Related papers: Provably Secure Integration Cryptosystem on Non-Co…
The braid group is an important non commutative group, at the same time, it is an important tool in quantum field theory with better topological structure, and often used as a research carrier for anti-quantum cryptographic algorithms. This…
In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts…
We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack.
Chosen-ciphertext security, which guarantees confidentiality of encrypted messages even in the presence of a decryption oracle, has become the defacto notion of security for public-key encryption under active attack. In this manuscript, for…
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…
One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the…
Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first undeniable signature schemes using the conjugacy problem and the decomposition problem in the braid groups…
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…
Braids groups provide an alternative to number theoretic public cryptography and can be implemented quite efficiently. The paper proposes five signature schemes: Proxy Signature, Designated Verifier, Bi-Designated Verifier, Designated…
The McEliece public-key encryption scheme has become an interesting alternative to cryptosystems based on number-theoretical problems. Differently from RSA and ElGa- mal, McEliece PKC is not known to be broken by a quantum computer.…
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 propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.
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…
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…
In this paper we proposed two identification schemes based on the root problem. The proposed schemes are secure against passive attacks assuming that the root problem (RP) is hard in braid groups.
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…
In this note, we describe a probabilistic attack on public key cryptosystems based on the word/conjugacy problems for finitely presented groups of the type proposed recently by Anshel, Anshel and Goldfeld. In such a scheme, one makes use of…
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 paper provides an explanation of NTRU, a post quantum encryption scheme, while also providing a gentle introduction to cryptography. NTRU is a very efficient lattice based cryptosystem that appears to be safe against attacks by quantum…
We show that a number of cryptographic protocols using non-commutative semigroups including the Cha-Ko-Lee-Han-Cheon braid group public-key cryptosystem and related public-key cryptosystems such as the Shpilrain-Ushakov public-key…