On Rangasamy's outsourcing algorithm for solving quadratic congruence equations

Abstract: Outsourcing computation is a desired approach for IoT (Internet of Things) devices to transfer their burdens of heavy computations to those nearby, resource-abundant cloud servers. Recently, Rangasamy presented a passive attack against two outsourcing algorithms proposed by Zhang et al. for solving quadratic congruence equations, which is widely used in IoT applications. Furthermore, he also proposed a modified algorithm to fix these schemes and claimed that his algorithm was correct and enabled secure and verifiable delegation of solving quadratic congruence equations in IoTs. However, we show that Rangasamy's modified algorithm has a flaw which makes it incorrect and also propose some further attacks to break the security claim, even when the flaw has been corrected.