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Math Help - RSA encryption

  1. #1
    Junior Member
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    Apr 2006
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    RSA encryption

    This problem is for my discrete math class - so I hope this is in the right section.

    This problem is to be done using only the computing power of a pocket calculator. Write out all your work in step-by-step form showing all computations.

    The Message M=9 is encrypted in the RSA system using p=11,q=13 and e =7 which is relatively prime to (p-1)(q-1)

    a.)Encrypt M to get C , which is to be transmitted.

    b.)find d, the inverse of e(mod(p-1)(q-1)).

    c.)using d, recover the original message M.
    Hope some1 can help me out


    Cheers
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  2. #2
    Member Ranger SVO's Avatar
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    M is the message you want to send.

    The public key is (n, e) , n = p*q , 143 = 11*13
    C is the coded message and it is coded by C = M^e mod n

    C= 48 = 9^7 mod 143, to decode we need d which is the inverse of e

    d*e is congruent to 1 mod (#'s relatively prime to n)
    d*e is congruent to 1 mod ((p-1)*(q-1)
    d*9 is congruent to 1 mod 120

    d = 103

    We can now decode the coded message C which is 48 by
    M = C^d mod n
    M = 48^103 mod 143
    M = 9


    I am not an expert in modular arithmetic so if you want to add something please do. I just joined this forum resently and only saw your post a couple of days ago. I hope you got an answer long before today
    Last edited by Ranger SVO; April 27th 2006 at 06:27 PM.
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