Elliptic Curve Based Zero Knowledge Proofs and Their Applicability on\n Resource Constrained Devices

Abstract

Elliptic Curve Cryptography (ECC) is an attractive alternative to\nconventional public key cryptography, such as RSA. ECC is an ideal candidate\nfor implementation on constrained devices where the major computational\nresources i.e. speed, memory are limited and low-power wireless communication\nprotocols are employed. That is because it attains the same security levels\nwith traditional cryptosystems using smaller parameter sizes. Moreover, in\nseveral application areas such as person identification and eVoting, it is\nfrequently required of entities to prove knowledge of some fact without\nrevealing this knowledge. Such proofs of knowledge are called Zero Knowledge\nInteractive Proofs (ZKIP) and involve interactions between two communicating\nparties, the Prover and the Verifier. In a ZKIP, the Prover demonstrates the\npossesion of some information (e.g. authentication information) to the Verifier\nwithout disclosing it. In this paper, we focus on the application of ZKIP\nprotocols on resource constrained devices. We study well-established ZKIP\nprotocols based on the discrete logarithm problem and we transform them under\nthe ECC setting. Then, we implement the proposed protocols on Wiselib, a\ngeneric and open source algorithmic library. Finally, we present a thorough\nevaluation of the protocols on two popular hardware platforms equipped with low\nend microcontrollers (Jennic JN5139, TI MSP430) and 802.15.4 RF transceivers,\nin terms of code size, execution time, message size and energy requirements. To\nthe best of our knowledge, this is the first attempt of implementing and\nevaluating ZKIP protocols with emphasis on low-end devices. This work's results\ncan be used from developers who wish to achieve certain levels of security and\nprivacy in their applications.\n