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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