Cryptography Reference
In-Depth Information
early days of public-key cryptography it was envisaged that this guarantee
could be provided by publishing the public keys in a 'directory', rather like
a phone book. Currently a more popular way of doing this is to embed the
public key in a
public-key certificate
. We will discuss this issue in more detail in
Section 11.1.
5.
It should not be feasible to deduce the plaintext fromknowledge of the ciphertext
and the public key
. This is just one of the standard security assumptions that
we introduced in Section 1.5.1. Public keys and ciphertexts are known values
and so we must assume that an attacker has knowledge of them.
6.
It should not be feasible to deduce the private key from the public key
. While
the public and private keys will need to be related in some way, we must make
sure that the private key cannot be deduced from knowledge of the public key.
A BETTER BRIEFCASE ANALOGY?
Perhaps a more accurate analogy for a public-key cryptosystem is thus the
following. Suppose that, once again, Alice wishes to send a secure message to
Bob by placing it into a locked briefcase. Instead of the previous protocol, Bob
now obtains a padlock and somehow gets the padlock to Alice. He could either
send it to Alice, or he could distribute thousands of copies of the padlock around
the world so that Alice can easily acquire one when she needs it. Alice locks the
briefcase using Bob's padlock and sends the locked briefcase back to Bob, who
then unlocks it using his key and obtains the message.
In this analogy, Alice faces two challenges. Firstly she has to acquire Bob's
padlock. We suggested two options for doing this, but a real public key will be
much easier to make available to Alice! Secondly, and more significantly, Alice
has to be sure that it really is Bob's padlock that she is using. This is the issue of
'authenticity' of the public key. In this analogy it is not clear how to solve this
(perhaps Bob will need to have his padlock engraved in a way that Alice can easily
recognise). We devote much of Chapter 11 to discussing how to do this in practice
for public-key cryptosystems.
5.1.3
Some mathematical preliminaries
In order to explain the public-key cryptosystems in this chapter we will need to
introduce a little bit of basic mathematics. However, taking the time to absorb
these fairly elementary ideas will greatly enrich the understanding of how public-
key cryptosystems work. If these ideas cause some difficulty then there are a couple
of approaches that could be taken:
1. Take a short break from reading this chapter in order to study the background
material in the Mathematics Appendix. This will not take long and explains all
that is needed. This is the approach that we recommend since we genuinely
believe that it is not hard, even for those with a fear of mathematics, to fully
understand these very elegant public-key cryptosystems.
