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From: sysop@stech.UUCP (Jan Harrington)
Newsgroups: comp.sys.ibm.pc,comp.unix.questions,sci.crypt
Subject: Re: Public Key systems
Message-ID: <326@stech.UUCP>
Date: Thu, 26-Nov-87 08:19:47 EST
Article-I.D.: stech.326
Posted: Thu Nov 26 08:19:47 1987
Date-Received: Sun, 29-Nov-87 16:12:45 EST
References: <283@caus-dp.UUCP>
Organization: Scholastech, Inc., Waltham, Mass.
Lines: 52
Xref: mnetor comp.sys.ibm.pc:10547 comp.unix.questions:5112 sci.crypt:734

in article <283@caus-dp.UUCP>, marcos@caus-dp.UUCP (Marcos R. Della) says:
> 
> Hello there, I am trying to put together a minor public key system (not a
> totally secure system with mega large prime numbers, but a resonably small
> one) mainly for the method of usage, not because it is really secure...
>  
> As I understand it, the public key system works on the principle of
> 
> 		K(D(P)) = P  where K is the key function and
> 			     D is the decryption function.
> 
> Now, I can't remember the entire algorythm, but I do remember that somehow
> you take your number, multiply it by your key and mod it by k*d. Is this
> right so far? Then you do something with your decrypt key and you should
> get the original number back...
> 
As I understand it, it works like this:

Choose r as the product of two large primes, p and q.  Your encryption
key, e, is another prime number, relatively prime to (p-1)*(q-1). Any
prime larger than p and q will do.

You publish r and e.  d, the decryption key is computed as:

    d * e mod (p-1)*(q-1) = 1  (this is the only part I'm not certain about,
as I'm doing this from memory)

To encrypt you do the following:

P (the plain text) ^^e mod r

To decrypt you do the opposite:

C (cyphered text) ^^d mod r

So, if anyone knows r and e they can encrypt, but without factoring r to
get p and q you can't decrypt.

Somebody out there should verify my formula for d.  I know it's close, but
I'm not confident that it's exactly right!


Jan Harrington, sysop
Scholastech Telecommunications
ihnp4!husc6!amcad!stech!sysop or allegra!stech!sysop

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