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Applying Euler's Totient Theory to Cryptography

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Please show/discuss extensively how number theory is applied in cryptography.

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Solution Summary

Euler's Totient Theory is also clearly reinforced.

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Number theory can be applied to public-key system in cryptograph. The core theory that we use is Euler's Totient Theory. Here is the statement.

For any a relatively prime to n, we have
a^(phi(n)) = 1 (mod n)
where phi(n) is the totient function of n and it means the number of integers relatively prime to n within Zn.

Based on Euler's Totient Theory, we can build a public-key system as ...

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