Throughput/Area Optimized Architecture for Elliptic-Curve Diffie-Hellman Protocol

Abstract

This paper presents a high-speed and low-area accelerator architecture for shared key generation using an elliptic-curve Diffie-Hellman protocol over GF(2233). Concerning the high speed, the proposed architecture employs a two-stage pipelining and a Karatsuba finite field multiplier. The use of pipelining shortens the critical path which ultimately improves the clock frequency. Similarly, the employment of a Karatsuba multiplier decreases the required number of clock cycles. Moreover, an efficient rescheduling of point addition and doubling operations avoids data hazards that appear due to pipelining. Regarding the low area, the proposed architecture computes finite field squaring and inversion operations using the hardware resources of the Karatsuba multiplier. Furthermore, two dedicated controllers are used for efficient control functionalities. The implementation results after place-and-route are provided on Virtex-7, Spartan-7, Artix-7 and Kintex-7 FPGA (field-programmable gate arrays) devices. The utilized FPGA slices are 5102 (on Virtex-7), 5634 (on Spartan-7), 5957 (on Artix-7) and 6102 (on Kintex-7). In addition to this, the time required for one shared-key generation is 31.08 (on Virtex-7), 31.68 (on Spartan-7), 31.28 (on Artix-7) and 32.51 (on Kintex-7). For performance comparison, a figure-of-merit in terms of throughputarea is utilized which shows that the proposed architecture is 963.3 and 2.76 times faster as compared to the related architectures. In terms of latency, the proposed architecture is 302.7 and 132.88 times faster when compared to the most relevant state-of-the-art approaches. The achieved results and performance comparison prove the significance of presented architecture in all those shared key generation applications which require high speed with a low area.

A Coprocessor Architecture for 80/112-bit Security Related Applications

“…If Node1 wants to communicate with Node2 then the ECDH steps include: (i) Node1 and Node2 use the same ECC configurations to prompt the required setup, (ii) computation of PM at each node (Node1 and Node2) for public key generation, (iii) exchange of generated public keys between two nodes (Node1 and Node2 in this demonstration example), and (iv) computation of PM on Node1 and Node2 for shared key generation. For mathematical structures and additional descriptions of ECDH protocol, we refer readers/designers to follow [6,14].…”

“…Several PM algorithms are available in the literature. According to [14,15,28,30,31], the Double and Add algorithm is more convenient for unified models of ECC, e.g., Edwards, Huff, Twisted Edwards, etc. The Lopez Dahab PM algorithm is an attractive choice for achieving instruction-level parallelism for performance improvement.…”

“…In addition to the ECC layer model, the prime, i.e., GF (P), and binary, i.e., GF (2 m ), fields are available choices for implementations, where m shows the field size or supported-key length. Comparatively, the prime field is more appealing for software implementations (e.g., on microcontrollers) while binary fields have a preference due to its accelerations on hardware platforms such as fieldprogrammable-gate-array (FPGA) and application-specific-integrated-circuits (ASICs) [6,[11][12][13][14][15]. Due to reconfigurability, ease of availability in the market, low development cost, etc, we have selected the GF (2 m ) field for implementations on FPGA in this work.…”

“…One of the examples includes the fourth industrial revolution (also named industry 4.0) which brings rapid growth in technology, industries and societal patterns due to the demand for increasing interconnectivity of several devices over the unsecured internet. Moreover, industry 4.0 emphasizes the notion of automation of numerous applications to facilitate human daily life [14]. More specifically, in the case of digitalization, automation requires higher security, e.g., key authentication or key agreement.…”

Evaluating Software Security in the Era of Quantum Computer by Using Fuzzy TOPSIS

“…The communication between the sender and receiver only decrypts the message by the secure key. One-way function follows a sort of calculation where you can compute a result for information [15]. Notwithstanding, it is hypothetically difficult to get the individual contribution from an arbitrary outcome.…”