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

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