Monthly Archives: March 2016

Basic concepts of Chinese Remainder Theorem with respect of RSA/AES


Chinese Remainder Theorem

Suppose n_{1},n_{2}, ... , n_{k} are positive integers and coprime in pair. For any sequence of integers a_{1}, a_{2}, ... , a_{n}, there exists an integer x solving the following system of congruence equations:

\begin{cases} x \equiv a_1 \pmod{n_1} \\ \quad \cdots \\ x \equiv a_k \pmod{n_k} \end{cases}
There exists an unique modulo solution of the system of simultaneous congruences above:

x = a_1 M_1 y_1+ \cdots +a_k M_k y_k \pmod{M }in which:
\begin{aligned}<br />
M &= m_1 \cdots m_k \\<br />
M_1 &= \frac{M}m_1 , \cdots, M_k = \frac{M}m_k \\<br />
y_1 &\equiv (M_1)^{-1} \pmod{m_1}, \cdots , y_k\equiv (M_k)^{-1}\pmod{m_k}<br />

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Introduction to Threshold signature scheme


  1. Introduction

Assuming there are 20 employees in a company, and if each employee has his or her own copy of the secret key then it is hard to assure on individuals due to compromise and machine break down. In the other hand, if there is a valid signature requires all 20 employees’ signature in the company then it will be very secure but not be easy to use. Therefore we can implement a scheme which requires only sign 5 or more out of 20 employees then it will be valid and that is exactly what a (5,20) threshold signature scheme tries to achieve. In addition, if a threat agent wants to compromise the system and obtain a message, he must compromise at least 5 people in the scheme and that is a harder thing to do compared to a traditional public scheme.

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Deciphering Ceasar basic concept



Ciphertext: “VaqrprzoreoeratraWhyvhfraJnygreUbyynaqreqrgjrroebrefinaRqvguZnetbganne





The given ciphertext has only letters without space, punctuation or separated key, there are two classic cipher systems such as substitution cipher and transposition cipher which are known to be easy to attack by using frequency analysis or bruteforce techniques. Continue reading Deciphering Ceasar basic concept