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Four $$\mathbb {Q}$$ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Large Prime Characteristic Fields [chapter]

Kimmo Järvinen, Andrea Miele, Reza Azarderakhsh, Patrick Longa
2016 Lecture Notes in Computer Science  
By adapting FourQ's algorithms to hardware, we design FPGA-tailored architectures that are significantly faster than any other ECC alternative over large prime characteristic fields.  ...  We present fast and compact implementations of FourQ (ASI-ACRYPT 2015) on field-programmable gate arrays (FPGAs), and demonstrate, for the first time, the high efficiency of this new elliptic curve on  ...  Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.  ... 
doi:10.1007/978-3-662-53140-2_25 fatcat:lnlme2ralvauljvmbyf4svpcsy

FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field

Hao Li, Jian Huang, Philip Sweany, Dijiang Huang
2008 Journal of systems architecture  
Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level.  ...  In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2 283 ) as well as Tate pairing computation on supersingular elliptic curve in GF (2 283 ).  ...  Design a hardware architecture for Tate pairing. • FPGA implementation of elliptic curve cryptography. • FPGA implementation of Tate pairing.  ... 
doi:10.1016/j.sysarc.2008.04.012 fatcat:3tlovro4lbfajgk3v2ffvheydu

Solving the Discrete Logarithm of a 113-Bit Koblitz Curve with an FPGA Cluster [chapter]

Erich Wenger, Paul Wolfger
2014 Lecture Notes in Computer Science  
However, until to date only CPU clusters succeeded in computing new elliptic curve discrete logarithm records.  ...  Until to date, no attack on such a large Koblitz curve succeeded using as little resources or in such a short time frame.  ...  to Wolfgang Kastl and Jürgen Fuß from the University of Applied Sciences Upper Austria who provided sixteen ML605 boards and continuously supported us and the authors would like to thank the reviewers for  ... 
doi:10.1007/978-3-319-13051-4_22 fatcat:dtwmpjqifjghtkl5ooibot2h4q

Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve

Philipp Koppermann, Fabrizio De Santis, Johann Heyszl, Georg Sigl
2018 Transactions on Cryptographic Hardware and Embedded Systems  
Synthesized on a Xilinx Zynq-7020 FPGA, our architectures perform a key exchange with lower latency and higher throughput than any other reported implementation using prime-field elliptic curves at the  ...  We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost's genus-2 curve targeting a 128-bit security level.  ...  Acknowledgements The authors would like to thank the anonymous reviewers for their useful comments that improved the quality of the paper.  ... 
doi:10.13154/tches.v2018.i1.1-17 dblp:journals/tches/KoppermannSHS18 fatcat:6ailneqbajdqpkgllnmcbzfbtu

A Survey on Hardware Implementations of Elliptic Curve Cryptosystems [article]

Bahram Rashidi
2017 arXiv   pre-print
We first discuss different elliptic curves, point multiplication algorithms and underling finite field operations over binary fields F2m and prime fields Fp which are used in the literature for hardware  ...  In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced.  ...  Field arithmetic in F p One of the popular fields which are choice for ECC are prime fields with large prime characteristic.  ... 
arXiv:1710.08336v1 fatcat:g3gpz5lzgvc27fboa5tv4kdhze

Hardware architectures for public key cryptography

Lejla Batina, Sıddıka Berna Örs, Bart Preneel, Joos Vandewalle
2003 Integration  
RSA and Elliptic Curve Cryptography (ECC), both based on modular arithmetic. We first discuss the mathematical background and the algorithms to implement these cryptosystems.  ...  This paper presents an overview of hardware implementations for the two commonly used types of Public Key Cryptography, i.e.  ...  Therefore, coprocessors for elliptic curve cryptography are primely designed to accelerate the field multiplication.  ... 
doi:10.1016/s0167-9260(02)00053-6 fatcat:u5pkdeitprh77hcaaui66nzv24

Breaking Ciphers with COPACOBANA –A Cost-Optimized Parallel Code Breaker [chapter]

Sandeep Kumar, Christof Paar, Jan Pelzl, Gerd Pfeiffer, Manfred Schimmler
2006 Lecture Notes in Computer Science  
The hardware can be used, e.g., to attack elliptic curve cryptosystems and to factor numbers.  ...  COPA-COBANA hosts 120 low-cost FPGAs and is able to, e.g., perform an exhaustive key search of the Data Encryption Standard (DES) in less than nine days on average.  ...  Acknowledgments: We like to thank the Xilinx Inc. for the generous donation of Spartan-3 FPGAs which formed the basis of our design.  ... 
doi:10.1007/11894063_9 fatcat:ijyulubiqvdqth5u4xoplyc7yy

A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem [chapter]

Brian Baldwin, Richard Moloney, Andrew Byrne, Gary McGuire, William P. Marnane
2009 Lecture Notes in Computer Science  
This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields GF (p).  ...  To the authors' knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields GF (p).  ...  Elliptic Curves We consider an elliptic curve over the field GF (p) for some prime p, given by the affine Weierstrass equation y 2 = x 3 + Ax + B. (1) In Jacobian projective coordinates, this curve is  ... 
doi:10.1007/978-3-642-00641-8_41 fatcat:zr667ciqi5fetkxxynylnssrwe

