Arkadius G. Kalka

Representation Attacks on the Braid Diffie-Hellman Public Key Encryption

AbstractThe Braid Diffie–Hellman public key cryptosystem is based on the Diffie–Hellman version of a decomposition problem (DP) in the braid group Bn. We propose a linear algebra attack on DP via the faithful Lawrence–Krammer representation

Cryptanalysis via Algebraic Spans.

\rho^{\prime}_n

NON-ASSOCIATIVE KEY ESTABLISHMENT FOR LEFT DISTRIBUTIVE SYSTEMS

. For generic and sufficiently long instance braids we recover the

Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser

\rho ^\prime _n

Complexity of relations in the braid group

-image of the private key using just one matrix inversion.

Cryptanalysis of the Algebraic Eraser and short expressions of permutations as products

It is an open problem whether the shifted conjugacy (decision) problem in B ∞ is solvable. We settle this problem by reduction to an instance of the simultaneous conjugacy problem in Bn for some n ∈ ℕ.