Related papers: The MOR cryptosystem and finite $p$-groups

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in…

This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…

Personal AI systems increasingly retain long-term memory of user activity, including documents, emails, messages, meetings, and ambient recordings. Trusted hardware can keep this data private, but struggles to scale with a growing…

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.…

We propose modifications of known quasigroup based stream ciphers. Systems of orthogonal n-ary groupoids are used.

Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…

A commitment scheme is a cryptographic tool that allows one to commit to a hidden value, with the option to open it later at requested places without revealing the secret itself. Commitment schemes have important applications in…

The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary…

Common random string model is a popular model in classical cryptography. We study a quantum analogue of this model called the common Haar state (CHS) model. In this model, every party participating in the cryptographic system receives many…

Importance of Elliptic Curves in Cryptography was independently proposed by Neal Koblitz and Victor Miller in 1985.Since then, Elliptic curve cryptography or ECC has evolved as a vast field for public key cryptography (PKC) systems. In PKC…

This article proposes a comprehensive approach to implementing encryption schemes based on the automorphism group of the Hermitian function field. We utilize a three-parameter group with logarithmic representations outside the group's…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

It is well known that Shor's quantum algorithm for integer factorization can break down the RSA public-key cryptosystem, which is widely used in many cryptographic applications. Thus, public-key cryptosystems in the quantum computational…

We show in some detail how to implement Shor's efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further…

D\'ech\`ene has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect…

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…

This paper presents a new fast public key cryptosystem namel : a key exchange algorithm, a public key encryption algorithm and a digital signature algorithm, based on the difficulty to invert the following function: $$F(x) =(a\times…

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig-Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for…

Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential…

Machine Learning (ML) has emerged as one of data science's most transformative and influential domains. However, the widespread adoption of ML introduces privacy-related concerns owing to the increasing number of malicious attacks targeting…