Pseudorandomness from Braid Groups

Recently the braid groups were introduced as a new source for cryptography. The group operations are performed efficiently and the features are quite different from those of other cryptographically popular groups. As the first step to put the braid groups into the area of pseudorandomness, this article presents some cryptographic primitives under two related assumptions in braid groups. First, assuming that the conjugacy problem is a one-way function, say f, we show which particular bit of the argument x is pseudorandom given f(x). Next, under the decision Ko-Lee assumption, we construct two provably secure pseudorandom schemes: a pseudorandom generator and a pseudorandom synthesizer.