Page 73 - Cyber Warnings

In the need for new encryption multivariate-quadratic public-key signature schemes are a great
option for quantum computer resistant signature schemes. These types of encryption are young
and similar systems to them have been broken in the past leaving only a few versions that are
still used today. Some versions commonly used include: Enhanced Tame Triangular System
(enTTS), Rainbow, and Unbalanced Oil and Vinegar(UOV). The strength behind this encryption
method comes from the multivariate polynomials which means the polynomials depend on more
than one variable to be created. In the UOV scheme variables are grouped into two separate
groups and then mixed into a central polynomial.

The unbalanced aspect of this scheme is referring to the relation of the two groups of variables,
oil and vinegar. There is always more vinegar than oil variables. The Rainbow scheme is built
on the UOV scheme and layers multiple polynomials developed using the UOV scheme on top
of each other dependent on the previous layer. The next layer uses the results from the
previous below it to calculate the new polynomial for that layer. This process can be repeated
an infinite amount of times, theoretically. Due to the layering aspect of this scheme the variables
can be smaller leading to a smaller public and private key which makes it easier to decrypt and
verify on part of the sender and receiver using the system (Czypek 8).

Quantum computers incorporate the laws of quantum mechanics into the way they operate so it
only makes sense for them to have new quantum encryption along with them. Fortunately for us
it just so happens that the laws of physics include its own form of encryption along with quantum
mechanics. The No-Go theorem, which states that a particular situation is not physically
possible, includes several sub-theorems: Bell’s theorem, Kochen-Specker theorem, Gleason’s
theorem, no-teleportation theorem, no-cloning theorem, no-broadcast theorem, and no-deleting
theorem.

Bell’s theorem is the name for a family of results, showing us that it’s impossible for a local
realistic interpretation of quantum mechanics (Bell) meaning it’s impossible to have an accurate
definition for quantum mechanics since there is a seemingly random aspect of quantum physics.
The Kochen-Specker theorem compliments Bell’s by placing limits on types of hidden variable
theories used to explain the probabilistic nature of quantum mechanics. It states that it is not
possible to add values to physical observables while, at the same time, preserving the functional
relations between them (Kochen).

A quantum particle cannot be observed and have a value added to the quantum particle and still
be paired with another particle through quantum entanglement. Gleason’s theorem, in summary,
says every quasi-state is already a state and that a quantum state is determined by only
knowing the answer to all of the possible yes or no questions (Gleason). These theories
together counter the hidden variable theories which attempt to explain the randomness of
quantum mechanics as a deterministic model featuring hidden states, saying that all
observables defined for a quantum system have definite values at all times.

The no-cloning, no-delete, no-teleportation, and no-broadcast theorem group explains why
quantum information is so secure and how it incorporates an encryption like system just from
the nature of quantum mechanics themselves. The no-cloning theorem says that it is impossible

73 Cyber Warnings E-Magazine – June 2017 Edition
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