Sangam: A Confluence of Knowledge Streams

A Hardware-Accelerated ECDLP with High-Performance Modular Multiplication

Show simple item record

dc.contributor Electrical and Computer Engineering
dc.creator Judge, Lyndon
dc.creator Mane, Suvarna
dc.creator Schaumont, Patrick R.
dc.date 2013-06-24T18:16:31Z
dc.date 2013-06-24T18:16:31Z
dc.date 2012-09-01
dc.date.accessioned 2023-03-01T18:54:15Z
dc.date.available 2023-03-01T18:54:15Z
dc.identifier Lyndon Judge, Suvarna Mane, and Patrick Schaumont, “A Hardware-Accelerated ECDLP with High-Performance Modular Multiplication,” International Journal of Reconfigurable Computing, vol. 2012, Article ID 439021, 14 pages, 2012. doi:10.1155/2012/439021
dc.identifier http://hdl.handle.net/10919/23259
dc.identifier https://doi.org/10.1155/2012/439021
dc.identifier.uri http://localhost:8080/xmlui/handle/CUHPOERS/281811
dc.description Elliptic curve cryptography (ECC) has become a popular public key cryptography standard. The security of ECC is due to the difficulty of solving the elliptic curve discrete logarithm problem (ECDLP). In this paper, we demonstrate a successful attack on ECC over prime field using the Pollard rho algorithm implemented on a hardware-software cointegrated platform. We propose a high-performance architecture for multiplication over prime field using specialized DSP blocks in the FPGA. We characterize this architecture by exploring the design space to determine the optimal integer basis for polynomial representation and we demonstrate an efficient mapping of this design to multiple standard prime field elliptic curves. We use the resulting modular multiplier to demonstrate low-latency multiplications for curves secp112r1 and P-192. We apply our modular multiplier to implement a complete attack on secp112r1 using a Nallatech FSB-Compute platform with Virtex-5 FPGA. The measured performance of the resulting design is 114 cycles per Pollard rho step at 100 MHz, which gives 878 K iterations per second per ECC core. We extend this design to a multicore ECDLP implementation that achieves 14.05 M iterations per second with 16 parallel point addition cores.
dc.description This research was supported in part by the National Science Foundation Grant no. 0644070.
dc.description The Virginia Tech Open Access Subvention Fund subsidized the article processing fees to make this article open access.
dc.description Published version
dc.format 15 pages
dc.format application/pdf
dc.format application/pdf
dc.language en
dc.publisher Hindawi Publishing Corporation
dc.rights Creative Commons Attribution 3.0 Unported
dc.rights http://creativecommons.org/licenses/by/3.0/
dc.rights Copyright © 2012 Lyndon Judge et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.subject Elliptic curve cryptography (ECC)
dc.subject Elliptic curve discrete logarithm problem (ECDLP)
dc.subject Prime field arithmetic
dc.title A Hardware-Accelerated ECDLP with High-Performance Modular Multiplication
dc.title International Journal of Reconfigurable Computing
dc.type Article - Refereed
dc.type Text


Files in this item

Files Size Format View
439021.pdf 1.796Mb application/pdf View/Open

This item appears in the following Collection(s)

Show simple item record

Search DSpace


Advanced Search

Browse