Related papers: A new multivariate primitive from CCZ equivalence
Let $\mathbf{f}=(f\_1,\ldots,f\_m)$ and $\mathbf{g}=(g\_1,\ldots,g\_m)$ be two sets of $m\geq 1$ nonlinear polynomials over $\mathbb{K}[x\_1,\ldots,x\_n]$ ($\mathbb{K}$ being a field). We consider the computational problem of finding -- if…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
In this paper a three fuzzy vault schemes which integrated with discrete logarithmic encryption scheme are proposed. In the first scheme, the message m is encoded with discrete logarithmic encryption scheme using randomly generated identity…
Substitution boxes with thorough cryptographic strengths are essential for the development of strong encryption systems. They are the only portions capable of inducing nonlinearity in symmetric encryption systems. Bijective substitution…
The inverse function $x \mapsto x^{-1}$ on $\mathbb{F}_{2^n}$ is one of the most studied functions in cryptography due to its widespread use as an S-box in block ciphers like AES. In this paper, we show that, if $n\geq 5$, every function…
This article presents the application of homomorphic authenticators, replication encodings to be precise, to multigroup fully homomorphic encryption schemes. Following the works of Gennaro and Wichs on homomorphic authenticators in…
The Bivariate Function Hard Problem (BFHP) has been in existence implicitly in almost all number theoretic based cryptosystems. This work defines the BFHP in a more general setting and produces an efficient asymmetric cryptosystem. The…
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…
The use of permutation polynomials has appeared, along to their compositional inverses, as a good choice in the implementation of cryptographic systems. Hence, there has been a demand for constructions of these polynomials which…
After introducing a bit-plane quantum representation for a multi-image, we present a novel way to encrypt/decrypt multiple images using a quantum computer. Our encryption scheme is based on a two-stage scrambling of the images and of the…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the…
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…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
In this paper an enhanced fuzzy vault scheme is proposed which we refer to as fuzzy-fuzzy vault scheme. The proposed scheme builds on the classical fuzzy vault by adding the concept of uncertainty and imprecision to the classical scheme. To…
Quantum cryptography leverages many unique features of quantum information in order to construct cryptographic primitives that are oftentimes impossible classically. In this work, we build on the no-cloning principle of quantum mechanics…
In this article, we have proposed a public key cryptography using Affine-Hill cipher with a generalized Fibonacci matrix(called multinacci matrix). Also proposed a key establishment(exchange of key matrix $K=Q_{\lambda}^{k}$ of order…