Towards generating secure keys for braid cryptography

Abstract

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 article, 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.

Conjugate adjoining problem in braid groups and new design of braid-based signatures

“…If the private keys are selected carefully, all known heuristic attacks on braid-based schemes will be unsuccessful [20]. According to [7], the complexity of carrying brute force attacks towards braid-based schemes is proportional to exp( 1 2 ln log n), where n and l are the braid index and the canonical length of the involved braids.…”

“…For details regarding the ways to construct such a CSP-hard pair generator, please refer to [10,16,20,26]. In particular in [20], Ko et al proposed several promising ways to generate hard instances of the conjugacy problem for braid cryptography.…”

“…In particular in [20], Ko et al proposed several promising ways to generate hard instances of the conjugacy problem for braid cryptography. The manner of choosing good parameters and CSP-hard pair generators is a nontrivial problem that is beyond the scope of this paper.…”

“…Recently, Ko et al [20] also analyzed the current attacks and proposed some new methods for generating secure keys for braid cryptography.…”

Key exchange protocols over noncommutative rings. The case of

“…Below we mention a few of them without going into details. In [3,4,20,19], the authors suggest to use the braid groups as platform groups for their respective protocols. In [25] the authors propose a PKC scheme whose security is based on the DLP problem for the automorphism defined by the conjugation operation and the difficulty to find the conjugate element on finite nonabelian groups.…”