Related papers: A new lightweight additive homomorphic encryption …
Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…
Traditional Fully Homomorphic Encryption (FHE) schemes often suffer from prohibitive computational overhead and complex noise management. In this paper, we propose a novel symmetric FHE through a mechanism of plaintext fragmentation and…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…
With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…
This paper introduces a new public key cryptosystem based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli) and the discrete logarithm problem. These two hard…
We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and…
Cloud computing is a popular distributed network and utility model based technology. Since in cloud the data is outsourced to third parties, the protection of confidentiality and privacy of user data becomes important. Different methods for…
In their 2022 study, Kuang et al. introduced Multivariable Polynomial Public Key (MPPK) cryptography, leveraging the inversion relationship between multiplication and division for quantum-safe public key systems. They extended MPPK into…
High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…
A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
We investigate the cryptanalysis of affine ciphers using a hybrid neural network architecture that combines modular arithmetic-aware and statistical feature-based learning. Inspired by recent advances in interpretable neural networks for…
Being able to compute efficiently a low-weight multiple of a given binary polynomial is often a key ingredient of correlation attacks to LFSR-based stream ciphers. The best known general purpose algorithm is based on the generalized…
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in…
Hyperdimensional Computing (HDC) is facing infringement issues due to straightforward computations. This work, for the first time, raises a critical vulnerability of HDC, an attacker can reverse engineer the entire model, only requiring the…
Bogdanov and Lee suggested a homomorphic public-key encryption scheme based on error correcting codes. The underlying public code is a modified Reed-Solomon code obtained from inserting a zero submatrix in the Vandermonde generating matrix…
This paper presents efficient algorithms, designed to leverage SIMD for performing Montgomery reductions and additions on integers larger than 512 bits. The existing algorithms encounter inefficiencies when parallelized using SIMD due to…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic…
Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted data without knowing its corresponding plaintext. For…