Related papers: Lattice-Based Vulnerabilities in Lee Metric Post-Q…
On July 5, 2022, the National Institute of Standards and Technology announced four possible post-quantum cryptography standards, three of them are based on lattice theory and the other one is based on Hash function. It is well-known that…
The McEliece cryptosystem based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes is first purposed in 2013\cite{QCMDPC} and is considered a promising contender in the post-quantum era. Understanding its security is hence…
Cryptography underpins the security of modern digital infrastructure, from cloud services to health data. However, many widely deployed systems will become vulnerable after the advent of scalable quantum computing. Although quantum-safe…
Homomorphic Encryption (HE) allows secure and privacy-protected computation on encrypted data without the need to decrypt it. Since Shor's algorithm rendered prime factorisation and discrete logarithm-based ciphers insecure with quantum…
Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based…
Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in…
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…
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…
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…
A new nonlinear Rao-Nam like symmetric key encryption scheme is presented in this paper. QC-LDPC lattices that are practically implementable in high dimensions due to their low complexity encoding and decoding algorithms, are used in our…
Nowadays, predominant asymmetric cryptographic schemes are considered to be secure because discrete logarithms are believed to be hard to be computed. The algorithm of Shor can effectively compute discrete logarithms, i.e. it can brake such…
In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error…
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…
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two…
We propose a novel quantum-resistant mutual authentication scheme for radio-frequency identification (RFID) systems. Our scheme uses lattice-based cryptography and, in particular, achieves quantum-resistance by leveraging the hardness of…
This paper reports a detailed cryptanalysis of a recently proposed encryption scheme based on the logistic map. Some problems are emphasized concerning the key space definition and the implementation of the cryptosystem using floating-point…
Recently, a few chosen-ciphertext secure (CCA2-secure) variants of the McEliece public-key encryption (PKE) scheme in the standard model were introduced. All the proposed schemes are based on encryption repetition paradigm and use general…
We proposed a new attack against Hwang et al.'s cryptosystem. This cryptosystem uses a super-increasing sequence as private key and the authors investigate a new algorithm called permutation combination algorithm to enhance density of…
Krouk, Tavernier and Kabatiansky proposed new variants of the McEliece cryptosystem. In this letter, it is shown that cryptosystem based on correction of errors erasures is equal to the Mc-Eliece cryptosystem with worse parametrs public…
With the constantly advancing capabilities of quantum computers, conventional cryptographic systems relying on complex math problems may encounter unforeseen vulnerabilities. Unlike regular computers, which are often deemed cost-ineffective…