Related papers: An authentication scheme based on the twisted conj…
In an open network environment, privacy of group communication and integrity of the communication data are the two major issues related to secured information exchange. The required level of security may be achieved by authenticating a…
The Baumslag group had been a candidate for a group with an extremely difficult word problem until Myasnikov, Ushakov, and Won succeeded to show that its word problem can be solved in polynomial time. Their result used the newly developed…
Identification schemes are interactive protocols typically involving two parties, a prover, who wants to provide evidence of his or her identity and a verifier, who checks the provided evidence and decide whether it comes or not from the…
One way of investigating how genes affect human traits would be with a genome-wide association study (GWAS). Genetic markers, known as single-nucleotide polymorphism (SNP), are used in GWAS. This raises privacy and security concerns as…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
In this paper we consider the problems of testing isomorphism of tensors, $p$-groups, cubic forms, algebras, and more, which arise from a variety of areas, including machine learning, group theory, and cryptography. These problems can all…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the…
Lal and Chaturvedi proposed two authentication schemes based on the difficulty of the Root Problem in the braid group. We point out that the first scheme is not really as secure as the Root Problem, and describe an efficient way to crack…
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…
Group Authentication Schemes (GAS) are methodologies developed to verify the membership of multiple users simultaneously. These schemes enable the concurrent authentication of several users while eliminating the need for a certification…
Biometric authentication systems pose privacy risks, as leaked templates such as iris or fingerprints can lead to security breaches. Fully Homomorphic Encryption (FHE) enables secure encrypted evaluation, but its deployment is hindered by…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
We consider the problem of secure identification: user U proves to server S that he knows an agreed (possibly low-entropy) password w, while giving away as little information on w as possible, namely the adversary can exclude at most one…
In this article, we solve the twisted conjugacy problem with respect to endomorphisms for solvable Baumslag--Solitar groups $BS(1,n)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(1,n)$ and an endomorphism $\psi \in…
An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equations for supersingular curves for which computing the…
Credential theft and remote attacks are the most serious threats to user authentication mechanisms. The crux of these problems is that we cannot control such behaviors. However, if a password does not contain user secrets, stealing it is…
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise…