Related papers: Use of Signed Permutations in Cryptography

With the increasing demands for privacy protection, privacy-preserving machine learning has been drawing much attention in both academia and industry. However, most existing methods have their limitations in practical applications. On the…

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…

General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…

S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…

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…

In discrete logarithm based cryptography, a method by Pohlig and Hellman allows solving the discrete logarithm problem efficiently if the group order is known and has no large prime factors. The consequence is that such groups are avoided.…

We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol.…

We offer a public key exchange protocol in the spirit of Diffie-Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This "nested structure" of the platform makes computation very efficient…

This article proposes a comprehensive approach to implementing encryption schemes based on the automorphism group of the Hermitian function field. We utilize a three-parameter group with logarithmic representations outside the group's…

Currently there is an active Post-Quantum Cryptography (PQC) solutions search, which attempts to find cryptographic protocols resistant to attacks by means of for instance Shor polynomial time algorithm for numerical field problems like…

The modified Paillier cryptosystem has become extremely popular and applied in many fields, owning to its additive homomorphism. This cryptosystem provides weak private keys and a strong private key. A weak private key only can decrypt…

The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of…

Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…

This paper is a primer on cryptographic accumulators and how to apply them practically. A cryptographic accumulator is a space- and time-efficient data structure used for set-membership tests. Since it is possible to represent any…

The discrete logarithm problem is one of the backbones in public key cryptography. In this paper we study the discrete logarithm problem in the group of circulant matrices over a finite field. This gives rise to secure and fast public key…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in…

We propose a novel digital signature cryptosystem that exploits the concept of the brute-force problem. To ensure the security of the cryptosystem, we employed several mechanisms: sharing a common secret for factorable permutations,…

We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…

Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…