arXiv subjects

Hrishi Narayanan

Publications and source records attributed to Hrishi Narayanan.

4 recordsLinked to original sources

arXiv2026

A Security Framework for Chemical Functions

In this paper, we provide a unified security framework with the goal of being able to evaluate and compare different (known and new) approaches for authentication and encryption using, for example, DNA-based schemes. Therefore, we introduce and rigorously define chemical functions which model chemical systems as noisy challenge--response primitives, and formalize the associated chemical function infrastructure. Building on the theory of physical functions, we rigorously define robustness, unclonability, and unpredictability for chemical functions in both finite and asymptotic regimes, and specify security games that capture the adversary's power and the security goals. We instantiate the framework with the data from two existing DNA-based constructions ("operable random DNA" and "Genomic Sequence Encryption") and derive quantitative bounds for robustness, unclonability, and unpredictability. These results place DNA-based chemical functions on a rigorous cryptographic footing, enabling principled design and comparison of chemically grounded authentication mechanisms. We demonstrate applications to in-product authentication and to shared key generation using standard extraction techniques, showing the significance of this work regarding real-world applications.

cs.CR↗

arXiv2026

Coding Schemes for Document Exchange under Multiple Substring Edits

We study the document exchange problem under multiple substring edits. A substring edit in a string $\mathbf{x}$ occurs when a substring $\mathbf{u}$ of $\mathbf{x}$ is replaced by an arbitrary string $\mathbf{v}$. The lengths of $\mathbf{u}$ and $\mathbf{v}$ are bounded from above by a fixed constant. Let $\mathbf{x}$ and $\mathbf{y}$ be two binary strings that differ by multiple substring edits. The aim of document exchange schemes is to construct an encoding of $\mathbf{x}$ with small length such that $\mathbf{x}$ can be recovered using $\mathbf{y}$ and the encoding. We construct a low-complexity document exchange scheme with encoding length of $4t\log n+o(\log n)$ bits, where $n$ is the length of the string $\mathbf{x}$. The best known scheme achieves an encoding length of $4t \log n+O(\log\log n)$ bits, but at a much higher computational complexity. Then, we investigate the average length of valid encodings for document exchange schemes with uniform strings $\mathbf{x}$ and develop a scheme with an expected encoding length of $(4t-1) \log n+o(\log n)$ bits. In this setting, prior works have only constructed schemes for a single substring edit.

cs.IT↗

arXiv2025

A Converse For the Capacity of the Shotgun Sequencing Channel with Erasures

The shotgun sequencing process involves fragmenting a long DNA sequence (input string) into numerous shorter, unordered, and overlapping segments (referred to as \emph{reads}). The reads are sequenced, and later aligned to reconstruct the original string. Viewing the sequencing process as the read-phase of a DNA storage system, the information-theoretic capacity of noise-free shotgun sequencing has been characterized in literature. Motivated by the base-wise quality scores available in practical sequencers, a recent work considered the \emph{shotgun sequencing channel with erasures}, in which the symbols in the reads are assumed to contain random erasures. Achievable rates for this channel were identified. In the present work, we obtain a converse for this channel. The arguments for the proof involve a careful analysis of a genie-aided decoder, which knows the correct locations of the reads. The converse is not tight in general. However, it meets the achievability result asymptotically in some channel parameters.

cs.IT↗

arXiv2024

On Achievable Rates for the Shotgun Sequencing Channel with Erasures

In shotgun sequencing, the input string (typically, a long DNA sequence composed of nucleotide bases) is sequenced as multiple overlapping fragments of much shorter lengths (called \textit{reads}). Modelling the shotgun sequencing pipeline as a communication channel for DNA data storage, the capacity of this channel was identified in a recent work, assuming that the reads themselves are noiseless substrings of the original sequence. Modern shotgun sequencers however also output quality scores for each base read, indicating the confidence in its identification. Bases with low quality scores can be considered to be erased. Motivated by this, we consider the \textit{shotgun sequencing channel with erasures}, where each symbol in any read can be independently erased with some probability $δ$. We identify achievable rates for this channel, using a random code construction and a decoder that uses typicality-like arguments to merge the reads.

cs.IT↗