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Decision of whether a Boolean equation system has a solution is an NPC problem and finding a solution is NP hard. In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if…
The blockchain system has emerged as one of the focal points of research in recent years, particularly in applications and services such as cryptocurrencies and smart contracts. In this context, the hash value serves as a crucial element in…
As of July 15, 2023, Ethererum, which is a Proof-of-Stake (PoS) blockchain [1] has around 410 Billion USD in total assets on chain (popularly referred to as total-value-locked, TVL) but has only 33 Billion USD worth of ETH staked in…
In a Note in this Monthly, Klazar raised the question of whether the alternating sum of the Stirling numbers of the second kind $B^\pm(n)=\sum_{k=0}^n(-1)^kS(n,k)$ is ever zero for $n\neq 2$. In this article, we present an exposition of the…
The Bivariate Function Hard Problem (BFHP) has been in existence implicitly in almost all number theoretic based cryptosystems. This work defines the BFHP in a more general setting and produces an efficient asymmetric cryptosystem. The…
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires…
This paper reviews and highlights how coding schemes have been used to solve various problems in blockchain systems. Specifically, these problems relate to scaling blockchains in terms of their data storage, computation and communication…
This paper discloses a simple algorithm for encrypting text messages, based on the NP-completeness of the subset sum problem, such that the similarity between encryptions is roughly proportional to the semantic similarity between their…
BitVMX is a new design for a virtual CPU to optimistically execute arbitrary programs on Bitcoin based on a challenge response game introduced in BitVM. Similar to BitVM1 we create a general-purpose CPU to be verified in Bitcoin script. Our…
In a zero forcing process, vertices of a graph are colored black and white initially, and if there exists a black vertex adjacent to exactly one white vertex, then the white vertex is forced to be black. A zero blocking set is an initial…
Random access coding is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an $n$-bit string $x$, and wishes to encode $x$ into a quantum state…
We describe random processes (with binary alphabet) whose entropy is less than 1 (per letter), but they mimic true random process, i.e., by definition, generated sequence can be interpreted as the result of the flips of a fair coin with…
This paper focuses on finding the smallest happy number for each height in any numerical base. Using the properties of the height, we deduce a recursive relationship between the smallest happy number and the height where the initial height…
In cryptography, encryption is the process of obscuring information to make it unreadable without special knowledge. This is usually done for secrecy, and typically for confidential communications. Encryption can also be used for…
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these…
We study the setting in which the bits of an unknown infinite binary sequence x are revealed sequentially to an observer. We show that very limited assumptions about x allow one to make successful predictions about unseen bits of x. First,…
Code secrets are sensitive assets for software developers, and their leakage poses significant cybersecurity risks. While the rapid development of AI code assistants powered by Code Large Language Models (CLLMs), CLLMs are shown to…
This paper explores special arrangements of clues in $m \times n$ Numbrix puzzles. The maximum number of clues which fails to define an $m \times n$ puzzle is demonstrated for all $m$ and $n$. In addition, a small upper bound on the minimum…
Large language models (LLMs) are now widely used to draft and refactor code, but code that works is not necessarily secure. We evaluate secure code generation using the Instruct Prime, which eliminated compliance-required prompts and cue…
We review different classes of cryptocurrencies with emphasis on their economic properties. Pure-asset coins such as Bitcoin, Ethereum and Ripple are characterized by not being a liability of any economic agent and most resemble commodities…