FPGA based Hardware Accleration for Elliptic Curve Cryptography ...

Chapter 1
Introduction
1.1 Motivation
Today there is a wide range of distributed systems, which use communication resources that can not be
safeguarded against eavesdropping or unauthorized data alteration. Thus cryptographic protocols are applied
to these systems in order to prevent information extraction or to detect data manipulation by unauthorized
parties.
In general, cryptographic methods can be subdivided into two categories: symmetric- and asymmetric
cryptographic algorithms.
In the case of symmetric cryptographic algorithms like DES [1] or AES [2] both communication partners
use the same secret key to encrypt and decrypt messages. Compared to asymmetric cryptography these
algorithms are considered to be faster and more efficient. However, the general problem of symmetric
methods is the distribution of the secret key. Sender and recipient both have to possess the same secret key
to process the message but no one else may have the key, because otherwise one would be able to decrypt
or alter the message just like the original author and recipient. So secure channels have to be established in
order to exchange the keys.
With regard of this problem, asymmetric algorithms have been developed. These algorithms, which are
also called public key algorithms, differ in the utilized set of keys consisting of a public- and a private key.
This key pair can only be computed by the original creator of the keys. For all others both keys are virtually
independent. The general principle of all public key schemes is then, that a message that is encrypted with
one of the keys can only be decrypted with the other one.
After publication of the public key, everyone can use this key, e.g. to encrypt a message. Afterwards,
this message can only be decrypted with the corresponding private key which is exclusively known by the
authorized recipient of the message.
Alternatively, public key algorithms can be used to compute and verify digital signatures. The author of
a message uses his secret, private key to compute a signature. By looking up the authors public key any
recipient of the message-signature-pair is able to verify this signature subsequently.
Public key algorithms provide much flexibility and a very high level of security. On the other hand,
in comparison to symmetric methods, they are based on much more complex and expensive arithmetic
operations. In practice a combination of both methods is frequently used. E.g. SSL [3]: public key methods
are used for key exchange and authentication while symmetric algorithms are applied for the encryption of
the data stream.
The most prominent public key method is the widely-used RSA algorithm [4]. It is based on the problem