TY - JOUR
T1 - On pseudorandom numbers from multivariate polynomial systems
AU - Ostafe, Alina
AU - Pelican, Elena
AU - Shparlinski, Igor E.
PY - 2010/9
Y1 - 2010/9
N2 - We bound exponential sums along the orbits of essentially arbitrary multivariate polynomial dynamical systems, provided that the orbits are long enough. We use these bounds to derive nontrivial estimates on the discrepancy of pseudorandom vectors generated by such polynomial systems. We generalize several previous results and in particular suggest a new approach that eliminates the need to control the degree growth of the iterations of these polynomial systems, which has been an obstacle in all previous approaches.
AB - We bound exponential sums along the orbits of essentially arbitrary multivariate polynomial dynamical systems, provided that the orbits are long enough. We use these bounds to derive nontrivial estimates on the discrepancy of pseudorandom vectors generated by such polynomial systems. We generalize several previous results and in particular suggest a new approach that eliminates the need to control the degree growth of the iterations of these polynomial systems, which has been an obstacle in all previous approaches.
UR - http://www.scopus.com/inward/record.url?scp=77956057327&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2010.05.002
DO - 10.1016/j.ffa.2010.05.002
M3 - Article
AN - SCOPUS:77956057327
SN - 1071-5797
VL - 16
SP - 320
EP - 328
JO - Finite Fields and their Applications
JF - Finite Fields and their Applications
IS - 5
ER -