Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2005: Advances in Cryptology – EUROCRYPT 2005 pp 234-250

Practical Cryptography in High Dimensional Tori

  • Marten van Dijk
  • Robert Granger
  • Dan Page
  • Karl Rubin
  • Alice Silverberg
  • Martijn Stam
  • David Woodruff
Conference paper

DOI: 10.1007/11426639_14

Volume 3494 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
van Dijk M. et al. (2005) Practical Cryptography in High Dimensional Tori. In: Cramer R. (eds) Advances in Cryptology – EUROCRYPT 2005. EUROCRYPT 2005. Lecture Notes in Computer Science, vol 3494. Springer, Berlin, Heidelberg

Abstract

At Crypto 2004, van Dijk and Woodruff introduced a new way of using the algebraic tori Tn in cryptography, and obtained an asymptotically optimal n/φ(n) savings in bandwidth and storage for a number of cryptographic applications. However, the computational requirements of compression and decompression in their scheme were impractical, and it was left open to reduce them to a practical level. We give a new method that compresses orders of magnitude faster than the original, while also speeding up the decompression and improving on the compression factor (by a constant term). Further, we give the first efficient implementation that uses T30, compare its performance to XTR, CEILIDH, and ECC, and present new applications. Our methods achieve better compression than XTR and CEILIDH for the compression of as few as two group elements. This allows us to apply our results to ElGamal encryption with a small message domain to obtain ciphertexts that are 10% smaller than in previous schemes.

Keywords

torus-based cryptographydiscrete-log based cryptography
Download to read the full conference paper text

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marten van Dijk
    • 1
  • Robert Granger
    • 2
  • Dan Page
    • 2
  • Karl Rubin
    • 3
  • Alice Silverberg
    • 3
  • Martijn Stam
    • 2
  • David Woodruff
    • 1
  1. 1.MIT CSAIL 
  2. 2.Department of Computer ScienceUniversity of Bristol 
  3. 3.Department of MathematicsIrvine