Efficient Hardware Implementation of Fp-Arithmetic for Pairing-Friendly Curves

Junfeng Fan, Frederik Vercauteren, Ingrid Verbauwhede
2012 IEEE transactions on computers  
This paper describes a new method to speed up Fp-arithmetic in hardware for pairing-friendly curves, such as the well known Barreto-Naehrig (BN) curves.  ...  As an application we show that the performance of pairings on BN curves in hardware can be significantly improved, resulting in a factor 2.5 speed-up compared with state-of-the-art hardware implementations  ...  Pairing-Friendly curves An elliptic curve E over F p is called pairing-friendly whenever there exists a large prime r | #E(F p ) with r ≥ √ p and the embedding degree k is small enough, e.g. k ≤ log 2  ... 
doi:10.1109/tc.2011.78 fatcat:zeafwfk2mvf2xf7rchrdwlihiq

Hardware Accelerator for the Tate Pairing in Characteristic Three Based on Karatsuba-Ofman Multipliers [chapter]

Jean-Luc Beuchat, Jérémie Detrey, Nicolas Estibals, Eiji Okamoto, Francisco Rodríguez-Henríquez
2009 Lecture Notes in Computer Science  
This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves.  ...  We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier.  ...  Acknowledgments The authors would like to thank Nidia Cortez-Duarte and the anonymous referees for their valuable comments.  ... 
doi:10.1007/978-3-642-04138-9_17 fatcat:wu7f4otgcfaarg6rrozqd2gv3a

Evaluation Study of Elliptic Curve Cryptography Scalar Multiplication on Raspberry Pi4

Fatimah Alkhudhayr, Tarek Moulahi, Abdulatif Alabdulatif
2021 International Journal of Advanced Computer Science and Applications  
This paper describes the application of elliptic curve cryptography (ECC) in a simulated IoT environment to ensure the confidentiality of data passed between the connected devices.  ...  The comparison was made on the scalar multiplication of both fast and basic ECC algorithms.  ...  [20] proposed hardware architecture with high performance for elliptic curve scalar multiplication over prime field.  ... 
doi:10.14569/ijacsa.2021.0120954 fatcat:itxxcbki2vak3duaw5ee26q25u

Faster Pairing Coprocessor Architecture [chapter]

Gavin Xiaoxu Yao, Junfeng Fan, Ray C. C. Cheung, Ingrid Verbauwhede
2013 Lecture Notes in Computer Science  
We prototype the design on a Xilinx Virtex-6 FPGA using 5237 slices and 64 DSPs; a 128-bit pairing is computed in 0.358 ms running at 230MHz.  ...  In this paper, we present a high-speed pairing coprocessor using Residue Number System (RNS) which is intrinsically suitable for parallel computation.  ...  We would like to thank Nicolas Guillermin for the helpful discussion on improving the scheduling of the RNS Montgomery algorithm.  ... 
doi:10.1007/978-3-642-36334-4_10 fatcat:4cxvdwctk5cjvp3anzqaqm5ykm

ECM on Graphics Cards [chapter]

Daniel J. Bernstein, Tien-Ren Chen, Chen-Mou Cheng, Tanja Lange, Bo-Yin Yang
2009 Lecture Notes in Computer Science  
This paper also reports speeds on other graphics processors: for example, 2414 280-bit elliptic-curve scalar multiplications per second on an older NVIDIA 8800 GTS (G80), again for a general 280-bit modulus  ...  For comparison, the CHES 2008 paper "Exploiting the Power of GPUs for Asymmetric Cryptography" reported 1412 elliptic-curve scalar multiplications per second on the same graphics processor despite having  ...  Let E be an elliptic curve over Q with neutral element O. Let P be a nontorsion point on E.  ... 
doi:10.1007/978-3-642-01001-9_28 fatcat:q3hhp3jckzcmlijmiy6ahxoaea

Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit, 16-Bit, and 32-Bit Microcontrollers

Jihoon Kwon, Seog Seo, Seokhie Hong
2018 Applied Sciences  
Our 16-bit and 32-bit implementation results set new speed records for variable-base scalar multiplication.  ...  In this paper, we present the first constant-time implementations of four-dimensional Gallant-Lambert-Vanstone and Galbraith-Lin-Scott (GLV-GLS) scalar multiplication using curve Ted127-glv4 on 8-bit AVR  ...  Elliptic Curve Cryptography Let F q be a finite field with odd characteristic.  ... 
doi:10.3390/app8060900 fatcat:46julxtp4re2hk2potlxkgbahy

Enhanced Elliptic Curve Cryptography based Secure Transmission in LTE Network

2020 International Journal of Engineering and Advanced Technology  
To accomplish this necessity, in this research OPSO based Elliptic Curve Cryptography (EECC) is exhibited.  ...  On the off chance that the client is not in range with the base station needs to speak with the base station. Be that as it may, the correspondence must be secured.  ...  The implementation of Elliptic Curve Cryptography by first transforming the message into an affine point on the Elliptic Curve, over the finite prime field. and the ECC algorithm is enhanced or optimized  ... 
doi:10.35940/ijeat.c5171.029320 fatcat:t2ycxjx3dfhofewtsihz6qitn4
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