Cryptography is the science of writing and deciphering code. In the last few years
Cyber-Cryptography, or the science of writing and deciphering digital code has
become central in our society. Many methods of Cyber-Cryptography are known and
used today by some of our most important institutions.
One of the most popular methods of Cyber-Cryptography is known as Public Key
Cryptography. Many variants of Public Key Cryptography are used today, such as the
popular Diffie–Hellman Protocol and the RSA Algorithm. To combat any potential
weaknesses alternative Public Key Cryptography methods have been proposed. One
of these Methods, known as The Korean Protocol relies heavily on a mathematical
structure known as a Braid Group.
Underlying the Korean Protocol is the division of a braid group into a pair of
commutative subgroups. There is a trivial division of B n into two subgroups, which is
what has been traditionally used. A list of all such commutative subgroup pairs would
be an invaluable addition to cryptography.
We set out to categorize all commutative pairs of subgroups. In the end we were able
to create an algorithm that can generate any arbitrary commutative pair of subgroups.
Senior honors thesis. Opt-out. For access, please contact email@example.com