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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…

Sparse binary LWE secrets are under consideration for standardization for Homomorphic Encryption and its applications to private computation. Known attacks on sparse binary LWE secrets include the sparse dual attack and the hybrid sparse…

We propose self-similar contracting groups as a platform for cryptographic schemes based on simultaneous conjugacy search problem (SCSP). The class of these groups contains extraordinary examples like Grigorchuk group, which is known to be…

Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard…

Let S be an m-system of a ring R, and P a submodule of a right R-module M. This paper, presents the notion of S-prime submodule and provides some properties and equivalent definitions. We define S-multiplication right module, and prove that…

We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack.

Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital communication. However, in scenarios involving sensitive interactions -- such as e-voting or e-cash -- there is a growing need…

In this thesis, we study algebraic coding theory based McEliece-type cryptosystems over quasi-cyclic codes. The main goal of this thesis is to construct a cryptosystem that resists quantum Fourier sampling making it quantum secure. We…

A (control) network over a finite ring is proposed. Using semi-tensor product (STP) of matrices, a set of algebraic equations are provided to verify whether a finite set with two binary operators is a ring. It is then shown that the…

This article presents an encryption scheme based on the small Ree groups. We propose utilizing the small Ree group structure to enhance the overall security parameters of the encryption scheme. By extending the logarithmic signature to…

The paper studies the lattice of subgroups of an isotropic reductive group G(R) over a commutative ring R, normalized by the elementary subgroup E(R). We prove the sandwich classification theorem for this lattice under the assumptions that…

Nowadays, the dataflux shared between IOT systems must be secured from 8-bits to 64-bits processors systems. Several symmetric cryptographic algorithm already exist such as AES (Advanced Encryption Standard), RC4, Blowfish, etc. In this…

Predicate encryption is a new type of public key encryption that enables searches on encrypted data. By using predicate encryption, we can search keywords or attributes on encrypted data without decrypting ciphertexts. Hidden vector…

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…

A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable…

In this paper we study the complexity of constructing a hitting set for the closure of VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the…

Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary…

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…

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…

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…