Scaling Digital Images Using Homomorphic Encryption

Abstract

Since time immemorial, cryptography has provided secure transmission of information in an insecure environment, keeping the data secret. Not so long ago the homomorphic cryptography began to actively develop. Its distinctive feature is that this type of cryptography allows you to process encrypted data without their preliminary decryption in such a way that the result of operations on encrypted data is equivalent, after decryption, to the result of operations on open data. Because of these features, homomorphic encryption can be effectively used in various cloud services to perform secure computing and secure image processing. At the same time, it is guaranteed that no one will have open data, even the service that performs the calculations. Purpose of the work: development of methods and tools for homomorphic encryption that allow performing homomorphic implementation of image processing algorithms. Research methods: analysis of possible implementations of digital image processing using homomorphic encryption, analysis of existing problems of performing a homomorphic implementation for image processing algorithms. Results: a method for homomorphic comparison of bits and numbers presented as an array of bits is proposed; a homomorphic implementation of the EPX image resizing algorithm is proposed; the complexity of the operation is analyzed when one pixel of the original image is enlarged using the proposed method; the analysis results are presented.