Abstract:
In this thesis, we study some computational problems in permutation group theory and
their applications to public-key cryptography. The primary goal of this thesis is to come
up with a cryptosystem similar to the McEliece cryptosystem using permutation groups
instead of vector spaces over finite fields. Like vector spaces, permutation groups too have
been explored as a setting for error-correcting codes. These objects are called permutation
codes. We propose a framework for such a cryptosystem and also come up with several
classical attacks on it. We prove that the cryptosystem using transitive permutation groups
is quantum-secure. We also explore using the permutation codes proposed by Bailey and
Cameron in our cryptosystem. Although our cryptosystem using permutation codes that
exist currently is insecure, we hope that this work would encourage research on coming up
with new classes of permutation codes with efficient decoding algorithms.