Efficient Elliptic-Curve Cryptography Using Curve25519 on Reconfigurable Devices

  • Pascal Sasdrich
  • Tim Güneysu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8405)


Elliptic curve cryptography (ECC) has become the predominant asymmetric cryptosystem found in most devices during the last years. Despite significant progress in efficient implementations, computations over standardized elliptic curves still come with enormous complexity, in particular when implemented on small, embedded devices. In this context, Bernstein proposed the highly efficient ECC instance Curve25519 that was shown to achieve new ECC speed records in software providing a high security level comparable to AES with 128-bit key. These very tempting results from the software domain have led to adoption of Curve25519 by several security-related applications, such as the NaCl cryptographic library or in anonymous routing networks (nTor). In this work we demonstrate that even better efficiency of Curve25519 can be realized on reconfigurable hardware, in particular by employing their Digital Signal Processor blocks (DSP). In a first proposal, we present a DSP-based single-core architecture that provides high-performance despite moderate resource requirements. As a second proposal, we show that an extended architecture with dedicated inverter stage can achieve a performance of more than 32,000 point multiplications per second on a (small) Xilinx Zynq 7020 FPGA. This clearly outperforms speed results of any software-based and most hardware-based implementations known so far, making our design suitable for cheap deployment in many future security applications.


FPGA DSP ECC Curve25519 Diffie-Hellman Xilinx Zynq 


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  1. 1.
    ANSI X9.62-2005. American National Standard X9.62: The Elliptic Curve Digital Signature Algorithm (ECDSA). Technical report, Accredited Standards Committee X9 (2005),
  2. 2.
    Bernstein, D.J.: Curve25519: New Diffie-Hellman Speed Records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 207–228. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    de Dormale, G.M., Quisquater, J.-J.: High-speed hardware implementations of elliptic curve cryptography: A survey. J. Syst. Archit. 53(2-3), 72–84 (2007)CrossRefGoogle Scholar
  4. 4.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644–654 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    ECRYPT. eBATS: ECRYPT Benchmarking of Asymmetric Systems. Technical report (March 2007),
  6. 6.
    ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31, 469–472 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Güneysu, T., Paar, C.: Ultra High Performance ECC over NIST Primes on Commercial FPGAs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 62–78. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48, 203–209 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Lenstra, A.K., Verheul, E.R.: Selecting Cryptographic Key Sizes. Journal of Cryptology 14(4), 255–293 (2001)zbMATHMathSciNetGoogle Scholar
  10. 10.
    McIvor, C., McLoone, M., McCanny, J.: An FPGA elliptic curve cryptographic accelerator over GF(p). In: Irish Signals and Systems Conference (ISSC), pp. 589–594 (2004)Google Scholar
  11. 11.
    Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)Google Scholar
  12. 12.
    Montgomery, P.L.: Speeding the Pollard and Elliptic Curve Methods of Factorization. Mathematics of Computation 48(177), 243–264 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Orlando, G., Paar, C.: A scalable GF(p) elliptic curve processor architecture for programmable hardware. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 348–371. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Örs, S.B., Batina, L., Preneel, B., Vandewalle, J.: Hardware implementation of elliptic curve processor over GF(p). pp. 433–443 (2003)Google Scholar
  15. 15.
    Sakiyama, K., Mentens, N., Batina, L., Preneel, B., Verbauwhede, I.: Reconfigurable Modular Arithmetic Logic Unit for High-Performance Public-Key Cryptosystems. In: Bertels, K., Cardoso, J.M.P., Vassiliadis, S. (eds.) ARC 2006. LNCS, vol. 3985, pp. 347–357. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Savas, E., Tenca, A.F., Ciftcibasi, M.E., Koc, C.K.: Multiplier architectures for GF(p) and GF(2n). IEE Proc. Comput. Digit Tech. 151(2), 147–160 (2004)CrossRefGoogle Scholar
  17. 17.
    Suzuki, D.: How to Maximize the Potential of FPGA Resources for Modular Exponentiation. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 272–288. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pascal Sasdrich
    • 1
  • Tim Güneysu
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityRuhr-Universität BochumGermany

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