Related papers: Non-associative public-key cryptography
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
We construct non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and other left distributive systems. Instantiations of these protocols using generalized shifted conjugacy in braid groups lead to…
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…
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of…
We construct new non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these protocols relies on variations of the (simultaneous) iterated LD-problem and its…
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…
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 provide implementation details for non-associative key establishment protocols. In particular, we describe the implementation of non-associative key establishment protocols for all left self-distributive and all mutually left…
The predominant grid authentication mechanisms use public key infrastructure (PKI). Nonetheless, certificate-less public key cryptography (CL-PKC) has several advantages that seem to well align with the demands of grid computing. Security…
Public key encryption with equality test (PKEET), proposed by Yang et al. (CT-RSA 2010), is a variant of public key encryption that enables an equality test to determine whether two ciphertexts correspond to the same plaintext. This test…
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…
In this paper, we propose a brand new public key encryption scheme in the Lie group that is a non-abelian group. In particular, we firstly investigate the intractability assumptions in the Lie group, including the non-abelian factoring…
Recently, Hwang et al. introduced a knapsack type public-key cryptosystem. They proposed a new algorithm called permutation combination algorithm. By exploiting this algorithm, they attempt to increase the density of knapsack to avoid the…
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…
In 1991 the first public key protocol involving automaton groups has been proposed. In this paper we give a survey about algorithmic problems around automaton groups which may have potential applications in cryptography. We then present a…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
We show that for every effective left conjugacy closed left quasigroup, there is an induced rack that retains the conjugation structure of the left translations. This means that cryptographic protocols relying on conjugacy search can be…
After the Anshel-Anshel-Goldfeld (AAG) key-exchange protocol was introduced in 1999, it was implemented and studied with braid groups and with the Thompson group as its underlying platforms. The length-based attack, introduced by Hughes and…
In this paper,we propose a modified Anshel-Anshel-Goldfeld(AAG) key exchange scheme. The hardness assumption underlying this modified construction is based on the membership problem for Mihailova subgroups of the braid group, a problem that…
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…