $H_2(τ)$ reduced order system. The nearness to the exact $H_2(τ)$ optimal reduced system is quantized in terms of the errors in the interpolation based $H_2(τ)$ optimality conditions. We demonstrate with numerical examples how the proposed algorithm nearly satisfies the time-limited optimality conditions and also how it performs with respect to the Time-Limited Two sided Iteration Algorithm (TL-TSIA), the Time-Limited Balanced Truncation (TL-BT), the Iterative Rational Krylov Algorithm (IRKA) and the Time-Limited Pseudo Optimal Rational Krylov (TL-PORK) Algorithm over a finite time interval.

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arXiv2021

The application of $σ$-LFSR in Key-Dependent Feedback Configuration for Word-Oriented Stream Ciphers

In this paper, we propose and evaluate a method for generating key-dependent feedback configurations (KDFC) for $σ$-LFSRs. $σ$-LFSRs with such configurations can be applied to any stream cipher that uses a word-based LFSR. Here, a configuration generation algorithm uses the secret key(K) and the initialization vector (IV) to generate a feedback configuration. We have mathematically analysed the feedback configurations generated by this method. As a test case, we have applied this method on SNOW 2.0 and have studied its impact on resistance to various attacks. Further, we have also tested the generated keystream for randomness and have briefly described its implementation and the challenges involved in the same.

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arXiv2020

On Passivity, Feedback Passivity, And Feedback Passivity Over Erasure Network: A Piecewise Affine Approximation Approach

In this paper, we deal with the problem of passivity and feedback passification of smooth discrete-time nonlinear systems by considering their piecewise affine approximations. Sufficient conditions are derived for passivity and feedback passivity. These results are then extended to systems that operate over Gilbert-Elliott type communication channels. As a special case, results for feedback passivity of piecewise affine systems over a lossy channel are also derived.

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arXiv2020

Fully Homomorphic Encryption based on Multivariate Polynomial Evaluation

We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the scheme uses a polynomial based technique that does not require relinearization (and key switching). The noise associated with the ciphertext increases only linearly with every multiplication.

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arXiv2019

$H_{\infty}$ Optimal Control of Jump Systems Over Multiple Lossy Communication Channels

In this paper, we consider the $H_{\infty}$ optimal control problem for a Markovian jump linear system (MJLS) over a lossy communication network. It is assumed that the controller communicates with each actuator through a different communication channel. We solve the $H_{\infty}$ optimization problem for a Transmission Control Protocol (TCP) using the theory of dynamic games and obtain a state-feedback controller. The infinite horizon $H_{\infty}$ optimization problem is analyzed as a limiting case of the finite horizon optimization problem. Then, we obtain the corresponding state-feedback controller, and show that it stabilizes the closed-loop system in the face of random packet dropouts.

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arXiv2019

A Somewhat Homomorphic Encryption Scheme based on Multivariate Polynomial Evaluation

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a generalization of the Learning with Errors problem called the Hidden Subspace Membership problem and show that the semantic security of the proposed scheme can be reduced to the hardness of this problem.

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arXiv2018

Analysis of Statistical Properties of Nonlinear Feedforward Generators Over Finite Fields

Due to their simple construction, LFSRs are commonly used as building blocks in various random number generators. Nonlinear feedforward logic is incorporated in LFSRs to increase the linear complexity of the generated sequence. In this work, we extend the idea of nonlinear feedforward logic to LFSRs over arbitrary finite fields and analyze the statistical properties of the generated sequences. Further, we propose a method of applying nonlinear feedforward logic to word-based σ-LFSRs and show that the proposed scheme generates vector sequences that are statistically more balanced than those generated by an existing scheme.

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arXiv2012

On Multisequences and their extensions

In this paper we deal with the dimension of multisequences and related properties. For a given multisequence W and an m tuple of positive integers R, we define the R extension of W. Further we count the number of multisequences W whose R extensions have maximum dimension and give an algorithm to derive such multisequences. We then go on to use this theory to count the number of Linear Feedback Shift Register(LFSR) configurations with multi input multi output delay blocks for any given primitive characteristic polynomial and also to design such LFSRs. Further, we use the result on multisequences to count the number of Hankel matrices of any given dimension.

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