Related papers: Public Key Encryption in Non-Abelian Groups
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…
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…
Ring signature is a kind of group-oriented signature. It allows a member of a group to sign messages on behalf of the group without revealing his/her identity. Certificateless public key cryptography was first introduced by Al-Riyami and…
Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The…
Braid group is a very important non-commutative group. It is also an important tool of quantum field theory, and has good topological properties. This paper focuses on the provable security research of cryptosystem over braid group, which…
Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation.…
We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle…
In his paper Stadler develops techniques for improving the security of existing secret sharing protocols by allowing to check whether the secret shares given out by the dealer are valid. In particular, the secret sharing is executed over…
A new cryptographic tool, anonymous quantum key technique, is introduced that leads to unconditionally secure key distribution and encryption schemes that can be readily implemented experimentally in a realistic environment. If quantum…
A group authentication protocol authenticates pre-defined groups of individuals such that: - No individual is identified - No knowledge of which groups can be successfully authenticated is known to the verifier - No sensitive data is…
We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement…
Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.
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…
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
In this paper, we propose to use a skew dihedral group ring given by the group $D_{2n}$ and the finite field $\mathbb{F}_{q^2}$ for public-key cryptography. Using the ambient space $\mathbb{F}_{q^{2}}^{\theta} D_{2n}$ and a group…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…
The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast…
We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new…
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation…