# RSA Questions

zaaaaaaaap! an56238 at anon.penet.fi
Wed Jan 19 13:36:28 PST 1994

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Norman Hardy writes:

>Laudable Paranoia!

Was that laudable or laughable ?

>In short the numbers: cipher, decipher, plain, d and e must all be
>relatively prime to p and q for all of this stuff to work.

In my example, p and q a primes.

Which means:
for all x<p x and p are relative primes
for all x<q x and q are relative primes

e is a prime as well, and since e<p, e and p are relative primes
e is a prime as well, and since e<q, e and q are relative primes

the _list of possible values for d_. You don't get to choose them. They're
imposed, not free-style.
If some of them are primes, well, cheers.

>In practice, since p and q are very large, the probability of the cryptanalyst
>finding another value d that deciphers your message is about the same as him
>finding p or q.

I'm willing to believe you. Any general formulas giving the probability of
solutions for the d's ? Maybe I'm asking the wrong question. I'll ask again.

What are the properties of those d that unlock ALL messages encrypted by e
What are the properties of those d that unlock a GIVEN message encrypted by e

- -zap

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