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