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This paper describes a novel bit level stream cipher based symmetric key cryptographic technique. At first, sender and receiver agree upon a symmetric key. Then the symmetric key is formed using Greatest Common Divisor (G.C.D) of sum of…
Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum…
For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is…
There had been well known claims of ``provably unbreakable'' quantum protocols for bit commitment and coin tossing. However, we, and independently Mayers, showed that all proposed quantum bit commitment (and therefore coin tossing) schemes…
Large Language Models (LLMs) have been suggested for use in automated vulnerability repair, but benchmarks showing they can consistently identify security-related bugs are lacking. We thus develop SecLLMHolmes, a fully automated evaluation…
An exact formula \[ B(n) = \frac{n}{2}(\lfloor \lg n \rfloor + 1) - \sum _{k=0} ^{\lfloor \lg n \rfloor} 2^k Zigzag(\frac{n}{2^{k+1}}), \] where \[ Zigzag (x) = \min (x - \lfloor x \rfloor, \lceil x \rceil - x), \] for the minimal number $…
Ethereum represents new innovation in the fields of cryptocurrency which has become relatively stagnate, promising many things, including an entire programming language and development enviroment built into the network. However the current…
In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of…
Sumplete is a logic puzzle famous for being developed by ChatGPT. The puzzle consists of a rectangular grid, with each cell containing a number. The player has to cross out some numbers such that the sum of uncrossed numbers in each row and…
A peer-to-peer network, enabling different parties to jointly store and run computations on data while keeping the data completely private. Enigma's computational model is based on a highly optimized version of secure multi-party…
We deterministically crack the secure, statistical key exchange protocol based on feedback proposed by Pao-Lo Liu [ J. Lightwave Techology 27 (2009) pp. 5230-34]. The crack is ultimate and absolute because it works under idealized…
There had been well known claims of unconditionally secure quantum protocols for bit commitment. However, we, and independently Mayers, showed that all proposed quantum bit commitment schemes are, in principle, insecure because the sender,…
Cryptographic hash functions are fundamental primitives widely used in practice. For such a function $f:\{0, 1\}^n\to\{0, 1\}^m$, it is nearly impossible for an adversary to produce the hash $f(x)$ without knowing the secret message…
We study to what extent the Bitcoin blockchain security permanently depends on the underlying distribution of cryptocurrency market outcomes. We use daily blockchain and Bitcoin data for 2014-2019 and employ the ARDL approach. We test three…
Linear (or differential) cryptanalysis may seem dull topics for a mathematician: they are about super simple invariants characterized by say a word on n=64 bits with very few bits at 1, the space of possible attacks is small, and basic…
We consider random character values X(g) of the symmetric group on n symbols, where X is chosen at random from the set of irreducible characters and g is chosen at random from the group, and we show that X(g)=0 with probability tending to…
Collateral is an item of value serving as security for the repayment of a loan. In blockchain-based loans, cryptocurrencies serve as the collateral. The high volatility of cryptocurrencies implies a serious barrier of entry with a common…
In this paper, we provide the first comprehensive study of user-chosen 4- and 6-digit PINs (n=1220) collected on smartphones with participants being explicitly primed for device unlocking. We find that against a throttled attacker (with 10,…
Fixing bugs is easiest by patching source code. However, source code is not always available: only 0.3% of the ~49M smart contracts that are currently deployed on Ethereum have their source code publicly available. Moreover, since contracts…
Quadratic functions have applications in cryptography. In this paper, we investigate the modular quadratic equation $$ ax^2+bx+c=0 \quad (mod \,\, 2^n), $$ and provide a complete analysis of it. More precisely, we determine when this…