Flexible Prime-Field Genus 2 Hyperelliptic Curve Cryptography Processor with Low Power Consumption and Uniform Power Draw

다국어 초록 (Multilingual Abstract)

This paper presents an energy-efficient (low power) prime-field hyperelliptic curve cryptography (HECC) processor with uniform power draw. The HECC processor performs divisor scalar multiplication on the Jacobian of genus 2 hyperelliptic curves defined over prime fields for arbitrary field and curve parameters. It supports the most frequent case of divisor doubling and addition. The optimized implementation, which is synthesized in a 0.13 m standard CMOS technology, performs an 81-bit divisor multiplication in 503 ms consuming only 6.55 J of energy (average power consumption is 12.76 W). In addition, we present a technique to make the power consumption of the HECC processor more uniform and lower the peaks of its power consumption.

참고문헌 (Reference)

1 J. Fan, "ight-Weight Implementation Options for Curve-Based Cryptography: HECC is also Ready for RFID" 1-6, 2009

2 W. Rankl, "Smart Card Handbook" John Wiley & Sons Inc. 2003

3 K. Sakiyama, "Small-Footprint ALU for Public-Key Processors for Pervasive Security" 93-104, 2006

4 M. Aigner, "Seven Reasons for Application of Standardized Crypto Functionality on Low Cost Tags" 70-73, 2007

5 L. Batina, "Secure Integrated Circuits and System" Springer 179-195, 2010

6 K. Sakiyama, "Secure Design Methodology and Implementation for Embedded Public-Key Cryptosystems" Katholieke Universiteit Leuven 2007

7 A. Perrig, "SPINS: Security Protocols for Sensor Networks" 8 (8): 521-534, 2002

8 T. Lange, "SCA Resistant Parallel Explicit Formula for Addition and Doubling of Divisors in the Jacobian of Hyperelliptic Curves of Genus 2" 403-416, 2005

9 K. Finkenzeller, "RFID Handbook" John Wiley & Sons Inc. 2010

10 D. Culler, "Overview of Sensor Networks" 37 (37): 41-49, 2004

11 P.P. López, "Lightweight Cryptography in Radio Frequency Identification (RFID) Systems" Carlos III Univ. of Madrid 2008

12 J. Pelzl, "Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves" 351-365, 2003

13 Howon Kim, "Hyperelliptic Curve Crypto-Coprocessor over Affine and Projective Coordinates" 한국전자통신연구원 30 (30): 365-376, 2008

14 H. Cohen, "Handbook of Elliptic and Hyperelliptic Curve Cryptography" Chapman and Hall/CRC 2006

15 J. Fan, "HECC Goes Embedded:An Area-Efficient Implementation of HECC" 387-400, 2008

16 D. Hankerson, "Guide to Elliptic Curve Cryptography" Springer-Verlag New York Inc. 2004

17 T. Lange, "Formulae for Arithmetic on Genus 2 Hyperelliptic Curves" 15 (15): 295-328, 2005

18 G. Elias, "FPGA Design of HECC Coprocessors" 343-346, 2004

19 Y.K. Lee, "Elliptic Curve–Based Security Processor for RFID" 57 (57): 1514-1527, 2008

20 X. Fan, "Efficient Explicit Formulae for Genus 2Hyperelliptic Curves over Prime Fields and their Implementations" 155-172, 2007

21 J.P. Kaps, "Cryptography on a Speck of Dust" 40 (40): 38-44, 2007

22 T. Wollinger, "Cantor versus Harley:Optimization and Analysis of Explicit Formulae for Hyperelliptic Curve Cryptosystems" 54 (54): 861-872, 2005

23 P. Rong, "An Analytical Model for Predicting the Remaining Battery Capacity of Lithium-Ion Batteries" 14 (14): 441-451, 2006

24 N. Koblitz, "Algebraic Aspects of Cryptography" Springer-Verlag 1998

25 P. Gaudry, "Advances in Elliptic Curve Cryptography" Cambridge University Press 133-150, 2005

26 H.R. Ahmadi, "A Power-Optimized Low-Energy Elliptic-Curve Crypto-Processor" 7 (7): 1752-1759, 2010

27 H.R. Ahmadi, "A Low-Power and Low-Energy Flexible GF(p) ECC Processor" 11 (11): 724-736, 2010

28 A. Hodjat, "A Hyperelliptic Curve Crypto Coprocessor for an 8051 Microcontroller" 93-98, 2005