Related papers: Tropical cryptography
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…
A graph profile records all possible densities of a fixed finite set of graphs. Profiles can be extremely complicated; for instance the full profile of any triple of connected graphs is not known, and little is known about hypergraph…
Quantum computers, that may become available one day, would impact many scientific fields, most notably cryptography since many asymmetric primitives are insecure against an adversary with quantum capabilities. Cryptographers are already…
We show that the attacks based on the linear decomposition method introduced by the author and the span-method introduced by Tsaban allow one to find the transmitted message in the cryptosystem and the exchanged key in the protocol which…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
The random oracle methodology has proven to be a powerful tool for designing and reasoning about cryptographic schemes. In this paper, we focus on the basic problem of correcting faulty or adversarially corrupted random oracles, so that…
Bitcoin uses blockchain technology to maintain transactions order and provides probabilistic guarantee to prevent double-spending, assuming that an attacker's computational power does not exceed %50 of the network power. In this paper, we…
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to…
We develop a general framework for parameter estimation that allows only trusted parties to access the result and achieves optimal precision. The protocols are designed such that adversaries can access some information indeterministically,…
We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements,…
Patchworking theorems serve as a basic element of the correspondence between tropical and algebraic curves, which is a core of the tropical enumerative geometry. We present a new version of a patchworking theorem which relates plane…
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…
In tropical geometry, one studies algebraic curves using combinatorial techniques via the tropicalization procedure. The tropicalization depends on a map to an algebraic torus and the combinatorial methods are most useful when the…
Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure…
Cryptocurrency off-chain networks such as Lightning (e.g., Bitcoin) or Raiden (e.g., Ethereum) aim to increase the scalability of traditional on-chain transactions. To support nodes in learning about possible paths to route their…
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use…
Commutative encryption is a useful but rather strict notion in cryptography. In this paper, we deny a loose variation of commutative encryption-commutative-like encryption and give an example: the generalization of ElGamal scheme. The…
Side-channel attacks have become a severe threat to the confidentiality of computer applications and systems. One popular type of such attacks is the microarchitectural attack, where the adversary exploits the hardware features to break the…
In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in…