  This paper presents a comprehensive investigation into encrypted computations
using the CKKS (Cheon-Kim-Kim-Song) scheme, with a focus on multi-dimensional
vector operations and real-world applications. Through two meticulously
designed experiments, the study explores the potential of the CKKS scheme in
Super Computing and its implications for data privacy and computational
efficiency. The first experiment reveals the promising applicability of CKKS to
matrix multiplication, indicating marginal differences in Euclidean distance
and near-to-zero mean square error across various matrix sizes. The second
experiment, applied to a wildfire dataset, illustrates the feasibility of using
encrypted machine learning models without significant loss in accuracy. The
insights gleaned from the research set a robust foundation for future
innovations, including the potential for GPU acceleration in CKKS computations
within TenSEAL. Challenges such as noise budget computation, accuracy loss in
multiplication, and the distinct characteristics of arithmetic operations in
the context of CKKS are also discussed. The paper serves as a vital step
towards understanding the complexities and potentials of encrypted
computations, with broad implications for secure data processing and privacy
preservation in various scientific domains.
