Biblio

This paper presents topological sorting methods to minimize the multiplicative depth of encrypted arithmetic expressions. The research aims to increase compatibility between nonlinear dynamic control schemes and homomorphic encryption methods, which are known to be limited by the quantity of multiplicative operations. The proposed method adapts rewrite rules originally developed for encrypted binary circuits to depth manipulation of arithmetic circuits. The paper further introduces methods to normalize circuit paths that have incompatible depth. Finally, the paper provides benchmarks demonstrating the improved depth in encrypted computed torque control of a dynamic manipulator and discusses how achieved improvements translate to increased cybersecurity.

In his book Outliers, Malcom Gladwell describes the 10,000-Hour Rule, a key to success in any field, as simply a matter of practicing a specific task that can be accomplished with 20 hours of work a week for 10 years [10]. Ongoing changes in technology and national security needs require aspiring excellent cybersecurity professionals to set a goal of 10,000 hours of relevant, hands-on skill development. The education system today is ill prepared to meet the challenge of producing an adequate number of cybersecurity professionals, but programs that use competitions and learning environments that teach depth are filling this void.