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Homework Help: HELP: Please verify my tasks

  1. Oct 11, 2006 #1
    Hi

    I have two problems

    (1) How do I solve the equation x^7 \equiv 21 modulo 66 ?

    My solution

    66 = 2.3.11 so I try solving it mod 3 and mod 11 (mod 2 doesn't give any new information). This show that x is divisible by 3, and x^7 = -1 mod 11. One solution to this is x = -1 mod 7. The smallest solution of these two congruences is x=21, so this seems like a good guess.

    Now notice that 21*21 = 3.7 (2.11 - 1) = 7.66 - 3.7 = -21 mod 66
    So 21 ^n = 21. (-1)^n mod 66. Therefore x=21 is a solution of your equation. There may be more however...

    (2)

    I need to construct a set of RSA keys in pseuodo code.

    The set needs to be able to encrypt, decrypt and sign a message.

    Any idears on howto does this as simply as possible?

    My solution

    start by choosing two large random primes p and q.

    Then I compute n = pq

    next I choose f as a coprime phi(n) = (p-1) (q-1)

    I publish (n,f) as a public key

    I compute private key such that df congruent 1 mod phi(n)

    The reciever encrypts a message M (where M < n) and form C = M^e mod n

    I then decrypt this mesage using f(C) = C^f mod n.

    Could somebody please verify my pseodo-code ? If there any mistakes please show me where :)

    What about the signing of the message? How do I do that ???

    Sincerely Yours
    Fred
     
  2. jcsd
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