Related papers: Group ring cryptography
We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens…
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…
The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the…
Neural cryptography is based on synchronization of tree parity machines by mutual learning. We extend previous key-exchange protocols by replacing random inputs with queries depending on the current state of the neural networks. The…
Ciphers are a powerful tool for encrypting communication. There are many different cipher types, which makes it computationally expensive to solve a cipher using brute force. In this paper, we frame the decryption task as a classification…
Generating secure random numbers is a central problem in cryptography that needs a reliable source of enough computing entropy. Without enough entropy available - meaning no good source of secure random numbers - a device is susceptible to…
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.…
A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then we use polyadic techniques…
A first multi-proxy multi-signcryption scheme from pairings, which efficiently combines a multi-proxy multi-signature scheme with a signcryption, is proposed. Its security is analyzed in detail. In our scheme, a proxy signcrypter group…
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…
Encrypted computing is an emerging technology based on a processor that `works encrypted', taking encrypted inputs to encrypted outputs while data remains in encrypted form throughout. It aims to secure user data against possible insider…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
This paper presents a quasigroup encryptor that has very good scrambling properties. We show that the output of the encryptor maximizes the output entropy and the encrypted output for constant and random inputs is very similar. The system…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
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,…
This article is meant to provide an additional point of view, applying known knowledge, to supply keys that have a series of non-repeating digits, in a manner that is not usually thought of. Traditionally, prime numbers are used in…
Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some…