Related papers: Improved Pseudorandom Generators for $\mathsf{AC}^…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these…
The pseudo-random number generators (PRNGs), sampling algorithms, and algorithms for generating random integers in some common statistical packages and programming languages are unnecessarily inaccurate, by an amount that may matter for…
This paper conducts a comparative study of three IoT-based PRNG models, including Logistic Map, Double Pendulum, and Multi-LFSR, implemented on an FPGA platform. Comparisons are made across key performance metrics like randomness, latency,…
We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of…
Pseudorandom codes (PRCs), introduced by Christ and Gunn (CRYPTO '2024), are error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings, while still being decodable by someone holding the key.…
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The…
Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that…
The objective of this project is to utilize an FPGA board which is the CMOD A7 35t to obtain a pseudo random number which can be used for encryption. We aim to achieve this by leveraging the inherent randomness present in environmental data…
We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided…
Statistical tests of pseudorandom number generators (PRNGs) are applicable to any type of random number generators and are indispensable for evaluation. While several practical packages for statistical tests of randomness exist, they may…
This paper focuses on the design and implementation of a high-quality and high-throughput true-random number generator (TRNG) in FPGA. Various practical issues which we encountered are highlighted and the influence of the various parameters…
In this work, we argue that the implications of Pseudo and Quantum Random Number Generators (PRNG and QRNG) inexplicably affect the performances and behaviours of various machine learning models that require a random input. These…
We analyze the trade-off between the undetected error probability (i.e., the probability that the channel decoder outputs an erroneous message without detecting the error) and the total error probability in the short blocklength regime. We…
Retrieval-augmented code generation utilizes Large Language Models as the generator and significantly expands their code generation capabilities by providing relevant code, documentation, and more via the retriever. The current approach…
We study the probabilistic degree over reals of the OR function on $n$ variables. For an error parameter $\epsilon$ in (0,1/3), the $\epsilon$-error probabilistic degree of any Boolean function $f$ over reals is the smallest non-negative…
A critical problem in the emerging high-throughput genotyping protocols is to minimize the number of polymerase chain reaction (PCR) primers required to amplify the single nucleotide polymorphism loci of interest. In this paper we study PCR…
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size $n^{O(1)}$ and treewidth $O(\log^i n)$ can be simulated by a…
Recently, Forbes, Kumar and Saptharishi [CCC, 2016] proved that there exists an explicit $d^{O(1)}$-variate and degree $d$ polynomial $P_{d}\in VNP$ such that if any depth four circuit $C$ of bounded formal degree $d$ which computes a…