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We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements,…
Complex machine learning (ML) inference algorithms like recurrent neural networks (RNNs) use standard functions from math libraries like exponentiation, sigmoid, tanh, and reciprocal of square root. Although prior work on secure 2-party…
We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method of majorants, and simple results from analytic combinatorics. We illustrate the power of…
This paper proposes a Fast Graph Convolutional Neural Network (FGRNN) architecture to predict sequences with an underlying graph structure. The proposed architecture addresses the limitations of the standard recurrent neural network (RNN),…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure…
Subgraph matching is a fundamental problem in various fields that use graph structured data. Subgraph matching algorithms enumerate all isomorphic embeddings of a query graph q in a data graph G. An important branch of matching algorithms…
In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
Regenerating codes are a class of codes for distributed storage networks that provide reliability and availability of data, and also perform efficient node repair. Another important aspect of a distributed storage network is its security.…
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital documents. In the post-quantum era, classical public key-based signature schemes become vulnerable to brute-force and…
The sequences produced by the cryptographic sequence generator known as the shrinking generator can be modelled as the output sequences of linear elementary cellular automata. These sequences are composed of interleaved m-sequences produced…
The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic…
Research in logic encryption over the last decade has resulted in various techniques to prevent different security threats such as Trojan insertion, intellectual property leakage, and reverse engineering. However, there is little agreement…
Perron-Frobenius theory developed for irreducible non-negative kernels deals with so-called $R$-positive recurrent kernels. If kernel $M$ is $R$-positive recurrent, then the main result determines the limit of the scaled kernel iterations…
In this letter, as a proof of concept, we propose a deep learning-based approach to attack the chaos-based image encryption algorithm in \cite{guan2005chaos}. The proposed method first projects the chaos-based encrypted images into the…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for both unique string…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…