Cryptanalysis of an Outsourced Modular Inversion Protocol

Abstract

Public-key cryptographic primitives involve mathematical operations that are computationally intensive for devices with limited resources. A typical approach is to offload time-consuming operations from a (computationally weak) client device to an untrusted yet computationally powerful server. Such a delegation protocol needs to achieve the privacy of the server's inputs. Recently, Tian, Yu, Zhang, Xue, Wang and Ren [IEEE Trans. Serv. Comput., vol. 15, no. 1, pp. 241-253, 2022] proposed a unimodular matrix transformation technique to realize secure outsourcing of modular inversion. We present an elementary cryptanalysis of their protocol and prove that it does not achieve the claimed security guarantees.