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Two algorithms for computing $P(n,m)$, the number of integer partitions of $n$ into exactly $m$ parts, are described, and using a combination of these two algorithms, the resulting algorithm is $O(n^{3/2})$. The second algorithm uses a list…
Consider n cards that are labeled 1 through n with n an even integer. The cards are put face down and their ordering starts with card labeled 1 on top through card labeled n at the bottom. The cards are top to random shuffled m times and…
Network slicing has emerged as an integral concept in 5G, aiming to partition the physical network infrastructure into isolated slices, customized for specific applications. We theoretically formulate the key performance metrics of an…
Coded computing has proved to be useful in distributed computing. We have observed that almost all coded computing systems studied so far consider a setup of one master and some workers. However, recently emerging technologies such as…
Secret sharing and multiparty computation (also called "secure function evaluation") are fundamental primitives in modern cryptography, allowing a group of mutually distrustful players to perform correct, distributed computations under the…
Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas…
Understanding how 5G networks correct errors is no trivial matter. At the heart of the process lie two sophisticated families of codes: LDPC and polar codes. This paper opens the black box, not only by explaining how these codes are…
Encrypted control systems allow to evaluate feedback laws on external servers without revealing private information about state and input data, the control law, or the plant. While there are a number of encrypted control schemes available…
An efficient quantum cryptography network protocol is proposed with d-dimension polarized photons, without resorting to entanglement and quantum memory. A server on the network, say Alice, provides the service for preparing and measuring…
This paper presents a novel graphical approach that counts the number of global 8-cycles on the SCRAM three-layer Tanner graph. SCRAM, which stands for Slotted Coded Random Access Multiplexing, is a joint decoder that is meets challenging…
Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the…
We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a…
I propose a new quantum key distribution protocol that uses the five qubit error correction code to detect the presence of eavesdropper reliably. The protocol turns any information theoretical attacks into a classical guess about the…
Threshold cryptography is a powerful and well-known technique with many applications to systems relying on distributed trust. It has recently emerged also as a solution to challenges in blockchain: frontrunning prevention, managing wallet…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our…
In this paper we present a new 5-pass identification scheme with asymptotic cheating probability 1/2 based on the syndrome decoding problem. Our protocol is related to the Stern identification scheme but has a reduced communication cost…
Polar codes have been selected as the channel coding scheme for control channel in the fifth generation (5G) communication system thanks to their capacity achieving characteristics. However, the traditional polar codes support only codes…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…