At CHES 2000, Schindler introduced a timing attack that enables the factorization of an RSA-modulus if RSA implementations use the Chinese Remainder Theorem and Montgomery multiplication. In this paper we introduce another approach for deriving the secret prime factor by focusing on the conditional branch Schindler used in his attack. One of the countermeasures against Schindler’s attack is the...

Node localization plays an important role in many practical applications of wireless underground sensor networks (WUSNs), such as finding the locations of earthquake epicenters, underground explosions, and microseismic events in mines. It is more difficult to obtain the time-difference-of-arrival (TDOA) measurements in WUSNs than in terrestrial wireless sensor networks because of the unfavorabl...

A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups. In case of compartmented secret sharing, the set of users is partitioned into compartments and the secret can be recovered only if the number of participants from any compartment is greater than a fixe...

This paper explores basic number theory including the groups, the rings and the units of modulo classes. It concludes with the Chinese Remainder Theorem. The goal is to examine these objects, their properties and to gain insight into their relationship with other sets.

Recent days, research in wireless network becomes major area for the past few decades. In wireless routing many routing methods such as table driven, source driven; many characteristics such as reactive routing, proactive routing; many routing algorithms such as dijikstra’s shortest path, distributed bell-man ford algorithm are proposed in the literature. For effective wireless routing, the rec...

We present a space-efficient algorithm to compute the Hilbert class polynomial HD(X) modulo a positive integer P , based on an explicit form of the Chinese Remainder Theorem. Under the Generalized Riemann Hypothesis, the algorithm uses O(|D|1/2+ log P ) space and has an expected running time of O(|D|1+ ). We describe practical optimizations that allow us to handle larger discriminants than othe...

This paper presents a fast parallel garner algorithm for Chinese remainder theorem. The variables in garner algorithm are divided into public parameters that are constants for fixed module and private parameters that represent random input integers. We design the parallel garner algorithm by analyzing the data dependencies of these arithmetic operations for computing public variables and privat...