Cryptography Reference
In-Depth Information
• Describe a simple version of the ElGamal cryptosystem.
• Compare the basic properties of RSA, ElGamal and elliptic-curve-based
approaches.
• Identify the main uses of public-key cryptography.
We begin this chapter with an overview of the principles behind public-key
cryptography.
5.1.1
Motivation for public-key cryptography
Public-key cryptography was initially invented in order to overcome some of
the problems with symmetric cryptography. It is important that we begin our
discussion by clearly understanding what these are.
PROBLEMS WITH SYMMETRIC CRYPTOGRAPHY
Recall that in a symmetric cryptosystem the same key is used to encrypt and
decrypt. There is nothing conceptually problematic with this requirement but
it has implications that may not always be desirable. The idea behind public-
key cryptography arose from an attempt to overcome two of the most restrictive
implications of symmetric cryptography:
Symmetric trust
. Since the sender and receiver have to share the same symmetric
key, there is an implication that, to an extent, the sender and receiver 'trust' one
another. This 'trust' arises since anything cryptographic that the sender can do
(by deploying the symmetric key), the receiver can also do (by deploying the
same key). We will see in Chapter 7 how problematic this requirement is for at
least one cryptographic service.
Key establishment
. The sender and the receiver need to agree on a symmetric key
in advance of use of a symmetric cryptosystem. Thus the sender and receiver
need to have access to a secure key establishment mechanism (see Section 10.4).
Both of these implications are quite constraining. Consider, just as an example, an
application such as an online store. A potential customer, browsing the store for
the first time, has no reason to trust the store, nor has any pre-existing relationship
with the store. Yet they may wish to make a purchase from this store and benefit
from the use of cryptography to protect any data that is communicated to and
from the store during the transaction. Symmetric cryptography, on its own, is
unsuitable for use in this situation.
We will see shortly that public-key cryptography can be used in an attempt
to overcome these problems. We apply the caveats because, as always, there are
