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Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
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…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…
This paper presents explicit constructions of bases for Riemann-Roch spaces associated with arbitrary divisors on elliptic curves. In the context of algebraic geometry codes, the knowledge of an explicit basis for arbitrary divisors is…
In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate scheme has found application in security credential management systems (SCMS) and secure vehicle-to-everything (V2X) communication to issue pseudonymous…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
We propose a cipher similar to the One Time Pad and McEliece cipher based on a subband coding scheme. The encoding process is an approximation to the One Time Pad encryption scheme. We present results of numerical experiments which suggest…
A key encapsulation mechanism (KEM) that takes as input an arbitrary string, i.e., a tag, is known as tag-KEM, while a scheme that combines signature and encryption is called signcryption. In this paper, we present a code-based signcryption…
The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
In this paper, we show that the Advanced Encryption Standard (AES) cryptosystem can be used as an error-correcting code to obtain reliability over noisy communication and data systems. Moreover, we characterize a family of computational…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
The HQC encryption framework is a general code-based encryption scheme for which decryption returns a noisy version of the plaintext. Any instantiation of the scheme will therefore use an error-correcting procedure relying on a fixed…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…
These lecture notes have been written for courses given at \'Ecole normale sup\'erieure de Lyon and summer school 2022 in post-quantum cryptography that took place in the university of Budapest. Our objective is to give a general…