Publickey encryption by ordering

In 1999, public key cryptography using the matrix was devised by a hish school student of 16 yesrs old girl Sarah Flannery. This cryptosystem seemed faster than RSA, and it's having the strength to surpass even the encryption to RSA. However, this encryption scheme was broken bfore har papers were published. In this paper, We try to construct publickey encryption scheme from permutation group that is equivalent to matrix as noncommutative group. And we explore the potential of this cryptsystem through implementation.