Abstract
Pervasive networks with low-cost embedded 8-bit processors are set to change our day-to-day life. Public-key cryptography provides crucial functionality to assure security which is often an important requirement in pervasive applications. However, it has been the hardest to implement on constraint platforms due to its very high computational requirements. This contribution describes a proof-of-concept implementation for an extremely low-cost instruction set extension using reconfigurable logic, which enables an 8-bit micro-controller to provide full size elliptic curve cryptography (ECC) capabilities. Introducing full size public-key security mechanisms on such small embedded devices will allow new pervasive applications. We show that a standard compliant 163-bit point multiplication can be computed in 0.113 sec on an 8-bit AVR micro-controller running at 4 Mhz with minimal extra hardware, a typical representative for a low-cost pervasive processor. Our design not only accelerates the computation by a factor of more than 30 compared to a software-only solution, it also reduces the code-size, data-RAM and power requirements.
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References
ANSI X9.62-1999. The Elliptic Curve Digital Signature Algorithm. Technical report, ANSI (1999)
Bailey, D.V., Paar, C.: Optimal Extension Fields for Fast Arithmetic in Public- Key Algorithms. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 472–485. Springer, Heidelberg (1998)
Blake, I., Seroussi, G., Smart, N.: Elliptic Curves in Cryptography. London Mathematical Society Lecture Notes Series, vol. 265. Cambridge University Press, Cambridge (1999)
Brown, M., Cheung, D., Hankerson, D., Hernandez, J.L., Kirkup, M., Menezes, A.: PGP in Constrained Wireless Devices. In: Proceedings of the 9th USENIX Security Symposium (August 2000)
Chung, J.W., Sim, S.G., Lee, P.J.: Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 57–70. Springer, Heidelberg (2000)
Ernst, M., Jung, M., Madlener, F., Huss, S., Blümel, R.: A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over GF(2n). In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 381–399. Springer, Heidelberg (2002)
Guajardo, J., Bluemel, R., Krieger, U., Paar, C.: Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP430x33x Family of Microcontrollers. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 365–382. Springer, Heidelberg (2001)
Handschuh, H., Paillier, P.: Smart Card Crypto-Coprocessors for Public-Key Cryptography. In: Quisquater, J.-J., Schneier, B. (eds.) Proceedings of the The International Conference on Smart Card Research and Applications, pp. 372–379. Springer, Heidelberg (2000)
Hankerson, D., López Hernandez, J., Menezes, A.: Software Implementation of Elliptic Curve Cryptography Over Binary Fields. In: Koç, Ç., Paar, C. (eds.) CHES 2000. LNCS, vol. 1965, p. 1. Springer, Heidelberg (2000)
Hasegawa, T., Nakajima, J., Matsui, M.: A Practical Implementation of Elliptic Curve Cryptosystems over GF(p) on a 16-bit Microcomputer. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 182–194. Springer, Heidelberg (1998)
IEEE. Standard Specifications for Public-Key Cryptography (2000)
ISO/IEC. Information technology – Security techniques – Cryptographic techniques based on elliptic curves (2002)
Janssens, S., Thomas, J., Borremans, W., Gijsels, P., Verhauwhede, I., Vercauteren, F., Preneel, B., Vandewalle, J.: Hardware/software co-design of an elliptic curve public-key cryptosystem (2001)
Koblitz, N.: Elliptic curve cryptosystems. Mathematics of Computation 48, 203–209 (1987)
Kumar, S., Girimondo, M., Weimerskirch, A., Paar, C., Patel, A., Wander, A.S.: Embedded End-to-End Wireless Security with ECDH Key Exchange. In: Proceedings of the 46th IEEE International Midwest Symposium on Circuits and Systems — MWSCAS 2003 (December 2003)
López, J., Dahab, R.: Fast multiplication on elliptic curves over GF(2m) without precomputation. In: Koç, Ç., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 316–327. Springer, Heidelberg (1999)
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)
NIST. Recommended Elliptic Curves for Federal Government Use (May 1999)
Schroeppel, R., Orman, H., O’Malley, S., Spatscheck, O.: Fast key exchange with elliptic curve systems. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 43–56. Springer, Heidelberg (1995)
Song, L., Parhi, K.K.: Low energy digit-serial/parallel finite field multipliers. Journal of VLSI Signal Processing 19(2), 149–166 (1998)
De Win, E., Bosselaers, A., Vandenberghe, S., De Gersem, P., Vandewalle, J.: A fast software implementation for arithmetic operations in GF(2n). In: Kim, K.-C., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 65–76. Springer, Heidelberg (1996)
Woodbury, A., Bailey, D.V., Paar, C.: Elliptic curve cryptography on smart cards without coprocessors. In: CARDIS 2000, Bristol, UK, September 20–22, Kluwer, Dordrecht (2000)
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Kumar, S., Paar, C. (2004). Reconfigurable Instruction Set Extension for Enabling ECC on an 8-Bit Processor. In: Becker, J., Platzner, M., Vernalde, S. (eds) Field Programmable Logic and Application. FPL 2004. Lecture Notes in Computer Science, vol 3203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30117-2_60
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DOI: https://doi.org/10.1007/978-3-540-30117-2_60
Publisher Name: Springer, Berlin, Heidelberg
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