  Secure multi-party computation provides a wide array of protocols for
mutually distrustful parties be able to securely evaluate functions of private
inputs. Within recent years, many such protocols have been proposed
representing a plethora of strategies to securely and efficiently handle such
computation. These protocols have become increasingly efficient, but their
performance still is impractical in many settings. We propose new approaches to
some of these problems which are either more efficient than previous works
within the same security models or offer better security guarantees with
comparable efficiency. The goals of this research are to improve efficiency and
security of secure multi-party protocols and explore the application of such
approaches to novel threat scenarios. Some of the novel optimizations employed
are dynamically switching domains of shared secrets, asymmetric computations,
and advantageous functional transformations, among others. Specifically, this
work presents a novel combination of Shamir and Additive secret sharing to be
used in parallel which allows for the transformation of efficient protocols
secure against passive adversaries to be secure against active adversaries.
From this set of primitives we propose the construction of a comparison
protocol which can be implemented under that approach with a complexity which
is more efficient than other recent works for common domains of interest.
Finally, we present a system which addresses a critical security threat for the
protection and obfuscation of information which may be of high consequence.
