Seong-Hun Paeng

Volume and diameter of a graph and Ollivier's Ricci curvature

We obtain upper bounds of diameter and volume for finite graphs by Olliviers Ricci curvature.

On the mean square displacement of a random walk on a graph

We study a relation between Olliviers Ricci curvature and the mean square displacement of a random walk on a graph. Also we obtain explicit formulas for the mean square displacement of random walks on regular polyhedra.

Ollivier's Ricci curvature and the coloring of graphs

We obtain lower bounds on the clique number and chromatic number for finite simple graphs using Olliviers Ricci curvature. Also we study the relations between girth and curvature. From these, we obtain curvature conditions for 3-colorability of a planar graph.

On the security of cryptosystem using automorphism groups

A public key cryptosystem using the discrete logarithm problem (DLP) in inner automorphism groups was proposed by Paeng et al. [Advances in Cryptology-Crypto, 2001, pp. 470-485; Preprint, 2001]. We show that there are subexponential time algorithms to solve the DLP in inner automorphism groups of suggested non-abelian groups.

Attacks to Xu-Tilborg's conference key distribution scheme

In this letter, we show that Xu-Tilborgs conference key distribution scheme does not meet the forward secrecy and is vulnerable to impersonation attacks. Also, we propose a modified version which satisfies the forward secrecy and is secure against impersonation attacks.

Volume entropy and integral Ricci curvatures over closed geodesics

We obtain an upper bound of the volume entropy and the simplicial volume with integrals of Ricci curvature over closed geodesics and apply it to the real Schwarz lemma by Besson, Courtois and Gallot.

Buser's isoperimetric inequalities with integral norms of Ricci curvature

We generalize Buser’s isoperimetric inequality with integral norms of Ricci curvature.

Approximately n-secting an angle

It is a well-known fact that there exists an angle that cannot be trisected with a straightedge and a compass. In general, it is impossible to divide an arbitrary angle into n-angles equally with only a straightedge and a compass, where n is a positive integer. We give an efficient algorithm to divide an arbitrary angle into n-angles almost equally with only a straightedge and a compass. Using this method, we can construct an almost regular n-gon for arbitrary n.

Representations of finite fields and the Naini-Seberry partitioning problem

Safavi-Naini and Seberry suggested a subliminal channel based on partitioning a set /spl Gamma/ of the generator matrices of error-correcting codes. We give a systematic procedure to partition /spl Gamma/ into E/sub i/s with |E/sub i/|=2/sup m/ for any m, which is more efficient than the method in Yang, C-N et al., (1997).

On the fundamental group of manifolds with almost nonnegative Ricci curvature

Gromov conjectured that the fundamental group of a manifold with almost nonnegative Ricci curvature is almost nilpotent. This conjecture is proved under the additional assumption on the conjugate radius. We show that there exists a nilpotent subgroup of finite index depending on a lower bound of the conjugate radius.