Related papers: Cryptographic transformations over polyadic rings

The promise of quantum computation and its consequences for complexity-theoretic cryptography motivates an immediate search for cryptosystems which can be implemented with current technology, but which remain secure even in the presence of…

We propose a new randomized ensemble technique with a provable security guarantee against black-box transfer attacks. Our proof constructs a new security problem for random binary classifiers which is easier to empirically verify and a…

Recently two encryption schemes were proposed by combining circular bit shift and XOR operations, under the control of a pseudorandom bit sequence (PRBS) generated from a chaotic system. This paper studies the security of these two…

Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…

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…

In this paper we present a new primitive for a key exchange protocol based on multivariate non-commutative polynomial rings, analogous to the classic Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et al. from…

Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation…

We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and…

Analytical thinking is dominated by binary ideas. From pair-wise interactions, to algebraic operations, to compositions of processes, to network models, binary structures are deeply ingrained in the fabric of most current scientific…

Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…

The polynomial method from circuit complexity has been applied to several fundamental problems and obtains the state-of-the-art running times. As observed in [Alman and Williams, STOC 2017], almost all applications of the polynomial method…

Cryptographic group actions are a leading contender for post-quantum cryptography, and have also been used in the development of quantum cryptographic protocols. In this work, we explore quantum state group actions, which consist of a group…

Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…

This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek, Guenda and Gulliver [24]. The system is based on the juxtaposition of quasi-cyclic LDPC and quasi-cyclic MDPC codes. The idea of our…

In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…

We introduce and analyze a novel class of binary operations on finite-dimensional vector spaces over a field K, defined by second-order multilinear expressions with linear shifts. These operations generate polynomials whose degree increases…

Error function analysis is an effective attack against chaotic cryptograph [PRE 66, 065202(R) (2002)]. The basin structure of the error function is crucial for determining the security of chaotic cryptosystems. In the present paper the…

The Legendre Pseudorandom Function (PRF) is a highly efficient cryptographic primitive built upon the Legendre symbol, valued for its low multiplicative complexity in Multi-Party Computation (MPC) and Zero-Knowledge Proof (ZKP) protocols.…

The binary bracket of a Courant algebroid structure on $(E,\langle \cdot,\cdot \rangle)$ can be extended to a $n$-ary bracket on $\Gamma(E)$, yielding a multi-Courant algebroid. These $n$-ary brackets form a Poisson algebra and were…

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is…