On Elliptic Curve Cryptography implementations and evaluation

Elliptic Curve Cryptography have known, in recent years, an increasing success in security applications thanks to their advantages such as a short keys size with a high security level. Their popularity has led to various implementations in terms of algorithms, curves, coordinate systems, platforms, etc. The aim of this work is first to explore actual trends of ECC-based implementations in different platforms through a review of a number of works. Secondly, to identify and gather the criteria and corresponding metrics used to evaluate the performance of these implementations. We also propose a platform for design exploration and evaluation of ECC designs.

[1]  Alfred Menezes,et al.  Guide to Elliptic Curve Cryptography , 2004, Springer Professional Computing.

[2]  Maurice Keller,et al.  Low Energy ASIC Elliptic Curve Processor , 2009, J. Low Power Electron..

[3]  Jean-Pierre Deschamps,et al.  Efficient Elliptic Curve Point Multiplication Using Digit-Serial Binary Field Operations , 2013, IEEE Transactions on Industrial Electronics.

[4]  Thomas Ristenpart,et al.  When Good Randomness Goes Bad: Virtual Machine Reset Vulnerabilities and Hedging Deployed Cryptography , 2010, NDSS.

[5]  Shuguo Li,et al.  Montgomery multiplier based on secondary booth encoded algorithm , 2007, 2007 7th International Conference on ASIC.

[6]  Leonel Sousa,et al.  A Flexible Architecture for Modular Arithmetic Hardware Accelerators based on RNS , 2014, J. Signal Process. Syst..

[7]  Reza Azarderakhsh,et al.  Efficient Algorithm and Architecture for Elliptic Curve Cryptography for Extremely Constrained Secure Applications , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Erich Wenger,et al.  An 8-bit AVR-Based Elliptic Curve Cryptographic RISC Processor for the Internet of Things , 2012, 2012 45th Annual IEEE/ACM International Symposium on Microarchitecture Workshops.

[9]  Hamad Alrimeih,et al.  Fast and Flexible Hardware Support for ECC Over Multiple Standard Prime Fields , 2014, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[10]  Ming-Der Shieh,et al.  An efficient countermeasure against power attacks for ECC over GF(p) , 2014, 2014 IEEE International Symposium on Circuits and Systems (ISCAS).

[11]  Miguel Morales-Sandoval,et al.  A performance comparison of elliptic curve scalar multiplication algorithms on smartphones , 2013, CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing.

[12]  Zhi-Hong Mao,et al.  High-Throughput Finite Field Multipliers Using Redundant Basis for FPGA and ASIC Implementations , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Ney Laert Vilar Calazans,et al.  A flexible soft IP core for standard implementations of elliptic curve cryptography in hardware , 2013, 2013 IEEE 20th International Conference on Electronics, Circuits, and Systems (ICECS).

[14]  Seok-Bum Ko,et al.  High performance scalable elliptic curve cryptosystem processor for Koblitz curves , 2013, Microprocess. Microsystems.

[15]  Jean-Luc Dekeyser,et al.  A Model-Driven Approach for Hybrid Power Estimation in Embedded Systems Design , 2011, EURASIP J. Embed. Syst..

[16]  Eric Senn,et al.  SoftExplorer: Estimating and Optimizing the Power and Energy Consumption of a C Program for DSP Applications , 2005, EURASIP J. Adv. Signal Process..

[17]  Christian Steger,et al.  Hardware/software co-design of elliptic-curve cryptography for resource-constrained applications , 2014, 2014 51st ACM/EDAC/IEEE Design Automation Conference (DAC).

[18]  Yu Zhang,et al.  A high performance ECC hardware implementation with instruction-level parallelism over GF(2163) , 2010, Microprocess. Microsystems.

[19]  Ali Afzali-Kusha,et al.  A low-power and low-energy flexible GF(p) elliptic-curve cryptography processor , 2009, Journal of Zhejiang University SCIENCE C.

[20]  Richard Moloney,et al.  Efficient Implementation of Elliptic Curve Point Operations Using Binary Edwards Curves , 2010, IACR Cryptol. ePrint Arch..

[21]  Francisco Rodríguez-Henríquez,et al.  Software implementation of binary elliptic curves: impact of the carry-less multiplier on scalar multiplication , 2011, IACR Cryptol. ePrint Arch..

[22]  Patrick Schaumont,et al.  Programmable and Parallel ECC Coprocessor Architecture: Tradeoffs between Area, Speed and Security , 2009, CHES.

[23]  Tim Güneysu,et al.  Utilizing hard cores of modern FPGA devices for high-performance cryptography , 2011, Journal of Cryptographic Engineering.

[24]  Yang,et al.  ASIP for Elliptic Curve Cryptography Based on VLIW Architecture , 2010 .

[25]  Zhe Liu,et al.  MoTE-ECC: Energy-Scalable Elliptic Curve Cryptography for Wireless Sensor Networks , 2014, ACNS.

[26]  Christof Paar,et al.  Implementation Options for Finite Field Arithmetic for Elliptic Curve Cryptosystems , 1999 .

[27]  Christof Paar,et al.  A Scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware , 2001, CHES.

[28]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[29]  Satoshi Obana,et al.  Flexible architecture optimization and ASIC implementation of group signature algorithm using a customized HLS methodology , 2011, 2011 IEEE International Symposium on Hardware-Oriented Security and Trust.

[30]  Christoph Nagl,et al.  Evaluation of the back-end design overhead for ASIC implementations of large-operand multipliers targeting resource-constrained environments , 2014, 22nd Austrian Workshop on Microelectronics (Austrochip).

[31]  Miguel Morales-Sandoval,et al.  Area/performance evaluation of digit-digit GF(2K) multipliers on FPGAS , 2013, 2013 23rd International Conference on Field programmable Logic and Applications.

[32]  N. Koblitz Elliptic curve cryptosystems , 1987 .

[33]  K. Järvinen Elliptic Curve Cryptography on FPGAs : How Fast Can We Go with a Single Chip ? , 2011 .

[34]  Patrick Longa,et al.  Efficient Techniques for High-Speed Elliptic Curve Cryptography , 2010, CHES.

[35]  Zhe Liu,et al.  New Speed Records for Montgomery Modular Multiplication on 8-Bit AVR Microcontrollers , 2014, AFRICACRYPT.

[36]  Keshab K. Parhi,et al.  Fast Reconfigurable Elliptic Curve Cryptography Acceleration for GF(2m) on 32 bit Processors , 2010, J. Signal Process. Syst..

[37]  Bülent Abali,et al.  IBM POWER7+ processor on-chip accelerators for cryptography and active memory expansion , 2013, IBM J. Res. Dev..

[38]  Reza Azarderakhsh,et al.  High-Performance Implementation of Point Multiplication on Koblitz Curves , 2013, IEEE Transactions on Circuits and Systems II: Express Briefs.

[39]  Selçuk Baktir,et al.  Elliptic Curve Cryptography on Constrained Microcontrollers Using Frequency Domain Arithmetic , 2014, ICCSA.

[40]  Tim Güneysu,et al.  Exploiting the Power of GPUs for Asymmetric Cryptography , 2008, CHES.

[41]  Hwajeong Seo,et al.  Performance enhancement of TinyECC based on multiplication optimizations , 2013, Secur. Commun. Networks.