Related papers: Deterministic Primality Testing - understanding th…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
Due to the superiority of quantum computing, traditional cryptography is facing severe threat. This makes the security evaluation of cryptographic systems in quantum attack models significant and urgent. For symmetric ciphers, the security…
Among notions of detectability for a discrete-event system (DES), strong detectability implies that after a finite number of observations to every output/label sequence generated by the DES, the current state can be uniquely determined.…
We survey the area of algebraic complexity theory; with the focus being on the problem of polynomial identity testing (PIT). We discuss the key ideas that have gone into the results of the last few years.
SIS problem has numerous applications in cryptography. Known algorithms for solving that problem are exponential in complexity. A new algorithm is suggested in this note, its complexity is sub-exponential for a range of parameters.
Two polynomials $f, g \in \mathbb{F}[x_1, \ldots, x_n]$ are called shift-equivalent if there exists a vector $(a_1, \ldots, a_n) \in \mathbb{F}^n$ such that the polynomial identity $f(x_1+a_1, \ldots, x_n+a_n) \equiv g(x_1,\ldots,x_n)$…
We investigate the security assumptions behind three public-key quantum money schemes. Aaronson and Christiano proposed a scheme based on hidden subspaces of the vector space $\mathbb{F}_2^n$ in 2012. It was conjectured by Pena et al in…
The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…
We define a variant of k-of-n testing that we call conservative k-of-n testing. We present a polynomial-time, combinatorial algorithm for the problem of maximizing throughput of conservative k-of-n testing, in a parallel setting. This…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension…
We show that Reed-Solomon codes of dimension $k$ and block length $n$ over any finite field $\mathbb{F}$ can be deterministically list decoded from agreement $\sqrt{(k-1)n}$ in time $\text{poly}(n, \log |\mathbb{F}|)$. Prior to this work,…
In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard's $p-1$ algorithm, which finds in random polynomial time the prime…
The development of large quantum computers will have dire consequences for cryptography. Most of the symmetric and asymmetric cryptographic algorithms are vulnerable to quantum algorithms. Grover's search algorithm gives a square root time…
The Permuted Kernel Problem (PKP) asks to find a permutation of a given vector belonging to the kernel of a given matrix. The PKP is at the basis of PKP-DSS, a post-quantum signature scheme deriving from the identification scheme proposed…
We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…
We develop an algebraic framework over arbitrary quadratic fields $L = \mathbb{Q}(\sqrt{D})$ to generalize the Miller-Rabin primality test. Consequently, we present a deterministic primality test for integers of the form $N = K p^{\ell} -…
Solving random subset sum instances plays an important role in constructing cryptographic systems. For the random subset sum problem, in 2013 Bernstein et al. proposed a quantum algorithm with heuristic time complexity…
In this paper, we introduce two primality tests based on new divisibility properties of binomial coefficients. These new properties were enunciated and proved in previous work. We also study two similar tests that can be obtained from…