Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors

  • Hwajeong Seo
  • Howon Kim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7690)


In this paper, we revisit the “operand caching” method for multi-precision multiplication, which reduces the number of required load instructions by caching the operands [6]. With the previous method, we can achieve high performance in terms of multiplication speed with modern micro-processors. However, this method does not provide full operand caching when changing the row of partial products. To overcome this problem, we propose a novel method, i.e., “consecutive operand caching”. We divide partial products and reconstruct them yielding common operands between previous and new partial products. Finally, we reduce the number of load instructions and boost the speed of multi-precision multiplication by 3.85%, as compared to previous best known results.


Multi-precision Multiplication Public-Key Cryptography Consecutive Operand-Caching Method Embedded Microprocessors 


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  1. 1.
    Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Comm. ACM 21(2), 120–126 (1977)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer (2004)Google Scholar
  3. 3.
    Devegili, A.J., Scott, M., Dahab, R.: Implementing Cryptographic Pairings over Barreto-Naehrig Curves. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 197–207. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Comba, P.: Exponentiation cryptosystems on the IBM PC. IBM Systems Journal 29(4), 526–538 (1990)CrossRefGoogle Scholar
  5. 5.
    Gura, N., Patel, A., Wander, A., Eberle, H., Shantz, S.C.: Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 119–132. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Hutter, M., Wenger, E.: Fast Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 459–474. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Hill, J.L., Culler, D.E.: Mica: A wireless platform for deeply embedded networks. IEEE Micro 22, 12–24 (2002)CrossRefGoogle Scholar
  8. 8.
    Atmel, 8 bit AVR Microcontroller ATmega128(L) Manual (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hwajeong Seo
    • 1
  • Howon Kim
    • 1
  1. 1.Computer EngineeringPusan National UniversityPusanRepublic of Korea

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