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Math Help - RSA Public Key Cryptosystem question

  1. #1
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    RSA Public Key Cryptosystem question

    I am trying to work a RSA problem with my two primes of p=17 and q=23 my n = 31

    I computed z = p q = 391
    (q-1) (p-1) = 352
    I need to compute s in n s mod 352 = 1

    I have gone through the examples time and time again and can not figure it out. I think I use the Euclidean Algorithm but I am missing something for sure. Any help would be much appreciated.
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    Hello,

    Quote Originally Posted by Frostking View Post
    I am trying to work a RSA problem with my two primes of p=17 and q=23 my n = 31

    I computed z = p q = 391
    (q-1) (p-1) = 352
    I need to compute s in n s mod 352 = 1

    I have gone through the examples time and time again and can not figure it out. I think I use the Euclidean Algorithm but I am missing something for sure. Any help would be much appreciated.
    a=352
    n=31
    for more convenience

    352=31x11+11 --> 11=a-11n

    31=11x2+9 --> 9=31-11x2=n-(2a-22n)=23n-2a

    11=9+2 --> 2=11-9=(a-11n)-(23n-2a)=3a-34n

    9=2x4+1 --> 1=9-2x4=(23n-2a)-4(3a-34n)=159n-14a

    1=159x31-14x352

    --> 159x31=1 mod 352

    s=159
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