Cryptanalysis of an Outsourced Modular Inversion Protocol

Supplementary Files



Secure Delegation
Euclidean lattices
Integer linear programming

How to Cite

Bouillaguet, C. (2023). Cryptanalysis of an Outsourced Modular Inversion Protocol. Mathematical Cryptology, 3(1), 29–43. Retrieved from


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.

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Copyright (c) 2023 Charles Bouillaguet