Hide the Modulus: A Secure Non-Interactive Fully Verifiable Delegation Scheme for Modular Exponentiations via CRT

Abstract

Security protocols using public-key cryptography often requires large number of costly modular exponentiations (MEs). With the proliferation of resource-constrained (mobile) devices and advancements in cloud computing, delegation of such expensive computations to powerful server providers has gained lots of attention. In this paper, we address the problem of verifiably secure delegation of MEs using two servers, where at most one of which is assumed to be malicious (the OMTUP-model). We first show verifiability issues of two recent schemes: We show that a scheme from IndoCrypt 2016 does not offer full verifiability, and that a scheme for n simultaneous MEs from AsiaCCS 2016 is verifiable only with a probability 0.5909 instead of the author’s claim with a probability 0.9955 for n= 10. Then, we propose the first non-interactive fully verifiable secure delegation scheme by hiding the modulus via Chinese Remainder Theorem (CRT). Our scheme improves also the computational efficiency of the previous schemes considerably. Hence, we provide a lightweight delegation enabling weak clients to securely and verifiably delegate MEs without any expensive local computation (neither online nor offline). The proposed scheme is highly useful for devices having (a) only ultra-lightweight memory, and (b) limited computational power (e.g. sensor nodes, RFID tags).