Related papers: Some Mathematical Problems Behind Lattice-Based Cr…
Lattices are very important objects in the effort to construct cryptographic primitives that are secure against quantum attacks. A central problem in the study of lattices is that of finding the shortest non-zero vector in the lattice.…
Technological advancements of Blockchain and other Distributed Ledger Techniques (DLTs) promise to provide significant advantages to applications seeking transparency, redundancy, and accountability. Actual adoption of these emerging…
The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor's work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical…
Recent advances in quantum computing pose a serious threat on the security of widely used public-key cryptosystems. Thus, new post-quantum cryptographic algorithms have been proposed as part of the associated US NIST process to enable…
The implications of sufficiently large quantum computers for widely used public-key cryptography is well-documented and increasingly discussed by the security community. An April 2016 report by the National Institute of Standards and…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a…
The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and…
Traditional cryptography is under huge threat along of the evolution of quantum information and computing. In this paper, we propose a new post-quantum voting scheme based on physical laws by using encrypted no-key protocol to transmit…
The impending arrival of cryptographically relevant quantum computers (CRQCs) threatens the security foundations of modern software: Shor's algorithm breaks RSA, ECDSA, ECDH, and Diffie-Hellman, while Grover's algorithm reduces the…
Quantum computers impose an immense threat to system security. As a countermeasure, new cryptographic classes have been created to prevent these attacks. Technologies such as post-quantum cryptography and quantum cryptography. Quantum…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
In recent years, quantum computers and Shor quantum algorithm have posed a threat to current mainstream asymmetric cryptography methods (e.g. RSA and Elliptic Curve Cryptography (ECC)). Therefore, it is necessary to construct a Post-Quantum…
This book arises from the need to provide a clear and up-to-date overview of the impacts of quantum computing on cryptography. The goal is to provide a reference in Portuguese for undergraduate, master's, and doctoral students in the field…
Learning with Errors (LWE) problems are the foundations for numerous applications in lattice-based cryptography and are provably as hard as approximate lattice problems in the worst case. Here we present a reduction from LWE problem to…
Post-quantum cryptography is inevitable. National Institute of Standards and Technology (NIST) starts standardizing quantum-resistant public-key cryptography (aka post-quantum cryptography). The reason is that investment in quantum…
The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman [19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers…
We define two new problems called SIAP and CAP related to solving SIVP and CVP in a subset of lattices called Simultaneous Approximation (SA) lattices. We give dimension- and gap-preserving, deterministic polynomial-time and space…
Post-quantum cryptography (PQC) is moving from evaluation to deployment as NIST finalizes standards for ML-KEM, ML-DSA, and SLH-DSA. This survey maps the space from foundations to practice. We first develop a taxonomy across lattice-,…
Blockchain is a Distributed Ledger Technology (DLT) that offers numerous benefits including decentralization, transparency, efficiency, and reduced costs. Hence, blockchain has been included in many fields. Blockchain relies on…
This survey is on forward-looking, emerging security concerns in post-quantum era, i.e., the implementation attacks for 2022 winners of NIST post-quantum cryptography (PQC) competition and thus the visions, insights, and discussions can be…