Cryptography Reference
In-Depth Information
should reach the headquarters automatically in the evenings, the described split-
ting over several channels is not acceptable.
In contrast, there is a considerable risk inherent in public keys. As you know,
a new and dramatically faster method for factoring the product of large prime
numbers in the RSA method would reveal all session keys at once.
But there are other possibilities for key distribution. You will learn two of them
in the following.
Diffie-Hellman Key Exchange
As mentioned in Section 4.5.3, this algorithm was the first asymmetric method
ever. But it is not a cipher in the usual sense, and strictly speaking, there are
two private and two public keys, which are used to generate a session key.
That sounds confusing, but the method itself is astonishingly simple.
1. Alice and Bob together choose a large prime number,
p
, and a primitive
number with regard to
p
,
g
(this means that all numbers 1
,...,p
−
1
can be represented in the form
g
i
mod
p
). These numbers
p
and
g
are
not secret.
2. Alice chooses a large secret number,
x<p
, and sends Bob the remainder
X
from the equation
X=g
x
mod p
3. Similarly, Bob chooses a large secret number,
y<p
, and sends Alice
the remainder
Y
from the equation
Y=g
y
mod p
Y
x
4. Alice computes the remainder s
=
mod
p
.
5. Bob computes the remainder
s
=
X
y
mod
p
.
The remainders
s
and
s
are equal, for
s=s'=g
xy
mod p
holds.
