openssl - is RSA private key less than public? -

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When I create a pair of RSA by OpenSL, it seems that the private key (personal exponent) is always less than the public key (modulus). ). Is it from RSA Design?

This is not a requirement, but there is no reason to grow it compared to modulus: < / P>

Personal exponent d is calculated to satisfy the public exponent e and the modulus n : 

  ed ≡ 1 mod φ (n)

Now, if we believe that d & gt; Φ (n) , then we can define d '= d mod φ (n) , and not only d' & lt; Φ (n) , but the above relationship still holds, that is: 

  ed '≡ 1 mod φ (n)

Thus D ' is also a valid private exponent, and since φ (n) , d ' should also be less than n .

Since a large private investor needs more storage, and (at least nostalgic implementation) decryption slows down, the least possible private exponent is most suitable.


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