Cryptography Reference
In-Depth Information
Chapter 4
Public-Key Cryptography
A golden key can open any door
.
Late sixteenth-century proverb
4.1 The Ideas behind PKC
We were first introduced to Alice and Bob on page 99, where we described the
idea behind
public-key cryptography
(PKC) by using the “open safe” analogy.
It is now time to give this a mathematical context.
Public-Key Cryptosystems (PKC)
A cryptosystem consisting of a set of enciphering transformations
{
E
e
}
and
a set of deciphering transformations
is called a
public-key cryptosystem
or an
asymmetric cryptosystem
if, for each key pair (
e, d
), the enciphering key
e
, called the
public key
, is made publicly available, while the deciphering key
d
, called the
private key
(
see page 100
), is kept secret. The cryptosystem must
satisfy the property that it is computationally infeasible to compute
d
from
e
.
In order to motivate the study of PKCs, rather than leave the issue to the
end, we begin by comparing the two types of cryptosystems, SKCs and PKCs,
and their mutual interdependence in the modern world, with some illustrations
before we begin to describe the various types of PKCs and their uses.
{
D
d
}
PKCs and SKCs — A Comparison
1.
Security
: With a PKC only the private key needs to be kept a secret,
concealed by one entity, and public keys may be distributed freely. With
an SKC there must be a shared secret key known by at least two entities.
No PKC has been proven secure, yet except for the one-time-pad, this is
also true for SKCs.
2.
Longevity
: With PKCs, key pairs may be used without change in most
cases over long periods of time, years in some situations. With SKCs,
there may have to be a change of keys for each session.
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