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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…

Cryptography and Security · Computer Science 2016-07-12 Frantisek Marko , Alexandr N. Zubkov , Martin Juras

Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…

Quantum Physics · Physics 2009-09-29 Michael Stephen Brown

Cryptographic access control has been studied for over 30 years and is now a mature research topic. When symmetric cryptographic primitives are used, each protected resource is encrypted and only authorized users should have access to the…

Cryptography and Security · Computer Science 2015-06-02 Jason Crampton , Naomi Farley , Gregory Gutin , Mark Jones , Bertram Poettering

The goal of any cryptographic system is the exchange of information among the intended users without any leakage of information to others who may have unauthorized access to it. A common secret key could be created over a public channel…

Cryptography and Security · Computer Science 2011-02-03 Sahana S. Bisalapur

Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…

Cryptography and Security · Computer Science 2021-09-21 Andrew M. Mironov

In this paper, we define and discuss {\phi}-cyclic code, which may be regarded as a general form of the ordinary cyclic code. As applications, we explain how to extend two public key encryption schemes, one is McEliece and Niederriter's…

Information Theory · Computer Science 2021-12-30 Zhiyong Zheng , Wenlin Huang , Jie Xu , Kun Tian

The simple security property in an information flow policy can be enforced by encrypting data objects and distributing an appropriate secret to each user. A user derives a suitable decryption key from the secret and publicly available…

Cryptography and Security · Computer Science 2015-05-01 Jason Crampton , Naomi Farley , Gregory Gutin , Mark Jones

We propose variations of the class of hidden monomial cryptosystems in order to make it resistant to all known attacks. We use identities built upon a single bivariate polynomial equation with coefficients in a finite field. Indeed, it can…

Cryptography and Security · Computer Science 2007-05-23 Ilia Toli

This paper is an attempt to build a new public-key cryptosystem; similar to the McEliece cryptosystem, using permutation error-correcting codes. We study a public-key cryptosystem built using two permutation error-correcting codes. We show…

Information Theory · Computer Science 2023-09-11 Adarsh Srinivasan , Ayan Mahalanobis

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…

Cryptography and Security · Computer Science 2007-05-23 Dima Grigoriev , Ilia Ponomarenko

The process of replacing an arbitrary Boolean function by a bijective one, a fundamental tool in reversible computing and in cryptography, is interpreted algebraically as a particular instance of a certain group homomorphism from the X-fold…

Category Theory · Mathematics 2022-08-25 Laurent Poinsot , Hans-E Porst

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,…

Cryptography and Security · Computer Science 2021-08-17 Vitaly Roman'kov

Quantum public-key encryption [Gottesman; Kawachi et al., Eurocrypt'05] generalizes public-key encryption (PKE) by allowing the public keys to be quantum states. Prior work indicated that quantum PKE can be constructed from assumptions that…

Quantum Physics · Physics 2023-03-03 Khashayar Barooti , Giulio Malavolta , Michael Walter

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…

Quantum Physics · Physics 2020-02-21 Si-Hui Tan , Joshua A. Kettlewell , Yingkai Ouyang , Lin Chen , Joseph F. Fitzsimons

Warnings have been raised about the steady diminution of privacy. More and more personal information, such as that contained electronic mail, is moving to cloud computing servers where it might be machine-searched and indexed. FauxCrypt is…

Cryptography and Security · Computer Science 2018-02-14 Devlin M. Gualtieri

Recently, Hwang et al. introduced a knapsack type public-key cryptosystem. They proposed a new algorithm called permutation combination algorithm. By exploiting this algorithm, they attempt to increase the density of knapsack to avoid the…

Cryptography and Security · Computer Science 2013-09-17 Roohallah Rastaghi

In this paper, a code-based public-key cryptosystem based on interleaved Goppa codes is presented. The scheme is based on encrypting several ciphertexts with the same Goppa code and adding a burst error to them. Possible attacks are…

Information Theory · Computer Science 2018-09-11 Molka Elleuch , Antonia Wachter-Zeh , Alexander Zeh

At Eurocrypt'99, Paillier presented a public-key cryptosystem based on a novel computational problem. It has interested many researchers because it was additively homomorphic. In this paper, we show that there is a big difference between…

Cryptography and Security · Computer Science 2015-11-19 Zhengjun Cao , Lihua Liu

Passwords are a fragile, inadequate, and insecure tool for authenticating users, and are especially fraught with problems when used to secure access to network resources and services. In many cases, passwords provide a false sense of…

Cryptography and Security · Computer Science 2012-09-06 Travis Z. Suel

This paper provides a double encryption algorithm that uses the lack of invertibility of the fractional Fourier transform (FRFT) on $L^{1}$. One encryption key is a function, which maps a ``good" $L^{2}$-signal to a ``bad" $L^{1}$-signal.…

Information Theory · Computer Science 2021-11-09 Wei Chen , Zunwei Fu , Loukas Grafakos , Yue Wu