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Math Help - RSA and number of decryption exponents

  1. #1
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    Post RSA and number of decryption exponents

    We must prove that in the RSA cryptographic system for the primes p, q and the encryption exponent e\bot\phi(pq) in set \{0,\dots,\phi(pq)-1\} is exactly gcd(p-1,q-1) elements that
    you can use as the decryption exponent d.
    (That is for every M\in\{0,\dots,pq-1\}, after encryption M using encryption exponent e, and then by using the decryption exponent d we get back the M).

    Thank you for all helpful answers.
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  2. #2
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    I forgot to say that what \phi means.
    \phi(n)=|\{1\leq k\leq n : k\bot n \}|
    In this situation ( p,q-primes) we have:
    \phi(pq)=(p-1)(q-1)
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