🚀 go-pugleaf

phr@telebit.com (Paul Rubin) writes:

> 
>     I read the article in popular mechanics and have a few questions
>     about how RSA works.  You take the ASCII value of the number,
>     raise it to an arbitrary high power, and mod it by the public key,
>     correct?  But how do you decrypt it?
> 
> The message "x" is just a number, not an ascii value.
> 
> RSA works like this:
> 1. Pick two large primes p and q (with certain extra properties). Let N=pq.

What are the extra properties, and how large should they be to be reasonable
secure?

> 2. Pick random exponent s.  The pair (N, s) will be the public key.
> 3. Compute secret key t, so that st = 1 mod (p-1)(q-1).  You can do
>    this efficiently if you know p and q, but it is intractable otherwise.

Huh?  1 mod x =x, correct?  That is. modulus is the remainder of integer
division, and when you take 1 and mod it, you will always have a remainder
equal to your original.   

> 4. To encrypt: E(x) = x^s mod N.
> 5. To decrypt: D(y) = y^t mod N.
> 
> From number theory, it turns out that x^st mod N is just x.
> (This is because st = 1 mod phi(N), where phi(N) is the Euler
> totient function, equal to (p-1)(q-1) when N=pq.)
> 
> Thus, D(E(x)) = x.


I finally discovered, at the age of 21, what all of my friends had found out
at 12 or 13-that your parents are just as fucked-up and wierd as everyone
else.  Politically Correct:  Socially, Politcally, and Environmentally
concious to the point of nausea.  tsa%cellar@tredysvr.tredydev.unisys.com