Ki Hyoung Ko
Towards Generating Secure Keys for Braid Cryptography
Braid cryptosystem was proposed in CRYPTO 2000 as an alternate public-key cryptosystem. The security of this system is based upon the conjugacy problem in braid groups. Since then, there have been several attempts to break the braid cryptosystem by solving the conjugacy problem in braid groups. In this paper, we first survey all the major attacks on the braid cryptosystem and conclude that the attacks were successful because the current ways of random key generation almost always result in weaker instances of the conjugacy problem. We then propose several alternate ways of generating hard instances of the conjugacy problem for use braid cryptography.
New Signature Scheme Using Conjugacy Problem
We propose a new digital signature scheme based on a non-commutative group where the conjugacy search problem is hard and the conjugacy decision problem is feasible. We implement our signature scheme in the braid groups and prove that an existential forgery of the implementation under no message attack gives a solution to a variation of conjugacy search problem. Then we discuss performance of our scheme under suggested parameters.