[107381] in Cypherpunks
Fwd: RSA Cracked?
daemon@ATHENA.MIT.EDU (Graham H Freeman)
Wed Jan 13 03:17:55 1999
Date: Wed, 13 Jan 1999 01:56:39 -0600
From: mib <mib@io.com>
To: cypherpunks@EINSTEIN.ssz.com
From: "Graham H Freeman" <gths@zikzak.net>
Date: Mon, 11 Jan 1999 23:55:22 +1100
Reply-To: "Graham H Freeman" <gths@zikzak.net>
Dude reckons RSA is crackable.
http://www.online.de/home/aernst/RSA.html
This part might be invalid tho' (according to someone who's
looked at it.):
[begin]
Proposition 9
For each modulus n=pq there exists a message m which can't be
encrypted with any key (n,*).
Proof.
Due to Euclid algorithm there exist two numbers k and k' so that the
equation kp-k'q = 1 is true.
So we choose the message m = kp and it is true that m-1=k'q. Then we
have:
m(m-1) = kk'pq=tn;
m^2 - tn = m;
m^2 mod n = m;
------------------------------//---------------------
It is clear that if m^2 mod n = m then for each t we have mt mod n =
m.
It is also clear that if m^2 mod n = m and n=pq then p divides m and
q divides (m-1) or p divides (m-1) and q
divides m.
[end]
--
Graham Hubert Freeman. Mad Uncle Graham. take your pick.
http://www.mpx.com.au/~gths mailto:gths@flat-earth.org
... i know! let's invade andorra!
