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Proof modolu

  1. Dec 1, 2009 #1
    In RSA: d_K (y)=y^d mod n and n=pq. Define

    d_p=d mod(p-1)

    d_q=d mod(q-1)

    M_p=q^(-1) mod p
    M_q=p^(-1) mod q

    x_p=y^(d_p ) mod p
    x_q=y^(d_q ) mod q
    x=M_p qx_p+M_q px_q mod n

    Show that y^d=x mod n
    any help would be appraciated, thanks
  2. jcsd
  3. Dec 15, 2009 #2
    homework eh?

    use fermat's thm to prove y^d = y^(d_p) mod p (same for q)
    show x = x_p mod p (same for q)
    then use CRT to solve for x
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