TY - JOUR
T1 - Pseudorandomness and dynamics of fermat quotients*
AU - Ostafe, Alina
AU - Shparlinski, Igor E.
PY - 2011
Y1 - 2011
N2 - We obtain some theoretical and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set {0, ⋯ , p - 1}. In particular, we improve the lower bound of Vandiver [Bull. Amer. Math. Soc., 22 (1915), pp. 61-67] on the image size of Fermat quotients on the above set (from p1/2 - 1 to (1+o(1))p(log p) -2). We also consider pseudorandom properties of Fermat quotients such as uniform distribution and linear complexity.
AB - We obtain some theoretical and experimental results concerning various properties (the number of fixed points, image distribution, cycle lengths) of the dynamical system naturally associated with Fermat quotients acting on the set {0, ⋯ , p - 1}. In particular, we improve the lower bound of Vandiver [Bull. Amer. Math. Soc., 22 (1915), pp. 61-67] on the image size of Fermat quotients on the above set (from p1/2 - 1 to (1+o(1))p(log p) -2). We also consider pseudorandom properties of Fermat quotients such as uniform distribution and linear complexity.
UR - http://www.scopus.com/inward/record.url?scp=79956119865&partnerID=8YFLogxK
U2 - 10.1137/100798466
DO - 10.1137/100798466
M3 - Article
AN - SCOPUS:79956119865
SN - 0895-4801
VL - 25
SP - 50
EP - 71
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 1
ER -