Related papers: Generating Hard Ising Instances With Planted Solut…

Private and public actors increasingly encounter use cases where they need to implement sensitive operations on mass-market peripherals for which they have little or no control. They are sometimes inclined to attempt this without using…

We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…

McEliece cryptosystem represents a smart open key system based on the hardness of the decoding of an arbitrary linear code, which is believed to be able to resist the advent of quantum computers. But the original McEliece cryptosystem,…

By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…

The NP-hard problem of decoding random linear codes is crucial to both coding theory and cryptography. In particular, this problem underpins the security of many code based post-quantum cryptographic schemes. The state-of-art algorithms for…

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been…

We propose an algorithm of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). The algorithm transforms instances of the integer factorization problem into SAT instances efficiently by using the Chinese…

When creating benchmarks for SAT solvers, we need SAT instances that are easy to build but hard to solve. A recent development in the search for such methods has led to the Balanced SAT algorithm, which can create k-SAT instances with m…

Due to the weakness of public key cryptosystems encounter of quantum computers, the need to provide a solution was emerged. The McEliece cryptosystem and its security equivalent, the Niederreiter cryptosystem, which are based on Goppa…

The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…

We will construct post-quantum encryption algorithms based on three-variable polynomial Beal-Schur congruence. After giving a proof of Beal's conjecture and citing some applications of it to selected cases where the discrete logarithm and…

In recent years, there have been many studies on quantum computing and the construction of quantum computers which are capable of breaking conventional number theory-based public key cryptosystems. Therefore, in the not-too-distant future,…

We study algorithms in the distributed message-passing model that produce secured output, for an input graph $G$. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the…

We present a security proof for establishing private entanglement by means of recurrence-type entanglement distillation protocols over noisy quantum channels. We consider protocols where the local devices are imperfect, and show that…

This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying…

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private…

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…

We present a way to create small yet difficult model counting instances. Our generator is highly parameterizable: the number of variables of the instances it produces, as well as their number of clauses and the number of literals in each…

While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…

We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing…