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# Inverse of a number watch

1. In congruences, I have a number 'a', which is co prime with another number 'n'. I factorized 'n' into primes and have worked out phi of 'n'.

The question is to do with RSA.

The question is to workout the decoding element x, and in brackets it's written, i.e a^(-1) mod phi(n).

So does that mean that I need to workout the inverse of a and that will give me the decoding element x?

If so, how do I do this?
2. The inverse of mod is the unique integer satisfying mod

To find , write the above congruence as a linear equation and use Euclid's Algorithm.
3. (Original post by Dragon)
The inverse of mod is the unique integer satisfying mod

To find , write the above congruence as a linear equation and use Euclid's Algorithm.
By linear equation, do you mean writing it like ax + by = 1

Where a is just a and b is phi(n)?
4. Yep.

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Updated: March 27, 2011
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