Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Please check the working and final answer to the question:

Question:
Given RSA encoding function $E: x\to x^{11} \pmod{3737}$ find the decoding function $D$

My working:
$\phi(3737) = \phi(37) \times \phi(101)$
$= 36 \times 100 = 3600$

Using euclid's algorithm (Skipping the fairly long gory details) we show:

$1 = 4\times3600 - 1309 \times 11$

Taking the coefficient of 11 (power of $x$), we get $-1309$ but we want this in positive congruent mod $3600$ so $3600-1309 = 2291$ and finally we have

$D:x\to x^{2291}\pmod{3737}$

share|improve this question
6  
Seems fine. Note that once you have (maybe) found the decoding number, you can check it easily: We have $(11)(2291)=25201$, which is easily congruent to $1$ modulo $3600$. –  André Nicolas Sep 25 '12 at 5:11

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.