HECC goes embedded: An area-efficient implementation of HECC In this paper we describe a high-performance, area-efficient implementation of hyperelliptic curve cryptosystems over GF (2 m ). A compact arithmetic logic unit (ALU) is proposed to perform multiplication and inversion. With this ALU, we show that divisor multiplication using affine coordinates can be efficiently supported. Besides, the required throughput of memory or register file (RF) is reduced so that area of memory/RF is reduced. We choose hyperelliptic curves using the parameters h(x)=x and f(x)=x 5 +f 3 x 3 +x 2 +f 0 . The performance of this coprocessor is substantially better than all previously reported FPGA-based implementations. The coprocessor for HECC over GF (2 83 ) uses 2316 slices and 2016 bits of Block RAM on Xilinx Virtex-II FPGA, and finishes one scalar multiplication in 311μs

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Hutter, Michael; Wenger, Erich: Fast multi-precision multiplication for public-key cryptography on embedded microprocessors (2020)
  2. Hutter, Michael; Wenger, Erich: Fast multi-precision multiplication for public-key cryptography on embedded microprocessors (2018)
  3. Gallin, Gabriel; Celik, Turku Ozlum; Tisserand, Arnaud: Architecture level optimizations for Kummer based HECC on FPGAs (2017)
  4. Costello, Craig; Lauter, Kristin: Group law computations on Jacobians of hyperelliptic curves (2012)
  5. You, Lin; Han, Guangguo; Zeng, Jiwen; Sang, Yongxuan: Computing the characteristic polynomials of a class of hyperelliptic curves for cryptographic applications (2011)
  6. Paar, Christof; Pelzl, Jan: Understanding cryptography. A textbook for students and practitioners. Foreword by Bart Preneel. (2010)
  7. Fan, Junfeng; Batina, Lejla; Verbauwhede, Ingrid: HECC goes embedded: an area-efficient implementation of HECC (2009)
  8. Sutherland, Andrew V.: A generic approach to searching for Jacobians (2009)
  9. Avanzi, R.; Thériault, N.; Wang, Z.: Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: Interplay of field arithmetic and explicit formulæ (2008)
  10. Avanzi, Roberto; Thériault, Nicolas: Effects of optimizations for software implementations of small binary field arithmetic (2007)
  11. Elias, Grace; Miri, Ali; Yeap, Tet-Hin: On efficient implementation of FPGA-based hyperelliptic curve cryptosystems (2007)
  12. Fan, Xinxin; Gong, Guang: Efficient explicit formulae for genus 2 hyperelliptic curves over prime fields and their implementations (2007)
  13. Gaudry, P.; Thomé, E.; Thériault, N.; Diem, C.: A double large prime variation for small genus hyperelliptic index calculus (2007)
  14. Jacobson, M. J.; Scheidler, R.; Stein, A.: Cryptographic protocols on real hyperelliptic curves (2007)
  15. Espinosa García, J.; Hernández Encinas, L.; Muñoz Masqué, J.: A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point (2006)
  16. Frey, Gerhard; Lange, Tanja: Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves (2006)
  17. Gaudry, P.; Houtmann, T.; Kohel, D.; Ritzenthaler, C.; Weng, A.: The 2-adic CM method for genus 2 curves with application to cryptography (2006)
  18. Jirón, I.; Soto, I.; Carrasco, R.; Becerra, N.: Hyperelliptic curves encryption combined with block codes for Gaussian channel (2006)
  19. Galbraith, Steven; Menezes, Alfred: Algebraic curves and cryptography (2005)
  20. Kitamura, Izuru; Katagi, Masanobu; Takagi, Tsuyoshi: A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two (2005)

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