Related papers: LWE from Non-commutative Group Rings
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…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first group signature schemes based on the conjugacy problem, decomposition problem and root problem in the braid…
This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek, Guenda and Gulliver [24]. The system is based on the juxtaposition of quasi-cyclic LDPC and quasi-cyclic MDPC codes. The idea of our…
The cycling operation is a special kind of conjugation that can be applied to elements in Artin's braid groups, in order to reduce their length. It is a key ingredient of the usual solutions to the conjugacy problem in braid groups. In…
In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output…
One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution problem to the Learning with Errors problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry that…
We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…
This paper presents a novel methodology to test the security of the Diffie-Hellman public key exchange protocol. The security of many cryptographic schemes rely on the hardness of this problem. We are presenting a purely statistical test to…
The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to…
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…
Since they were introduced in the 1990s, Lie group integrators have become a method of choice in many application areas. These include multibody dynamics, shape analysis, data science, image registration and biophysical simulations. Two…
This article presents an encryption scheme based on the small Ree groups. We propose utilizing the small Ree group structure to enhance the overall security parameters of the encryption scheme. By extending the logarithmic signature to…
The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism…
We investigate the notion of untelegraphable encryption (UTE), a quantum encryption primitive that is a special case of uncloneable encryption (UE), where the adversary's capabilities are restricted to producing purely classical information…
S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…
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…
In this paper, we present a novel ciphertext-policy attribute based encryption (CP-ABE) scheme that offers a flexible access structure. Our proposed scheme incorporates an access tree as its access control policy, enabling fine-grained…
Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…
The security of code-based cryptography usually relies on the hardness of the syndrome decoding (SD) problem for the Hamming weight. The best generic algorithms are all improvements of an old algorithm by Prange, and they are known under…
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the…