The KMOV scheme is a public key cryptosystem based on an RSA modulus n = pq where p and q are large prime numbers with p ≡ q ≡ 2 (mod 3). It uses the points of an elliptic curve with equation y 2 ≡ x 3 + b (mod n). In this paper, we propose a generalization of the KMOV cryptosystem with a prime power modulus of the form n = p r q s and study its resistance to the known attacks.
In [5] it was proved that, given a distribution with zero mean and finite second moment, we can find a simply connected domain ª such that if Ø is a standard planar BM, then Ê ´ ª µ has the distribution . In this note, we extend his method to prove that if has a finite Ä Ô moment then the exit time ª has a finite moment of order Ô ¾ .
In this paper we address the question of finding the point which maximizes the pth moment of the exit time of planar Brownian motion from a given domain. We present a geometrical method for excluding parts of the domain from consideration which makes use of a coupling argument and the conformal invariance of Brownian motion. In many cases the maximizing point can be localized to a relatively small region. Several illustrative examples are presented.
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