Related papers: Tropical cryptography III: digital signatures
In this paper we propose a new digital signature protocol inspired by the DSA algorithm. The security and the complexity are analyzed. Our method constitutes an alternative if the classical scheme DSA is broken.
The Hill cipher is a classical symmetric encryption algorithm that succumbs to the know-plaintext attack. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in…
Consider the classical ElGamal digital signature scheme based on the modular relation $\alpha^m\equiv y^r\, r^s\ [p]$. In this work, we prove that if we can compute a natural integer $i$ such that $\alpha^i\ mod\ p$ is smooth and divides…
In this paper, we give an explicit description of tropical cohomology of smooth algebraic varieties over trivially valued fields. We also construct ``monodromy weight'' spectral sequences for tropical cohomology of geometric strictly…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
We study singularities in tropical hypersurfaces defined by a valuation over a field of positive characteristic. We provide a method to compute the set of singular points of a tropical hypersurface in positive characteristic and the p-adic…
Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials…
A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.
We show how tropical varieties of ideals I over a field K with non-trivial valuation can be traced back to tropical varieties of ideals in R[[t]][x] over some dense subring R in its ring of integers. Moreover, for homogeneous ideals, we…
Blockchain like Bitcoin and Ethereum suffer from scalability issues. Sharding is one of the most promising and leading solutions to scale blockchain. The basic idea behind sharding is to divide the blockchain network into multiple…
This paper discloses a simple algorithm for encrypting text messages, based on the NP-completeness of the subset sum problem, such that the similarity between encryptions is roughly proportional to the semantic similarity between their…
This paper proposes a signature scheme where the signatures are generated by the cooperation of a number of people from a given group of senders and the signatures are verified by a certain number of people from the group of recipients.…
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…
Another threat is the development of large quantum computers, which have a high likelihood of breaking the high popular security protocols because it can use both Shor and Grover algorithms. In order to fix this looming threat,…
Voting is a primary democratic activity through which voters select representatives or approve policies. Conventional paper ballot elections have several drawbacks that might compromise the fairness, effectiveness, and accessibility of the…
Iterated-integral signatures and log signatures are vectors calculated from a path that characterise its shape. They come from the theory of differential equations driven by rough paths, and also have applications in statistics and machine…
Information and computer security is supported largely by passwords which are the principle part of the authentication process. The most common computer authentication method is to use alphanumerical username and password which has…
Entropically Secure Encryption (ESE) offers unconditional security with shorter keys compared to the One-Time Pad. In this paper, we present the first implementation of ESE for bulk encryption. The main computational bottleneck for bulk ESE…
Signcryption is a cryptographic primitive which performs encryption and signature in a single logical step. In conventional signcryption only receiver of the signcrypted text can verify the authenticity of the origin i.e. signature of the…
We study the complexity of securely evaluating arithmetic circuits over finite rings. This question is motivated by natural secure computation tasks. Focusing mainly on the case of two-party protocols with security against malicious…