Related papers: Hidden Polynomial(s) Cryptosystems

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…

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…

We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…

We've been able to show recently that Permutable Chebyshev polynomials (T polynomials) defined over the field of real numbers can be used to create a Diffie-Hellman-like key exchange algorithm and certificates. The cryptosystem was…

We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…

In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…

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…

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…

Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…

We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…

We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…

In this paper homomorphic cryptosystems are designed for the first time over any finite group. Applying Barrington's construction we produce for any boolean circuit of the logarithmic depth its encrypted simulation of a polynomial size over…

To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit…

We discuss a new attack, termed a dimension or linear decomposition attack, on several known group-based cryptosystems. This attack gives a polynomial time deterministic algorithm that recovers the secret shared key from the public data in…

In 2019 G\'omez described a new public key cryptography scheme based on ideas from multivariate public key cryptography using hidden irreducible polynomials. We show that the scheme's design has a flaw which lets an attacker recover the…

This study concentrates on preserving privacy in a network of agents where each agent seeks to evaluate a general polynomial function over the private values of her immediate neighbors. We provide an algorithm for the exact evaluation of…

We describe an algorithm which finds binomials in a given ideal $I\subset\mathbb{Q}[x_1,\dots,x_n]$ and in particular decides whether binomials exist in $I$ at all. Binomials in polynomial ideals can be well hidden. For example, the lowest…

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes…

We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the…