1,757 research outputs found
The Rabin cryptosystem revisited
The Rabin public-key cryptosystem is revisited with a focus on the problem of
identifying the encrypted message unambiguously for any pair of primes. In
particular, a deterministic scheme using quartic reciprocity is described that
works for primes congruent 5 modulo 8, a case that was still open. Both
theoretical and practical solutions are presented. The Rabin signature is also
reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic
reciprocity that works for primes congruent 5 modulo
Exponential sums and polynomial congruences in two variables: the quasi-homogeneous case
We adapt ideas of Phong, Stein and Sturm and ideas of Ikromov and M\"uller
from the continuous setting to various discrete settings, obtaining sharp
bounds for exponential sums and the number of solutions to polynomial
congruences for general quasi-homogeneous polynomials in two variables. This
extends work of Denef and Sperber and also Cluckers regarding a conjecture of
Igusa in the two dimensional setting by no longer requiring the polynomial to
be nondegenerate with respect to its Newton diagram
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