Related papers: Post-Quantum Cryptography: An Analysis of Code-Bas…
We consider the framework of the McEliece cryptosystem based on LDPC codes, which is a promising post-quantum alternative to classical public key cryptosystems. The use of LDPC codes in this context allows to achieve good security levels…
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…
Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key…
Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE,…
The Code Equivalence problem is that of determining whether two given linear codes are equivalent to each other up to a permutation of the coordinates. This problem has a direct reduction to a nonabelian hidden subgroup problem (HSP),…
Trust is the core building block of secure systems, and it is enforced through methods to ensure that a specific system is properly configured and works as expected. In this context, a Root of Trust (RoT) establishes a trusted environment,…
The quantum threat to cybersecurity has accelerated the standardization of Post-Quantum Cryptography (PQC). Migrating legacy software to these quantum-safe algorithms is not a simple library swap, but a new software engineering challenge:…
As quantum computing advances toward practical deployment, it threatens a wide range of classical cryptographic mechanisms, including digital signatures, key exchange protocols, public-key encryption, and certain hash-based constructions…
The imminent realization of fault-tolerant quantum computing precipitates a systemic collapse of classical public-key infrastructure and necessitates an urgent transition to post-quantum cryptography. However, current standardization…
This is a survey on some topics in Lattice based cryptography and Homomorphic Encryption. In particular, we define some lattice problems, LWE and RLWE, and state the reductions given by Regev and Peikert. We also give a full treatment of…
Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to…
In this paper we consider a post-quantum digital signature scheme based on low-density generator matrix codes and propose efficient algorithmic solutions for its implementation. We also review all known attacks against this scheme and…
Post-Quantum cryptography is about to substitute current cryptographic schemes as being resilient in attacks from quantum computers. McEleiece and Bit Flip Key Encapsulation (BIKE) are two delight representatives based on coding theory…
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…
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 computing (QC) holds the promise of revolutionizing problem-solving by exploiting quantum phenomena like superposition and entanglement. It offers exponential speed-ups across various domains, from machine learning and security to…
Recent oracle separations [Kretschmer, TQC'21, Kretschmer et. al., STOC'23] have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if the polynomial hierarchy collapses. We…
The learning parity with noise (LPN) problem is a well-established computational challenge whose difficulty is critical to the security of several post-quantum cryptographic primitives such as HQC and Classic McEliece. Classically, the…