分野別セミナー

Pseudorandom sequences, that is, sequences which are generated with
deterministic algorithms but look random, have many applications, for
example in cryptography, in wireless communication or in numerical methods.
In this work, we are interested in studying the properties of
pseudorandomness of sequences derived from hyperelliptic curves of genus
2. In particular, we look at two different ways of generating
sequences, that is, the linear congruential generator and the Frobenius
endomorphism generator over hyperelliptic curves of genus 2. We show
that these sequences possess good pseudorandom properties in terms of
linear complexity. Our method uses an embedding of the Jacobian into
the projective space of dimension 8 provided by David Grant, which gives
explicit addition formulas for elements on the Jacobian.


（連絡先：縫田 nuida@imi.kyushu-u.ac.jp ）