Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards Curve

Abstract

In this article, we present a high-performance hardware architecture for Elliptic curve based (authenticated) key agreement protocol “Elliptic Curve Menezes, Qu and Vanstone” (ECMQV) over Binary Edwards Curve (BEC). We begin by analyzing inversion module on a 251-bit binary field. Subsequently, we present Field Programmable Gate Array (FPGA) implementations of the unified formula for computing elliptic curve point addition on BEC in affine and projective coordinates and investigate the relative performance of these two coordinates. Then, we implement the w -coordinate based differential addition formulae suitable for usage in Montgomery ladder. Next, we present a novel hardware architecture of BEC point multiplication using mixed w -coordinates of the Montgomery laddering algorithm and analyze it in terms of resistance to Simple Power Analysis (SPA) attack. In order to improve the performance, the architecture utilizes registers efficiently and uses efficient scheduling mechanisms for the BEC arithmetic implementations. Our implementation results show that the proposed architecture is resistant against SPA attack and yields a better performance when compared to the existing state-of-the-art BEC designs for computing point multiplication (PM). Finally, we present an FPGA design of ECMQV key agreement protocol using BEC defined over GF(2 251 ). The execution of ECMQV protocol takes 66.47μs using 32,479 slices on Virtex-4 FPGA and 52.34μs using 15,988 slices on Virtex-5 FPGA. To the best of our knowledge, this is the first FPGA design of the ECMQV protocol using BEC.

Field Programmable Gate Array based elliptic curve Menezes‐Qu‐Vanstone key agreement protocol realization using Physical Unclonable Function and true random number generator primitives

“…This is due to the fact that our design uses a 251-bit finite field while those in [13,26] use 163-bit and 233-bit finite fields, respectively. Moreover, the proposed design consumes a larger area but outperforms the BEC design [19] in both speed and area-time (AT) metrics. Furthermore, our proposed BEC PM design yields a better performance when compared to the earlier reported BEC designs [13,19,23,24,26,27].…”

“…Moreover, it is intrinsically resistant to a simple power analysis (SPA). When ECPM adopts the same module for PD and PA, the bit pattern of the private key cannot be revealed by SPA [19].…”

“…Further, BEC designs on w-coordinate using the digit-level multiplier have been investigated in [13,[25][26][27]. Recently, we have reported the FPGA implementation of Elliptic Curve MQV key agreement protocol over BEC [19]. In that prototype implementation [19], the longterm (static) secret key and the seed of the short-term secret key are stored in read-only memory (ROM).…”

Secure Key Exchange Against Man-in-the-Middle Attack: Modified Diffie-Hellman Protocol

“…On the one hand, this protocol offers key authentication and transmission confidentiality. On the other hand, MQV is vulnerable to the attack of unknown key sharing [18].…”

An Optimized Architecture for Binary Huff Curves With Improved Security

“…Other models (Hessian, Edward and Huff) contain built-in unified PA laws to provide a resistance against SPA attacks [8], [9], [17]. Furthermore, the use of double and add PM algorithm in Hessian, Edward and Huff models provides some additional security [18], [19]. It is important to note that the preventive models of Hessian and Edward provide higher throughputs as compared to BHC model.…”