# A computer science problem by Rocco Dalto

Computer Science Level pending

A data base B contains four files $$b_{1} = (10000001)_{2}, \: b_{2} = (10001010)_{2}, \: b_{3} = (10011001)_{2}, \: b_{4} = (00000001)_{2}.$$ 

Let the prime divisors $$m_{1} = 131, \: m_{2} = 139, \: m_{3} = 157, \: m_{4} = 2$$ be the read sub keys. 

Encipher the data base using the Chinese remainder theorem and determine the Cipher text $$X.$$ 

Convert each $$b_{j}$$ in base 2 to base 10 prior to doing the problem, then set up each congruence $$X \equiv b_{j} \mod {m_{j}}$$ where $$(1 <= j <= 4)$$ and solve for $$X$$. 

Given $$N$$ files in a database and $$N$$ prime divisors(read sub keys), write a general program(in any language) to encipher the data base using the Chinese remainder theorem and determine the Cipher text $$X.$$. Do not use any predefined functions or procedures.



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