[Ilugc] .a-tip-a-day. (cksum utility in OpenBSD)
- From: kapil@xxxxxxxxxxx (Kapil Hari Paranjape)
- Date: Mon Nov 16 10:09:44 2009
Hello,
On Mon, 16 Nov 2009, Mano wrote:
On matters mathematics I would trust Dr. Kapil more than anyone else
on this list!
Never (at least almost never) _trust_ someone else's mathematics. The
whole point of mathematics is that if it is correct you should be
able to verify things for yourself. A bit like open source --- if the
program has a flaw you can check it!
In this case, perhaps I interpreted incorrectly what Girish had to
say. My only justification is his obtuse style of writing! :-)
Though this is a little OT now, I am explaining this since Girish has
no time!
Here is a brief description of RSA which ignores some technical
points:
Take a number N which is a product of two (large primes) p and q.
Take a smallish prime r like 23 or 31 which does not divide (p-1) or
(q-1). Using p, q, r you can calculate s so that (p-1)(q-1)
divides (rs-1).
Your public key is (N,r). Your private key is (N,s).
It is assumed that the p and q are not known to anyone except the
person who holds the private key.
Encryption takes m | 0 < m < N and takes it to (m^r modulo N).
Decryption takes n | 0 < n < N and takes it to (n^s modulo N).
One can show that (m^(rs)-m) is divisible by N providing that m is
different from p and q.
I hope this explains my remark that encryption and decryption are
inverses of each other.
Here is a brief description of Diffie-Hellman key exchange which also
ignores some technical points:
Let P be a large prime and g | 1<g<P be a "suitable" number.
I choose a number a | 1 < a < (P-1) and broadcast k=(g^a modulo P).
You choose a number b | 1 < b < (P-1) and broadcast l=(g^b modulo P).
Now, we use the "shared" key m=g^(ab) modulo P which:
- I can get by taking m=(l^a modulo P)
- You can get by taking m=(k^b modulo P)
It is generally believed that someone who does not know a or b
cannot calculate m.
I hope this clarifies why I thought that Girish was talking about the
Diffie-Hellman key exchange.
Regards,
Kapil.
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