Cryptanalysis of Modular Exponentiation Outsourcing Protocols

Abstract Public-key cryptographic primitives are time consuming for resource-constrained devices. A classical problem is to securely offload group exponentiations from a (comparatively) weak device—the client—to an untrusted more powerful server. delegation protocol must usually meet two security objectives: privacy—the exponent or the base should not be revealed passive adversary—and verifiability—a malicious server able make client accept invalid value as result of delegated computation. Most proposed protocols relies on secret splitting and base, considerable amount literature has been devoted their analysis. Recently, Su et al. (Su, Q., Zhang, R. Xue, (2020) Secure outsourcing algorithms composite modular exponentiation based single cloud. Comput. J., 63, 1271.) Rangasamy Kuppusamy (Rangasamy, J. Kuppusamy, L. (2018) Revisiting Single-Server Algorithms Outsourcing Modular Exponentiation. In Chakraborty, D. Iwata, T. (eds), Progress in Cryptology - INDOCRYPT 2018: 19th International Conference India, New Delhi, December 912, Vol. 11356, Lecture Notes Computer Science. Springer, Heidelberg, Germany, pp. 320. exponentiations. They claim that achieve (privacy verifiability). We show these claims flawed schemes broken beyond repair. remain insecure even if one increases significantly parameters (and consequently computational communication complexities). Our attacks rely standard lattice-based cryptanalytic techniques, namely Coppersmith methods find small integer zeroes multivariate polynomials simultaneous Diophantine approximation so-called approximate greatest common divisor problem.