Related papers: Attacking ApSimon's Mints
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
In this article we show for the first time that quantum coin flipping with security guarantees that are strictly better than any classical protocol is possible to implement with current technology. Our protocol takes into account all…
The remarkably long-standing problem of cryptography is to generate completely secure key. It is widely believed that the task cannot be achieved within classical cryptography. However, there is no proof in support of this belief. We…
The Change-Making Problem is to represent a given value with the fewest coins under a given coin system. As a variation of the knapsack problem, it is known to be NP-hard. Nevertheless, in most real money systems, the greedy algorithm…
Motivated by the recent 10 million dollar AIMO challenge, this paper targets the problem of finding all functions conforming to a given specification. This is a popular problem at mathematical competitions and it brings about a number of…
To solve tiling puzzles, such as "pentomino" or "tetromino" puzzles, we need to find the correct solutions out of numerous combinations of rotations or piece locations. Solving this kind of combinatorial optimization problem is a very…
Thompson sampling is one of the most popular learning algorithms for online sequential decision-making problems and has rich real-world applications. However, current Thompson sampling algorithms are limited by the assumption that the…
Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…
The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular…
A digital currency is money in a digital form. In this model, maintaining integrity of the supply is a core concern, therefore protections against double-spending are often at the heart of a secure digital money scheme. Quantum money…
The classic forgery attacks on COPA, AES-COPA and Marble authenticated encryption algorithms need to query about 2^(n/2) times, and their success probability is not high. To solve this problem, the corresponding quantum forgery attacks on…
Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit [Blu81]. Quantum information allows for protocols in the information theoretic setting where no…
In 1998, M. S. Baptista proposed a chaotic cryptosystem, which has attracted much attention from the chaotic cryptography community: some of its modifications and also attacks have been reported in recent years. In [Phys. Lett. A 307 (2003)…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
Deep learning models suffer from a phenomenon called adversarial attacks: we can apply minor changes to the model input to fool a classifier for a particular example. The literature mostly considers adversarial attacks on models with images…
The concept of quantum money (QM) was proposed by Wiesner in the 1970s. Its main advantage is that every attempt to copy QM unavoidably leads to imperfect counterfeits. In the Wiesner's protocol, quantum banknotes need to be delivered to…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
Cryptocurrencies have garnered a lot of attention by governments and internet enthusiasts over the past three years. These currencies are celebrated for their security and speedy transactions in a modern era of digital commerce. Bitcoin was…