Marten van Dijk
Consultant, Inventor, Researcher, Applied Mathematician, & Computer Scientist
Torus Based Cryptography:
In [1] we introduced a representation for certain algebraic tori known as T_n, yielding an
asymptotically optimal n/phi(n) (phi is Euler's totient function) savings in bandwidth and storage
for key agreement, signature and encryption schemes. The drawback is the increased computational
workload.
Reducing the workload to a more practical level is addressed in [2] by developing a new representation
that is significantly faster than the original, while retaining the same level of compression. We give
the first efficient implementation of T_30(F_q), compare its performance to XTR, CEILIDH, and ECC, and
discuss further applications. The compression method outperforms CEILIDH for homomorphic ElGamal
encryption for single messages.
[1] M. van Dijk and D. Woodruff, Assymptotical optimal communication for torus based cryptography,
Advances in Cryptology - Crypto 2004, LNCS 3152, p. 157-178, 2004.
[2] M. van Dijk, R. Granger, D. Page, K. Rubin, A. Silverberg, M. Stam, and D. Woodruff, Practical
cryptography in high dimensional tori, Advances in Cryptology - Eurocrypt 2005, p. 234-250, 2005.
© 2009 Marten van Dijk .
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